Graph this linear relationship with x =#hours, and y = dollars earned.

How much does she earn per hour?

**Answer:**

To graph this linear relationship, we can plot two points on a coordinate plane: (3,12) and (5,20). These points represent the number of hours Jen babysits (x-coordinate) and the amount of money she earns (y-coordinate).

We can connect these two points with a line to form a linear equation that represents the relationship between the number of hours babysat and the money earned.

The slope of this line can be found using the formula: (change in y) / (change in x) = (20-12) / (5-3) = 8/2 = 4

Therefore, Jen earns $4 per hour by babysitting.

It is important to note that this is a linear relationship, and the earnings are proportional to the number of hours babysat. This means that for any number of hours babysat, the earnings can be found by multiplying that number by $4.

**Step-by-step explanation:**

**Answer: For every hour she babysits, she earns ****$4. ✅**

**Step-by-step explanation:**

To graph the linear relationship, we can start by plotting two points: (3,12) and (5,20).

This represents that for 3 hours of babysitting, Jen earns $12, and for 5 hours of babysitting, she earns $20.

We can then use these points to find the slope of the line, which is the rate at which her earnings change as the number of hours increases.

The slope can be found by using the formula: (change in y) / (change in x) = (20 - 12) / (5 - 3) = 8/2 = 4

This means that for every hour she babysits, she earns $4.

So, the equation of the line is : y = 4x + b

Where b is the y-intercept, which can be found by substituting one of the points into the equation.

For example, by substituting (3,12) in the equation:

12 = 4(3) + b

b = 0

So, she earns per hour $4. ✅

Find the median and mean of the data set below: 9,23,38,45,14

**Answer:**

mean, 25.8 median 23

**Step-by-step explanation:**

Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.

The mean of a set of numbers is the sum divided by the number of terms.

if 4.2 pounds of strawberry sells for an income of $12 what is 24,990 pounds income

**Answer: **$71,400

**Step-by-step explanation:**

We will set up a **proportion **with income in the **numerator **and pounds in the **denominator**.

[tex]\displaystyle \frac{\$12}{4.2\;lbs} =\frac{\$x}{24,990\;lbs}[/tex]

Then we will **cross-multiply**.

4.2 * x = 12 * 24,990

4.2x = 299,880

Lastly, we will **divide **both sides of the equation by 4.2.

x = $71,400

The income from 24,990 pounds of strawberries would be approximately $71,690.14.

To find the income from 24,990 pounds of strawberries, we need to use a proportion:

4.2 pounds of strawberries sells for $12, so 1 pound of strawberries sells for $12/4.2 = $2.86 (rounded to two decimal places).

Therefore, 24,990 pounds of strawberries would sell for:

$2.86 x 24,990 = $71,690.14 (rounded to two decimal places).

Which statement is the converse of the following conditional? If a polygon has three sides, then it is a triangle. A. If a polygon does not have three sides, then it is not a triangle. B. If a polygon is not a triangle, then it does not have three sides. C. If a polygon is a triangle, then it does not have three sides. D. If a polygon is a triangle, then it has three sides.

**Answer:**

**Step-by-step explanation:**

The converse of the conditional statement "If a polygon has three sides, then it is a triangle" is:

D. If a polygon is a triangle, then it has three sides.

In the original conditional statement, the "if" part is "a polygon has three sides," and the "then" part is "it is a triangle." The converse switches the positions of the "if" and "then" parts, resulting in the statement "If a polygon is a triangle, then it has three sides."

Alfred has a coupon for 35 cents off a 32-ounce bottle of detergent that sells for $1.39. Another brand offers a 20-ounce bottle for 79 cents. If he uses the coupon, which will be the better buy?

The detergent with the coupon is the better buy since it has a lower **price **per ounce.

To determine which option is the better buy, we need to **compare **the prices per ounce for each detergent brand.

First, let's calculate the price per ounce for the 32-ounce bottle of detergent **after **applying the coupon:

Price per ounce = (Price - Coupon) / Ounces

Price per ounce = ($1.39 - $0.35) / 32

Price per ounce = $1.04 / 32

Price per ounce ≈ $0.0325

Next, let's **calculate **the price per ounce for the 20-ounce bottle of the other brand:

Price per ounce = Price / Ounces

Price per ounce = $0.79 / 20

Price per ounce = $0.0395

Comparing the two price per ounce values, we can see that the price per ounce for the detergent with the coupon is **approximately **$0.0325, while the price per ounce for the other brand is $0.0395.

Therefore, the detergent with the coupon is the better buy since it has a **lower price **per ounce.

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Consider this equation.

cos(0) = 4/41

If 0 is an angle in quadrant IV, what is the value of sin(0)

**Answer: sin(0) = 40.804/41**

**Step-by-step explanation:**

Plsss help plsss help

**Answer:**

It's B

**Step-by-step explanation:**

Look at the sides with the number compare them with each other and you will find they are the most similar ones with each other.

Suppose the prices of a certain model of new homes are normally distributed with a mean of 150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid between $149,000 and $151,000 if the standard deviation is $1000

The percentage of buyers is **approximately **68.26% of buyers of new houses paid between [tex]$149,000[/tex] and [tex]$151,000[/tex] .

We are given that the prices of the new homes are normally distributed with a mean of [tex]$150,000[/tex] and a standard deviation of $1000.

Using the 68-95-99.7 rule, we know that: approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the data falls within two standard deviations of the** mean, **approximately 99.7% of the data falls within three standard deviations of the mean.

In order to determine the proportion of customers who spent between $149,000 and , we must first determine the z-scores for these values:

z1 = (149,000 - 150,000) / 1000 = -1 z2 = (151,000 - 150,000) / 1000 = 1

Now, we can determine the proportion of data that falls between z1 and z2 using the z-table or a calculator. The **region **to the left of z1 is 0.1587, and the area to the left of z2 is 0.8413, according to the z-table. Thus, the region bounded by z1 and z2 is:

0.8413 - 0.1587 = 0.6826

We can get the percentage of consumers who spent between by multiplying this by 100% is [tex]$149,000[/tex] and [tex]$151,000[/tex]:

0.6826 x 100% = 68.26%

Therefore, the **standard deviation** of customers who paid between is [tex]$149,000[/tex] and [tex]$151,000[/tex] for this model of new homes.

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hey i have a question about this assignment and want to check if my answers are right

The value of x from the given **triangle **with angle 55° and side 27 units is 15.5 units.

A) By using **Pythagoras **theorem,

x²=16²+6²

x²=292

x=17.1 units

B) By using Pythagoras theorem,

23²=x²+9²

x²=529-81

x²=448

x=21.2 units

C) By using Pythagoras theorem,

10²=x²+8.5²

x²=100-72.25

x²=27.75

x=5.3 units

D) By using Pythagoras theorem,

x²=12²+15²

x²=369

x=19.2 units

E) Here, cos60°=6√3/x

1/2=6√3/x

x=12√3 units

F) Here, cos45°=√10/x

1/√2=√10/x

x=10 units

G) Here, sin60°=30/x

2/√3=30/x

x=15√3 units

H) Here, cos30°=x/16

2/√3=x/16

x=32/√3 units

I) Here, sinx=25/26

x=74°

J) Here, sin45°=x/16√2

1/√2=x/16√2

x=16 units

K) tan34°=x/28

0.6745=x/28

x=18.886

L) tanx°=17/18.5

tanx°=0.9189

x=42.5°

M) Here, cosx=9/12

x=41.4°

N) Here, sin16°=4/x

0.2756=4/x

x=4/0.2756 units

x=14.5

O) Here, cos55°=x/27

0.5735=x/27

x=15.4845

Therefore, the value of x from the given **triangle **with angle 55° and side 27 units is 15.5 units.

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The total cost of a tie and a pair of pants was $87.18. If the price of the tie was $2.12 less than the pair of pants, what was the price of the tie?

**This is a linear equation problem with two variables. One way to solve it is by using the substitution method. Let x be the price of the tie and y be the price of the pair of pants. Then we have:**

**$$**

**\begin{aligned}**

**x + y &= 87.18 \\**

**x &= y - 2.12**

**\end{aligned}**

**$$**

**Substituting x into the first equation, we get:**

**$$**

**\begin{aligned}**

**(y - 2.12) + y &= 87.18 \\**

**2y - 2.12 &= 87.18 \\**

**2y &= 89.30 \\**

**y &= 44.65**

**\end{aligned}**

**$$**

**Therefore, the price of the pair of pants is $44.65. To find the price of the tie, we plug y into the second equation:**

**$$**

**\begin{aligned}**

**x &= y - 2.12 \\**

**x &= 44.65 - 2.12 \\**

**x &= 42.53**

**\end{aligned}**

**$$**

**Therefore, the price of the tie is $42.53.**

**Answer:**

42.53

**Step-by-step explanation:**

write equation

tie + pants = 87.18

since ties cost 2.12 less than pants,

tie = pants -2.12

now substitute back into first equation

pants - 2.12 + pants = 87.18

solve for pants by adding 2.12 to the other side

divide by 2 since there are 2 pants on one side

find pants and then substitute value into the tie equation to find the price of the tie

What is the end behavior of this radical function? f(x) = -2½ + 7

**Answer:**

**Step-by-step explanation:**

The function you provided, f(x) = -2.5 + 7, represents a linear function rather than a radical function. A linear function has a constant slope and a constant y-intercept.

The end behavior of a linear function is determined by its slope. In this case, the slope of the function is 0 since there is no term involving x. When the slope is 0, it means the function is a horizontal line.

The function f(x) = -2.5 + 7 represents a horizontal line at y = 4.5. As x approaches positive infinity (∞) or negative infinity (-∞), the value of y remains constant at 4.5. Therefore, the end behavior of this linear function is that y approaches 4.5 as x approaches both positive and negative infinity.

In conclusion, the end behavior of the function f(x) = -2.5 + 7 is that y approaches 4.5 as x approaches positive and negative infinity.

When comparing the f(x) = –x2 + 2x and g(x) = log(2x + 1), on which interval are both functions positive

(–∞, 0)

(0, 2)

(2, ∞)

(–∞, ∞)

**Answer:**

They are both positive on (2, ∞)

**Step-by-step explanation:**

g(x) > 0

log(2x + 1) > 0

2x + 1 > 0

x > –1/2

(-1/2, ∞)

Which model represents the expression 87 - 42?

The **model **that represents the **expression** 87 - 42 is (d)

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

87 - 42

Using their **place values**, we have

87 = 8 tens 7 units

42 = 4 tens 2 units

This means that

87 - 42 = 8 tens 7 units - 4 tens 2 units

Subtract the **tens**

87 - 42 = 4 tens 7 units - 2 units

Subtract the **units**

87 - 42 = 4 tens 5 units

The model that represents the **expression **87 - 42 is 4 tens 5 units

This is represented by **model **(d) bottom right

Hence, the **model **that represents the **expression** 87 - 42 is (d)

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Which system is equivalent to

O

O

O

[5-x=9x²

y = 5-x

[y=9y²-90y+225

1x=y-5

[5+x=9x²

y = 5+x

y = 3x

x+3x=5

y=9x²?

x+y=5

The first equation is a quadratic equation, and the second equation is a** linear equation. **The solution to the system is x = -2 and y = 7, which satisfies both equations.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

The system that is **equivalent** to:

O

O

O

[5-x=9x²

y = 5-x

is: x = -2, y = 7

In the given system, the first equation is a **quadratic equation**, and the second equation is a** linear equation. **The solution to the system is x = -2 and y = 7, which satisfies both equations.

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ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)

Karen measures the width of a garden plot and records that it is 40 meters. Its actual width is 42 meters.

What is the percent error in the measurement?

A: 2%

B: 3%

C: 4%

D: 5%

Explanation:

The error is 42-40 = 2 meters

Divide this over the actual width

2/42 = 0.0476 = 4.76% approximately

This rounds to **5%**

**Answer:**

D. 5%

**Step-by-step explanation:**

Percent Error = (|40 - 42| / 42) × 100

Percent Error = (2 / 42) × 100

Percent Error ≈ 4.76%

Find the 9th term of the geometric sequence 4 , − 16 , 64 , . . . 4,−16,64,...

The 9th term of the **geometric** **sequence** 4, -16, 64, ... is 262144.

To find the 9th term of the geometric sequence 4, -16, 64, ... , we need to determine the **common** ratio (r) of the sequence.

To do this, we can divide any term by its preceding term:

-16 / 4 = -4

64 / -16 = -4

We see that the common ratio (r) is -4.

To find the 9th term, we can use the formula for the nth term of a geometric sequence:

Tn = a * r^(n-1)

Where Tn is the nth term, a is the **first term**, r is the common ratio, and n is the term number.

In this case, the first term a is 4, the common ratio r is -4, and we want to find the 9th term.

T9 = 4 * (-4)^(9-1)

T9 = 4 * (-4)^8

T9 = 4 * 65536

T9 = 262144

Therefore, the 9th term of the geometric sequence 4, -16, 64, ... is 262144.

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Focus: (-5,3); Directrix: y = 1

The **equation** of the **parabola** is: y = (1/4)(x-3)²+ 2

In Parabola mathematics, it is defined as a set of points that are **equidistant** from a fixed point called the focus and a fixed line called the directrix. In this case, we are given the focus (3,5) and the directrix y=1, y=1, and we need to find the equation of the parabola.

To find the equation of the parabola, we first need to determine the vertex. The **vertex** is the midpoint between the focus and the **directrix**, which in this case is (3,3). Since the parabola is symmetric, we know that the axis of **symmetry** passes through the vertex and is perpendicular to the directrix. Therefore, the equation of the **axis** of symmetry is x=3.

Next, we need to find the distance between a **point** on the parabola and the focus, as well as the **distance** between that same point and the directrix. Let (x,y) be a point on the parabola. The distance between (x,y) and the focus is given by the distance formula: √((x-3)² + (y-5)²)

The distance between (x,y) and the directrix is simply the **absolute value** of the difference between y and 1: |y-1|

Since the point (x,y) is equidistant from the focus and the directrix, we have: √((x-3)²+ (y-5)²) = |y-1|

Squaring both sides and simplifying, we get: (x-3)²= 4(y-2)

Therefore, the **equation** of the **parabola** is: y = (1/4)(x-3)²+ 2

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NOTE : I HAVE ANSWERED THE QUESTION IN GENERAL AS GIVEN QUESTION IS INCOMPLETE.

**Complete Question : **Find the Parabola with Focus (3,5) and Directrix y=1 (3,5) , y=1

Apples cost $1.29 per pound. How much would a bag of apples weighing 4.7 pounds cost? (Round your answer to the nearest cent.)

Answer:

$6.06

Step-by-step explanation:

$1.29 x 4.7 = 6.063

Round: 6.06

Can anyone help me answer this question?

Define y as an explicit function of x; x + y + y^2 = x^2

We have two **explicit functions **of x for y:

[tex]y = -1/2 + \sqrt{(x^2 - x + 1/4)} \\or\\y = -1/2 - \sqrt{(x^2 - x + 1/4)}[/tex]

To define y as an explicit function of x, we need to solve for y in terms of x in the given equation:

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

First, let's simplify the **equation** by moving all the terms to one side:

[tex]y^2 + y + (x - x^2) = 0[/tex]

Now, we can use the quadratic formula to solve for y:

[tex]y = (-b + \sqrt{(b^2 - 4ac)} ) / 2a[/tex]

where a = 1, b = 1, and [tex]c = x - x^2.[/tex]**Substituting **these values, we get:

[tex]y = (-1 + \sqrt{(1 - 4(x - x^2)} )) / 2[/tex]

**Simplifying** further:

[tex]y = (-1 + \sqrt{(1 - 4x + 4x^2)} ) / 2\\y = (-1 + \sqrt{(4x^2 - 4x + 1)} ) / 2\\y = (-1 + 2\sqrt{(x^2 - x + 1/4)} ) / 2\\y = -1/2 + \sqrt{(x^2 - x + 1/4)}[/tex]

Therefore, we have two explicit functions of x for y:

[tex]y = -1/2 + \sqrt{(x^2 - x + 1/4)} \\or\\y = -1/2 - \sqrt{(x^2 - x + 1/4)}[/tex]

Either of these expressions** represents** y as an explicit function of x.

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In AABC, AB=32, AC = 23, and BC= 20. What is mZA?

The **measure** of m∠A in the **triangle** is:

m∠A = 38.44°

How to find the measure of m∠A?The **cosine rule** is used for solving** triangles** which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula for **angles**:

cos(A) = (b² + c² − a²)/2bc

cos(B) = (c² + a² − b²)/ 2ac

cos(C) = (a² + b² − c²)/2ab

Where a, b and c are the length of the sides, and A, B, and C are the **measures** of the angles

We have:

a = BC = 20

b = AC = 23

c = AB = 32

Substituting into:

cos(A) = (b² + c² − a²)/2bc

cos(A) = (23² + 32² − 20²)/(2*23*32)

cos(A) = 0.7833

A = cos⁻¹(0.7833)

A = 38.44°

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(10)

In 2008, the average new car price was approximately $27,700. In 2010,

the average new car price had increased to $29,200. Assuming a linear

relationship, what will be the approximate new car price in 2014?

A $33,700

B. $32,200

C. $30,700

D. $29,950

The approximate **price** of the new **car** in 2014 is:

B. $32,200

How to find the approximate new car price in 2014?The general form of a **linear equation** is given by:

y = mx + c

where y is the future **price **of the car, x is the number of years, m is the rate of change of price and c is the initial price of the **car**

c = $27,700

m = ($29,200 - $27,700)/(2010 - 2008)

m = 1500/2

m = $750 per year

In 2014, x = 2014 - 2008 = 6 years

Substituting into y = mx + c:

y = 750(6) + 27,700

y = 4500 + 27700

y = $32,200

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A plane takes off from an airport andtravels 13 miles on its path.

if the plane is 12 milesfrom its takeoff poin horizontally, what is its height?

The **height** of the plane is 5 miles.

To solve this problem, we can visualize it as a right triangle. The **horizontal** distance traveled by the plane forms the base of the triangle, which is 12 miles. The total distance traveled by the plane forms the hypotenuse of the triangle, which is 13 miles. We need to find the height, which corresponds to the vertical side of the triangle.

Using the **Pythagorean theorem**, we can calculate the height as follows:

height^2 + 12^2 = 13^2

height^2 + 144 = 169

height^2 = 169 - 144

height^2 = 25

Taking the **square** root of both sides, we get:

height = √25

height = 5

Therefore, the height of the plane is 5 miles.

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Do it please i will reward brainlest

**Answer:**

**Step-by-step explanation:**

5

Enter the correct answer in the box.

Solve the quadratic equation by completing the square.

2x² + 12x = 66

Fill in the values of a and b to complete the solutions.

x=a-√b

x=a+√b

The values of a and b are a = -3 and b = 42. The** solutions** for x can be written as:

x = -3 - √42

x = -3 + √42

To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:

Step 1: Move the constant term to the right side:

2x² + 12x - 66 = 0

Step 2: Divide the equation by the leading coefficient (2):

x² + 6x - 33 = 0

Step 3: To complete the square, we take half of the **coefficient** of x, square it, and add it to both sides of the equation:

x² + 6x + (6/2)² = 33 + (6/2)²

x² + 6x + 9 = 33 + 9

x² + 6x + 9 = 42

Step 4: Rewrite the left side as a **perfect square**:

(x + 3)² = 42

Step 5: Take the **square root** of both sides:

√(x + 3)² = ±√42

x + 3 = ±√42

Step 6: Solve for x:

x = -3 ± √42.

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Find the area of a triangle with the base of 3x²y2 and a height of 4x4y³. Use the formula: A=bh

The **area** of the **triangle** is 6x³y⁵

The space enclosed by the boundary of a plane figure is called its area.

A **triangle** is a polygon with three sides having three vertices.

There are different types of **triangle**, scalene **triangle**, equailteral triangle, isosceles **triangle**, right **triangle** e.t.c

The **area** of a **triangle** is expressed as ;

A = 1/2 bh

where b is the base and h is the height of the of the triangle.

Base = 3x²y²

height = 4x4y³

A = 1/2 × 3x²y² × 4x4y³

A = 1/2 × 12x³y⁵

A = 6x³y⁵

Therefore the **area** of the **triangle** is 6x³y⁵

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The area of the **Triangle is **[tex]48x^{3} y^{4}[/tex]

**Triangle **is a two-dimensional three-sided polygon, which has **three vertices, three sides and three angles. **It is a shape formed when three straight lines meet.

How to determine this

Area of triangle = **1/2 base * height **as given

Where area of triangle = ?

Base = [tex]3x^{2} y2[/tex]

i.e 3 * 2 [tex]x^{2} y[/tex]

Base, b = [tex]6x^{2} y[/tex]

Height = [tex]4x4y^{3}[/tex]

i.e [tex]4x[/tex] * [tex]4y^{3}[/tex]

Height,b = [tex]16xy^{3}[/tex]

Area of triangle = 1/2 * [tex]6x^{2} y[/tex] * [tex]16xy^{3}[/tex]

Area = 1/2 * 96* [tex]x^{2+1}[/tex] * [tex]y^{1+3}[/tex]

Area = 1/2 * 96 * [tex]x^{3}[/tex] * [tex]y^{4}[/tex]

Area = 48 * [tex]x^{3} y^{4}[/tex]

Area of the triangle = [tex]48x^{3} y^{4}[/tex]

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Determine the value of real parameters p in such a way that the equation 3x2−24x+p=0 has one root equal to triple of the second root

has one root equal to triple of the second root.

The value of the** parameter** p that satisfies the given conditions is 36.

Let the roots of the quadratic equation [tex]3x^2 - 24x + p = 0[/tex] be denoted by α and β, where α is the **root** that is triple the value of β.

Then we have:

α = 3β

The sum and product of the roots of the quadratic equation are given by:

α + β = 8 (from the coefficient of x in the linear term)

αβ = p/3 (from the constant term)

**Substituting **α = 3β in the first equation gives:

3β + β = 8

4β = 8

β = 2

Therefore, α = 6.

So the roots of the **quadratic equation **are α = 6 and β = 2.

The product of the roots is:

αβ = 6 × 2 = 12

From the equation αβ = p/3, we have:

p/3 = 12

p = 36

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You Draw two marbles (without replacement) from a bag containing 4 green 2 yellow and 6 red marbles.what is the probability that both marbles are yellow? round to the nearest thousand

The **probability** of drawing two **yellow marbles** is 0.015 to the nearest thousandth.

The **probability** of drawing two** yellow marbles** after drawing a yellow marble on the first draw and **without replacement **drawing another yellow marble is determined as follows:

Total number of marbles in the bag = 4 + 2 + 6

Total number of marbles in the bag = 12 marbles in the bag.

P(Yellow on first draw) = 2/12 or 1/6

P(Yellow on second draw | Yellow on first draw) = 1/11

The probability of both marbles being yellow will be:

P(Both marbles yellow) = (1/6) * (1/11)

P(Both marbles yellow) = 1/66 or 0.015

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Mrs. Garcia invests a total of $6331 in two savings accounts. One account yields 8.5% simple interest and the other 8% simple interest. Find the amount placed in each account if she receives a total of $517.68 in interest after one year.

Mrs. Garcia **invested** $2240 in the 8.5% account and $4091 in the 8% account.

Let x be the amount invested in the 8.5% account, and y be the amount invested in the 8% **account**. Since the total investment is $6331, we have x + y = 6331.

The total **interest** received is $517.68, which can be expressed as 0.085x + 0.08y = 517.68, where 0.085 and 0.08 are the decimal equivalents of the interest rates.

We can now solve this system of equations to find x and y. One possible method is to use **substitution**, where we solve for one variable in terms of the other from one of the equations, and substitute it into the other equation. From x + y = 6331, we have y = 6331 - x. Substituting this into the second equation, we get:

0.085x + 0.08(6331 - x) = 517.68

**Simplifying** and solving for x, we get:

0.005x + 506.48 = 517.68

0.005x = 11.2

x = 2240

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Given that ∅ = 12.2° , calculate the area of the triange below

give your answer to 2 d.p.

**Answer:**

A = (1/4)√(4 + 11 + 14)√(-4 + 11 + 14)√(4 - 11 + 14)√(4 + 11 - 14)

A = (1/4)√29√21√7

= about 16.32 mm²

**Answer:**

** 16.27 mm²** (see comment)

**Step-by-step explanation:**

You want the **area** of a **triangle** with side **lengths 11 mm and 14 mm**, and the **angle** between them **12.2°**.

The area is given by the formula ...

A = 1/2ab·sin(C)

A = 1/2(11 mm)(14 mm)·sin(12.2°) ≈ 16.27 mm²

**The area of the triangle is about 16.27 square millimeters**.

__

*Additional comment*

If you use Heron's formula for the area from the three side lengths, you find it is about **16.32 mm²**. That's the trouble with over-specified geometrical figures. The result you get depends on which of the given values you use. (To get the area accurate to 4 sf, the angle needs to be specified to 4 sf: 12.24°.)

s = (4 +11 +14)/2 = 14.5

A = √(s(s -a)(s -b)(s -c))

A = √(14.5(14.5 -4)(14.5 -11)(14.5 -14)) = √(14.5·10.5·3.5·0.5) = √266.4375

A ≈ 16.32

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A head teacher shared 27 notebooks among 9 students.one of them students found that each of his books combined 155 pages.how many pages were in the books he received

The **number of pages** that each book contained is given as follows:

465 pages.

How to obtain the number of pages?The number of pages that each book contained is obtained applying the **proportions **in the context of the problem.

A head teacher shared 27 notebooks among 9 students, hence the number of the **notebooks per student** is given as follows:

27/9 = 3 notebooks per student.

One of them students found that each of his books combined 155 pages, hence the number of** pages on the book** is given as follows:

155 x 3 = 465 pages.

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A volunteer walks 1 mile to a dog

shelter. She walks 4 dogs for 1/2mile

each. Then she walks 1 mile

home. She does this each day for

3 days, How many miles does she

walk in all?

The volunteer walks 1 mile to the dog shelter and another 1 mile back home, so she walks 1 + 1 = 2 miles each day.

She walks 4 dogs for 1/2 mile each, so she walks 4 x 1/2 = 2 miles with the dogs each day.

Therefore, she walks a total of 2 + 2 = 4 miles each day.

Over the course of 3 days, she walks a total of 4 x 3 = 12 miles.

So, the volunteer walks 12 miles in all.

She walks 4 dogs for 1/2 mile each, so she walks 4 x 1/2 = 2 miles with the dogs each day.

Therefore, she walks a total of 2 + 2 = 4 miles each day.

Over the course of 3 days, she walks a total of 4 x 3 = 12 miles.

So, the volunteer walks 12 miles in all.

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