The number of **candy** **bars** that the student can buy is given by the inequality c < 6 which means **less** than 6.

It shows a relationship between two numbers or two expressions.

There are commonly used four **inequalities**:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

The **inequality** represents the amount of money a student can spend on c candy bars.

2c - 3 < 9

2c < 9 + 3

2c < 12

c < 6

This means,

c is **less** than 6.

Thus,

The number of **candy** **bars** that the student can buy is **less** than 6.

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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, ∞)

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.

A softball player hits a pitched ball when it is 4 feet above the ground. The initial velocity is 75 feet per second. Use the formula h=-16t^2+vt+s. How long will it take for the ball to hit the ground?

If the initial **velocity** is 75 feet per second, it will take approximately 5.125 **seconds** for the ball to hit the ground.

The given formula h= -16t²+vt+s represents the height (h) of an object thrown **vertically** in the air at time (t), with initial velocity (v) and initial height (s). In this case, we are given that the initial height of the softball is 4 feet and the initial velocity is 75 feet per second.

We want to find out how long it will take for the ball to hit the **ground**, which means we want to find the time (t) when the height (h) is 0.

**Substituting** the given values into the formula, we get:

0 = -16t² + 75t + 4

This is a **quadratic** equation in standard form, which we can solve using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Where a=-16, b=75, and c=4. **Substituting** these values into the formula, we get:

t = (-75 ± √(75² - 4(-16)(4))) / 2(-16)

t = (-75 ± √(5625 + 256)) / (-32)

t = (-75 ± √(5881)) / (-32)

We can **simplify** the expression under the square root as follows:

√(5881) = √(49121) = 711 = 77

So we have:

t = (-75 ± 77) / (-32)

Simplifying further, we get two possible **solutions**:

t = 0.5 seconds or t = 5.125 seconds

Since the softball player hits the ball when it is 4 feet above the ground, we can disregard the solution t=0.5 seconds (which corresponds to when the ball is at its maximum **height**) and conclude that it will take approximately 5.125 seconds for the ball to hit the ground.

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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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(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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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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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."

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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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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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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Explain why you cannot use the product of powers property to simplify (3z + y)^3. Be specific.

Any badd answer will be reported

The **product **of powers of **exponents **cannot be used to simplify the **binomial **expansion

Given data ,

Let the **binomial **expansion be represented as A

A = ( 3z + y )³

According to the property of **products **of powers, **exponents **can be multiplied when a power is increased to a higher power.

The **product **of **powers **characteristic cannot be applied to the equation (3z + y)³. This is due to the fact that (3z + y)³ is a **binomial **raised to the power of 3, not just a power of a single word.

These terms cannot be simplified further using the **product **of powers property because they involve different variables or variable combinations.

In this case, it is more appropriate to expand the expression using the **binomial **expansion

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A rectangle has an area of 114cm squared and a perimeter of 50cm. What are the dimensions

If **rectangle** has an area of 114cm squared and a perimeter of 50 cm, the **dimensions** of the rectangle are approximately 5 cm by 22.8 cm.

Let's assume the **length** of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².

So, we have:

lw = 114

Next, we can use the formula for the **perimeter** of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.

So, we have:

2l + 2w = 50

We now have two equations with two variables, which we can solve using **substitution** or elimination. Let's use substitution by solving the first equation for l:

l = 114/w

We can then substitute this **expression** for l in the second equation:

2(114/w) + 2w = 50

**Multiplying** both sides by w to eliminate the fraction, we get:

228 + 2w² = 50w

Rearranging and **simplifying**, we get a quadratic equation:

2w² - 50w + 228 = 0

We can solve for w using the **quadratic** formula:

w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5

Since the length and width must be **positive**, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:

l(5) = 114

l ≈ 22.8

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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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Solve.

10 - 9x^2 + 4x = -6x^210−9x

2

+4x=−6x

2

**Answer: **the solutions to the equation are x = √(10/3) and x = -√(10/3).

**Step-by-step explanation:**

To solve the equation 10 - 9x^2 + 4x = -6x^2 + 4x, we can simplify it and then solve for x.

Rearranging the equation, we have:

10 - 9x^2 + 4x = -6x^2 + 4x

Combining like terms, we get:

10 - 9x^2 = -6x^2

Subtracting -6x^2 from both sides, we have:

10 - 9x^2 + 6x^2 = 0

Simplifying further, we get:

10 - 3x^2 = 0

To solve for x, we can isolate the term with x^2:

-3x^2 = -10

Dividing both sides by -3, we have:

x^2 = 10/3

Taking the square root of both sides, we get:

x = ±√(10/3)

Therefore, the solutions to the equation are x = √(10/3) and x = -√(10/3).

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).

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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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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6x^2=-3x+1 to the nearest hundredth

The **solutions **to the **quadratic equation **6x² = -3x + 1 to the nearest hundredth are -0.73 and 0.23.

Given the **quadratic** **equation **in the question:

6x² = -3x + 1

To solve the **quadratic equation **6x² = -3x + 1, we can rearrange it into **standard form**, where one side is set to zero:

6x² + 3x - 1 = 0

Now we can solve the equation using the **quadratic** **formula**, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:

[tex]x = \frac{-b \±\sqrt{b^2-4ac} }{2a}[/tex]

Here; a = 6, b = 3, and c = -1.

Let's substitute these values into the quadratic formula:

[tex]x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\\\\ x= \frac{-3 \±\sqrt{3^2-4\ *\ 6\ *\ -1} }{2*6}\\\\x = \frac{-3 \±\sqrt{9+24} }{12}\\\\x = \frac{-3 \±\sqrt{33} }{12}\\\\x = -0.73, \ x=0.23[/tex]

Therefore, the **values **of x are -0.73 and 0.23.

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The population of bees worldwide has been in decline. There are estimated to be 2,000,000,000 bees worldwide and each year there is estimated to be 10% less. How many bees worldwide will there be in 10 years?

**ANSWER: 100% of 2000000000 is 2000000000**

**What is 100 Percent of 2000000000?**

100 percent *2000000000

= (100/100)*2000000000

= (100*2000000000)/100

= 200000000000/100 = 2000000000

Now we have: 100 percent of 2000000000 = 2000000000

Question: What is 100 percent of 2000000000?

We need to determine 100% of 2000000000 now and the procedure explaining it as such

Step 1: In the given case Output Value is 2000000000.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 2000000000 = 100%.

Step 4: In the Same way, x = 100%.

Step 5: On dividing the pair of simple equations we got the equation as under

2000000000 = 100% (1).

x = 100% (2).

(2000000000%)/(x%) = 100/100

Step 6: Reciprocal of both the sides results in the following equation

x%/2000000000% = 100/100

Step 7: Simplifying the above obtained equation further will tell what is 100% of 2000000000

x = 2000000000%

Therefore, **100% of 2000000000 is 2000000000**

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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Me mason likes to work around the yard during the weekends

A) One way to write **mixed fractions** [tex]6\frac{2}{4} \\[/tex] is 3 + 3 + [tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}\\[/tex]

B) Saturday: 3 to 4 hours work = trim bushes and weed garden

Sunday: 4 to 5 hour work = paint sheet and mow lawn

A) [tex]6\frac{2}{4} \\[/tex] can be written as a **simple fraction** 6 + [tex]\frac{2}{4}[/tex]

This can be further broken into and written as

3 + 3 + [tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}\\[/tex]

B) Saturday : 3 to 4 **hours **of work

Trim bushes + Weed garden

[tex]1\frac{1}{6} +2\frac{2}{6}[/tex]

1 + [tex]\frac{1}{6}[/tex] + 2+ [tex]\frac{2}{6}\\[/tex]

3 + [tex]\frac{3}{6}[/tex]

3 + [tex]\frac{1}{2}[/tex]

[tex]3\frac{1}{2}[/tex]

Sunday: 4 to 5 hours of work

Paint sheet + mow lawn

[tex]1\frac{3}{6} +3 \frac{4}{6}[/tex]

1 + 3 + [tex]\frac{3}{6} +\frac{4}{6}[/tex]

4 + [tex]\frac{8}{6}[/tex]

[tex]4\frac{8}{6}[/tex]

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The Given question is incomplete the complete question is :

Mr. mason likes to work around the yard during the weekends

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.

a certain radioactive isotope has leaked into a small stream. one hundred days after the leak 8% of the original amount of substance remained. Determine the half life of this radioactive isotope

**Answer:**

The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. We can use the fact that 8% of the original amount remains after 100 days to determine the half-life of the isotope.

Let's assume that the initial amount of the substance is 1 unit (it could be any amount, but we're assuming 1 unit for simplicity). After one half-life, half of the original amount remains, or 0.5 units. After two half-lives, half of the remaining amount remains, or 0.25 units. After three half-lives, half of the remaining amount remains, or 0.125 units. We can see that the amount of substance remaining after each half-life is half of the previous amount.

We can use this information to set up the following equation:

0.08 = (1/2)^n

where n is the number of half-lives that have elapsed. We want to solve for n.

Taking the logarithm of both sides, we get:

log(0.08) = n*log(1/2)

Solving for n, we get:

n = log(0.08) / log(1/2) = 3.42

So the number of half-lives that have elapsed is approximately 3.42. Since we know that 100 days is the time for three half-lives (from the previous calculation), we can find the half-life by dividing 100 days by 3.42:

Half-life = 100 days / 3.42 = 29.2 days (rounded to one decimal place)

Therefore, the half-life of the radioactive isotope that leaked into the stream is approximately 29.2 days.

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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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.

Pretest: Unit 5

Question 6 of 25

If a sample proportion is 0.65, which range of possible values best describes

an estimate for the population parameter?

OA. (0.6, 0.69)

B. (0.65, 0.7)

O C. (0.5, 0.89)

OD. (0.5, 0.8)

SUBMIT

The range of possible values for the population parameter can be estimated using the margin of error, which is calculated as the critical value times the standard error.

Assuming a 95% confidence level, the critical value is approximately 1.96. The standard error for a sample proportion can be calculated as:

SE = sqrt[(p * (1 - p)) / n]

Where p is the sample proportion and n is the sample size. Substituting the values given in the question, we get:

SE = sqrt[(0.65 * 0.35) / n]

We do not know the sample size, so we cannot calculate the standard error exactly. However, we can use a rule of thumb that states that if the sample size is at least 30, we can use the normal distribution to estimate the margin of error.

With a sample proportion of 0.65, the margin of error can be estimated as:

ME = 1.96 * sqrt[(0.65 * 0.35) / n]

We do not know the sample size, so we cannot calculate the margin of error exactly. However, we can use the rule of thumb that a margin of error of about ±5% is typical for a 95% confidence level.

Using this margin of error, we can construct the following range of possible values for the population parameter:

0.65 ± 0.05

This range can be expressed as (0.6, 0.7), which corresponds to option A.

Therefore, the correct answer is option A) (0.6, 0.69).

Sophia says that you can solve the problem in the example by multiplying both quantities and the ratio is 60 to 36 by 1/6 is Sofia correct explain

This is a **ratio **problem and Sophia is expected to simplify the ratio by finding the smallest possible values and not compounding them by multiplying them by some values.

We can represent the given ratio as 60:36,

60/36

We proceed to reduce the **fraction **by dividing both the numerator and the denominator by a common factor say 6,

10/6

We can further reduce this with a common **factor **of 2

5/2

Thus, the ratio we have 5:2

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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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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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