Mathematics High School

## Answers

**Answer 1**

The **correlation coefficient **of the least squares **regression line **is 0.9

How to determine the slope?

To do this, we enter the **data values **in a **graphing calculator**, and we interpret the results:

Using a **graphing calculator, **we have the following **calculation summary**

Sum of X = 83Sum of Y = 123Mean X = 13.8333Mean Y = 20.5Sum of squares (SSX) = 356.8333Sum of products (SP) = 365.5R = 0.8728

The **slope** (b) is calculated using:

b = SP/SSX

This gives

b = 365.5/356.83

b = 1.0

Hence, the **slope** is 1.0

How to determine the y-intercept?

The **y-intercept** (a) is calculated using:

a = MY - bMX

a = 20.5 - (1.02*13.83)

a = 6.3

Hence, the **y-intercept** is 6.3

How to determine the correlation coefficient?

In (a), we have:

R = 0.8728

Approximate

R = 0.9

This means that the **correlation coefficient **is 0.9

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## Related Questions

Solve the inequality for x and identify the graph of its solution.

4|x + 3| < 8

Choose the answer that gives both the correct solution and the correct graph.

A.

Solution: x < 1 or x > 5; graph:

B.

Solution: x < –5 or x > –1; graph:

C.

Solution: x > –5 and x < –1; graph:

D.

Solution: x > –5 and x < –1; graph:

### Answers

**Answer:**

D

**Step-by-step explanation:**

^^^

When rolling a number cube (dice), what is the probability of rolling a number greater than or equal to 4?

### Answers

**Answer:**

3/6

**Step-by-step explanation:**

the probability of rolling a number greater than or equal to 4 is 3 out of 6 chances.

What are the x-intercepts of this function?

g(x) = -0.25x²-0.25x + 5

### Answers

The x intercepts of the equation are -5 and 4.

Find \displaystyle \lim_{x\to 1}f(x)

x→1

lim

f(x)limit, start subscript, x, \to, 1, end subscript, f, left parenthesis, x, right parenthesis for f(x)=\sqrt{51-2x}f(x)=

51−2x

f, left parenthesis, x, right parenthesis, equals, square root of, 51, minus, 2, x, end square root.

### Answers

[tex]\lim \limits_{x \to 1} \sqrt{51 -2x}\\\\=\sqrt{51 -2 (1)}\\\\=\sqrt{51-2}\\\\=\sqrt{49}\\\\=7[/tex]

What is the Volume of the prism?

### Answers

**Answer:**

296.4cm

**Step-by-step explanation:**

you do 9.5cm x 5.2cm x 6cm = 296.4cm

Which box plot represents the data set 1, 1, 3, 3, 3, 7, 9, 9, 9, 9, 15?

### Answers

The answer is C since it goes through all of the numbers

The answer is C because there’s a point at each number and the box needs to start on 3 then end on 9

Find the area bounded by the curve ay = x2 and the lines y = a and y = 4a.

### Answers

The **area bounded **by the **curve **ay = x² and the lines y = a and y = 4a is [tex]\mathbf{ \dfrac{14a^2}{3} }[/tex]

How do you find the area bounded by a curve:

The** area bounded** by the **curve **can be determined by taking the integral of the curve such that: [tex]\mathbf{\int^{2a}_{a} x dy}[/tex]

From the given information:

[tex]\mathbf{\implies \int^{4a}_{a} (ay)^{1/2} \ dy}[/tex]

[tex]\implies \mathbf{ a^{1/2} \int^{4a}_{a} y^{1/2} \ dy}[/tex]

Applying power rule

[tex]\implies \mathbf{ a^{1/2} \Big[\dfrac{2}{3}y^{3/2}\Big] ^{4a}_0 }[/tex]

Taking the boundaries, we have:

[tex]\implies \mathbf{ a^{1/2}\dfrac{14}{3}a^{5/2} }[/tex]

[tex]\implies \mathbf{ \dfrac{14a^2}{3} }[/tex]

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Joni has a circular

garden with a diameter of 14;, feet. If

she uses 2 teaspoons of fertilizer for

every 25 square feet of garden, how

much fertilizer will Joni need for her

entire garden? Round to the nearest

tenth.

### Answers

**Answer:**

12.31 teaspoons

**Step-by-step explanation:**

Calculate the area of a garden with a radius of 7 feet:

Area = [tex]\pi[/tex][tex]r^{2}[/tex]

Conversion factor (2 teaspoons/25ft^2)

Area = (3.14)(7)^2

Area = 153.9 ft^2

(153.9 ft^2)(2 teaspoons/25ft^2) = 12.31 teaspoons

How many full cases and additional items are needed to fulfill the order? 90 items ordered 8 per case

### Answers

The** required number** of cases are 11 and** the number** of rest units **are 2.**

If any number a is **divided **by the number b then we **write a/b** and find the **numerical values** of this fraction.

How to find divide of two numbers?

Here we have given

One case = **8 units**

Also we have given **90 units**

If each case can **accommodate 8 units** and we want to calculate the **overall number **of cases, we must **divide the** number of **units (8) **in each case by the **total number** of **units (90).**

As you can see, we have **a total** of **11 cases** and a **2 unit **leftover after **dividing by 8**.

We won't be able to fill another case with **8 units**, thus **the remainder** will be the number of **additional units.**

Therefore **11 cases **and rest **2 units** are** the answers.**

This is the c**onclusion** to the answer.

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Find the value of X

Round to the nearest tenth

### Answers

[tex]\tan 10^{\circ}=\frac{x}{500}\\\\x=500 \tan 10^{\circ} \approx \boxed{88.2}[/tex]

Geometry: Angle

d) If 2p° and (p + 15)° are a pair of complementary angles, find them.

e) If x° andare a pair of supplementary angles find them.

f) If pair of complementary angles are in the ratio 4:11, find them.

g) If a pair of supplementary angles are in the ratio 7:5, find them.

### Answers

**Answer:**

d) 2p° and (p+15) ° are complementary angles.

2p° + p° + 15° = 90°

3p° = 90° - 15°

p° = 75°/3

p = 25°

Now, 2p° = 2×25° = 50°

(p+15)° = 25°+15° = 40°

e) x° and x°÷4 are supplementary angles.

x° + x°÷4 = 180°

4x + x = 180°×4

5x = 180°×4

x = 180°×4/5

x° = 36° × 4 = 144°

And x°÷4 = 144/4 = 36°

f) Complementary angles in the ratio 4:11

Let the angles be 4x and 11x .

4x + 11x = 90°

15x = 90°

x = 6°

Now, 4x = 4×6 = 24°

11x = 11×6 = 66°

g) Supplementary angles in the ratio 7:5.

Let the angles be 7x and 5x.

7x + 5x = 180°

12x = 180°

x = 180°/12

x = 15°

Hence, 7x = 7×15 = 105°

5x = 5×15 = 75°.

Drag each tile to the correct location on the inequality. each tile can be used more than once. consider the graphed function. what are the domain and the range of this function? < ≤ -5 -4 1 7

### Answers

The domain and range of the given **graphed function** attached in the brainly link are;

**Domain**; -5 ≤ x < 1

**Range**; -4 ≤ y < 7

How to Interpret Inequality Graph?

**Domain** is simply defined as the set of all **possible input values**. This means it's the values on the x-axis in the graph. Meanwhile, the** range** is the set of all **output values** which in this case is the values on the y-axis.

Now, from the graph, we see that the line stopped at 2 points.

The bottom one is **shaded** which means it includes the numbers at that point.

It's **coordinates **are (-5, -4)

Thus, we can write the **domain** here as; x ≥ -5

While the **range** will be; y ≥ -5

For the second point above on the graph, we see the point where it is is not shaded and this means that the coordinates at that point are not included in the range or domain.

Thus, **domain **here is; x < 1

The **range** is ; y < 7

Combining **domain intervals** for both points, we will get;

Domain; -5 ≤ x < 1

Similarly, combining** range intervals** for both points, we have;

Range; -4 ≤ y < 7

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what is the ratio of 150 , 240, and 400

### Answers

Answer:

**15 : 24 : 40**

Step-by-step explanation:

**Prime factorizing each term :**

⇒ 150 = 5² × 3 × 2

⇒ 240 = 2⁴ × 5 × 3

⇒ 400 = 5² × 2⁴

⇒ The **HCF** is 5 × 2 = 10

⇒ Remove this factor when taking the ratio

**==========================================================**

**Taking the ratio :**

⇒ 150 : 240 : 400

⇒ 5 × 3 × 2 : 2³ × 3 : 2³ × 5

⇒ **15 : 24 : 40**

**Answer:**

[tex]15:24:40[/tex]

**Step-by-step explanation:**

[tex]~~~150:240:400\\\\=(15 \times 10):(24 \times 10):(40 \times 10)\\\\=15:24:40[/tex]

Which graph represents this system?

2x-5y=-5

y = ² x + 1

5

### Answers

**Answer:**

[tex]x = \frac{5(y - 1)}{2} \\ \\ x = \frac{y - 1}{2} [/tex]

**Step-by-step explanation:**

[tex]2x = - 5 + 5y \\ 2x = 5y - 5 \\ x = \frac{5y - 5}{2} \\ \\ y - 1 = 2x \\ \frac{y - 1}{2} = x[/tex]

Which of the following is the equation for the graph shown?

### Answers

**Answer:**

x equals 0

**Step-by-step explanation:**

it is a vertical line on zero and this is 1st grade level math

A dog is leashed to a point in the center of a large yard, so the area the dog is able to explore is circular. the leash is 15 feet long. what is the area of the region the dog is able to explore? round to the nearest tenth.

### Answers

Answer:

About 706.5 ft.

Step-by-step explanation: The formula for area of a circle is the radius squared (multiplied by itself) times 3.14. So 15 times 15= 225, times 3.14=706.5

help me w circle theorems!! will give you a virtual hug

### Answers

**Answer:**

I'm sorry I can't help if I can't see the problems clearly. :/

**Step-by-step explanation:**

Please Help I Don't Understand!!!

### Answers

**Answer:**

A) the SSS similarity theorem

**Step-by-step explanation:**

Given triangles with **all sides known**.

**Find the ratio of corresponding sides** to determine if they are similar:

**AC** = 6 + 3 = 9

**Ratio**: 9/3 = **3**

**BC **= 8 + 4 = 12

**Ratio**: 12/4 = **3**

**AB **= 15

**Ratio**: 15/5 = **3**

All three sides have **same ratio**. It means the triangles are **similar by SSS** similarity.

Correct choice is **A.**

Which of the following equations is written in standard form?

A) 4x-2y=0

B) -8x+4y=1

C) -3y+x-4=0

D) 2+3x-6y=0

### Answers

**Answer:**

sorry

**Step-by-step explanation:**

..............

........

........

**Answer: Choice B.**

**4R - 2Y = 0 **

**Step-by-step explanation: Has integer coefficients and equal to 0.**

the question is the image

### Answers

**Answer:**

(- 4, 16 ) , ([tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex] )

**Step-by-step explanation:**

y = x² → (1)

7x + 2y = 4 → (2)

substitute y = x² into (2)

7x + 2x² = 4 ( subtract 4 from both sides )

2x² + 7x - 4 = 0 ← in standard form

(x + 4)(2x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

substitute these values into (1) for corresponding values of y

x = - 4 : y = (- 4)² = 16 ⇒ (- 4, 16 )

x = [tex]\frac{1}{2}[/tex] : y = ([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex] ⇒ ( [tex]\frac{1}{2}[/tex] , [tex]\frac{1}{4}[/tex] )

need help! please be quick, love you

### Answers

**Answer:**

r = [tex]\sqrt{ \frac{V}{pi h }[/tex]

**Step-by-step explanation:**

V = pi r^2 h

Divide both sides by pi h

V / pi h = pi r^2 h / pi h

V / pi h = r^2

Take the square root of each side

sqrt( V / pi h) =sqrt( r^2)

sqrt( V / pi h) = r

r = [tex]\sqrt{ \frac{V}{pi h }[/tex]

Study the steps used to solve the equation. Given: StartFraction c Over 2 EndFraction minus 5 equals 7 Step 1: StartFraction c Over 2 EndFraction minus 5 plus 5 equals 7 plus 5 Step 2: StartFraction c Over 2 EndFraction plus 0 equals 12 Step 3: StartFraction c Over 2 EndFraction equals 12 Step 4: 2 (StartFraction c Over 2 EndFraction) equals 12 (2) Step 5: c equals 24 Choose the property that justifies each step of the solution. Step 1: Step 2: Step 3: Step 4:

### Answers

The **answers **are as **follows**:-

**addition **property of **equality****integers **are closed to **addition**identity **element****multiplication **property of **equality**commutative **property **of multiplication; reals are **closed **to **multiplication**; identity element

What is addition?

The **process **of summing up the **things **or numbers or integrating something is **termed **the **addition**.

**Given that:-**

c/2 -5 = 7

Step 1: c/2 -5 +5 = 7 +5

Step 2: c/2 +0 = 12

Step 3: c/2 = 12

Step 4: 2(c/2) = 12(2)

Step 5: c = 24

The **solution **of the given **expression **will be **done **as:-

Step 1: **addition **property of **equality **(lets you add the same to both sides)

Step 2: **integers **are closed to **addition**

Step 3: identity **property **of addition (adding** 0 **changes nothing)

Step 4: **multiplication **property of **equality**

Step 5: closure of real **numbers **to multiplication; identity **property **of multiplication

It is **hard **to say what "**property**" you want to claim **when **you simplify an arithmetic expression. **Above**, we have used the **property **that the sets of **integers **and real numbers are **closed **to addition and **multiplication**. That is, adding or **multiplying **real numbers gives a **real **number.

In Step 5, we can **rearrange **2(c/2) to c(2/2) using the **commutative **property of multiplication. 2/2=1, and c×1 = c. The **latter **is due to the identity **element **for multiplication: **multiplying **by 1 changes nothing.

Apart from the **arithmetic**, the other properties used are **properties **of equality. Those let you **perform **any operation on an equation, as long as you do it to **both **sides of the equation. The **operations **we have performed in this fashion are **adding **5 and multiplying by **2.**

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**Answer: 1. A**

**2. D**

**3. C**

**4. B**

**Step-by-step explanation:**

Just did it, edge 2023

Find the area of the square

Pleaseeee helpp meeee

### Answers

It’s a square, so all 4 sides are the same length, 16.8 inches, multiply 16.8 x 16.8 for area, 282.24 inches squared, or 23 feet and 6.24 inches squared, or 23.52 feet squared

Can someone help me please

### Answers

**Answer:** Option B

**Step-by-step explanation:**

Prooving **congruent** through HL means that we can prove the **hypotenuse **and one of the **legs** between the two **right-triangles **are **congruent**. The only answer option that meets these requirements is option B.

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The scale on a map is 1 : 50000.

How many kilometres on the ground are represented by 8cm on the map?

### Answers

The **distance** on ground that is represented by 8 cm on the **map** with the given **scale** is: 4 km.

What is the Scale of a Map?

The **scale **of a **map** relates the actual **distance **between two places in real life and the **distance **on paper.

Given the **map scale** as, 1:50,000, the number of km on ground that 8 cm on the **map** would be is calculated as shown below:

8 × 50,000 = 400,000 cm

Convert 400,000 cm to km. [1 km = 100,000]

400,000/100,000 = 4 km.

The **distance **on the ground would be: 4 km.

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Add (5x22x) +(6x-4).

### Answers

**Answer: -2640**

**Step-by-step explanation:**

5x22 = 110 but you still have an multiplication symbol just ignore it for now

and multiply 6x-4 and when you multiply a positive and a negative you get a negative so it's -24 and you have to multiply 110 and -24

and that would be -2640

A commercial airplane broke a record when it traveled 5,540 kilometers from new york to london in 5 hours because of a strong jet stream. on the same day, a different airplane traveled 2,964 kilometers from denver to hartford in 3 hours. part a: how much further, in kilometers, did the plane from new york to london fly in one hour compared to the plane from denver to hartford?

### Answers

The **plane **from new york to london fly 515.2 km per hour **compared **to the **plane **from denver to hartford .

What is Ratio ?

**Ratio **is when a **number **is divided by any other number and written in the form p:q.

It is given in the **question **that

A commercial airplane broke a record when it traveled 5,540 kilometers from new york to london in 5 hours .

a different airplane traveled 2,964 kilometers from denver to hartford in 3 hours.

The airplane travelled 5,540 kilometers in 5 hours

In 1 hour , the commercial airplane **covered **5540/5 = 1108 km.

In 1 hour , the other airplane **covered **2964/5 = 592.8 km

Therefore the plane from new york to london fly 1108- 592.8 = 515.2 km per hour compared to the plane from denver to hartford .

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In how many hours would they be 800 km apart?

*two cars a and b are having average speeds of 30 and 50 km per hours respectively leave the same point in opposite direction

pa help!!

### Answers

The **two cars (**a and b) will be** 800 km** apart after **10 hours.**

What is the average speed of a car?

The** average speed **of a car is the total distance traveled by a car within a specific period of covering such **distance**.

From the given information:

If the speed of car A (v_a) = 30 km/hr; andThe speed of car B (v_b) = 50 km/hr

The **distance **between both cars will be the hours they will meet:

i.e.

[tex]\mathbf{(v_a \times t)+(v_b\times t)= 800 \ km}[/tex]

[tex]\mathbf{(30 \times t)+(50\times t)= 800 \ km}[/tex]

30t + 50t = 800

80t = 800

t = 800/80 hrs

**t = 10 hrs**

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Question 4(Multiple Choice Worth 5 points)

(01.05 LC)

If x³ = 125, what is the value of x?

3

5

12

42

### Answers

x=5

The value of x would equal 5, since 5 cubed would equal 125

One factor of f (x ) = 4 x cubed minus 4 x squared minus 16 x 16 is (x – 2). what are all the roots of the function? use the remainder theorem.

### Answers

The** factor **of the** function **will be (x - 1), (x - 2), and (x + 2). Then the **roots **of the **function **will be 1, 2, and **negative **2.

What is a factorization?

It is a **method **for dividing a **polynomial **into pieces that will be **multiplied **together. At this moment, the **polynomial's **value will be **zero**.

The **function **is given below.

f(x) = 4x³ - 4x² - 16x + 16

Then the** factor **of the** function **will be

f(x) = 4x²(x - 1) - 16(x - 1)

f(x) = 4(x - 1) (x² - 4)

f(x) = 4(x - 1) (x² - 2²)

f(x) = 4(x - 1)(x - 2)(x + 2)

Then the **roots **of the **function **will be

x = 1, 2, -2

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