Norman, this is the solution to the exercise:

According to the information provided, we have:

• Highest interest rate = 8.81%

,• Second highest interest rate = 8 4/5 % = 8.8%

,• Middle interest rate = 8 1/2 % = 8.5%

,• Second lowest interest rate = 8.313%

,• Lowest interest rate = 8.3%

Translate the following: "twice the sum of a number and 7

is negative fifteen"

A **variable **is a letter or term that represents an unknown number, value, or quantity. Variables are especially useful in **algebraic expressions** or algebra.

let a number be x

then "twice the sum of a number be 2x

given

"twice the sum of a number and 7 is **negative fifteen**"

⇒ 2x + 7 = -15

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Find the equation of the circle (2, 3) and radius 4

**Answer: **[tex](\text{x}-2)^2+(\text{y}-3)^2 = 16[/tex]

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

Explanation:

The general circle template is

[tex](\text{x}-\text{h})^2+(\text{y}-\text{k})^2 = \text{r}^2[/tex]

(h,k) = center

r = radius

Assuming the center is (2,3) then we have h = 2 and k = 3. We also have a radius of r = 4.

[tex](\text{x}-\text{h})^2+(\text{y}-\text{k})^2 = \text{r}^2\\\\(\text{x}-2)^2+(\text{y}-3)^2 = 4^2\\\\(\text{x}-2)^2+(\text{y}-3)^2 = 16\\\\[/tex]

Gravel is being dumped from a conveyor belt at a rate of 30 ft^3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high?

The **height of the pile **increasing at the **rate **of 4.56 inches per minute when the pile is 10 ft high.

In given situation, the** rate of change of height **is equal to the** rate of change of volume**, divided by the base area.

First we find the** base area**.

**base area = (π/4)d² **

base area = (π/4)10²

base area = 25π ft²

base area ≈ 78.5 ft²

Then the** rate of change of height **would be,

(30 ft³/min)/(78.5 ft²)

≈ 0.38 ft/min

= 4.56 inches / minute

Therefore, the **height of the pile **increasing at the **rate **of 4.56 inches per minute when the pile is 10 ft high.

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find the lateral area and surface area the lateral area of the prism is __in squared. the surface area of the prism is __ in squared

**Answer**

The lateral area of the prism is **900** in squared

The surface area of the prism is **960** in squared

**Explanation**

Given:

The first side of the triangular base, a = 12 in

The second side of the triangular base, b = 13 in

The height of the prism, h = 30 in

What to find:

The lateral area and surface area of the prism.

Step-by-step solution:

The first step is to find the third side, c of the triangular base using **Pythagoras rule.**

Now, the next step is to calculate the **lateral area of the prism** using the formula below.

The lateral area of the prism is **900** in squared

The final step is to calculate the surface area of the prism using the formula below.

[tex]S.A=Lateral\text{ }Area+Base\text{ }Area[/tex]The base area is

[tex]=2(\frac{1}{2}cb)=2(\frac{1}{2}\times5\times12)=2(\frac{60}{2})=60\text{ }in^2[/tex]Therefore, the **Surface Area** = (900 + 60) = **960** in squared

Does the graph represent a function? 4 5 6 7 -3+ no O yes

To prove:

The given graph is a function.

The given graph is a function if and only if no x value has more than one value of y, or we can say that **a graph is a function iff no vertical line intersects the graph in more than one point.**

Thus, by the given graph it is clear that for x = 7 their are two values for y that is y = -6 , -7

**So, the given graph is not a function**

The rear window of Alex's van is shaped like a trapezoid with an upper base measuring 36 inches, a lower base measuring 48 inches, and a height of 21 inches. An 18-inch rear window wiper clears a 150° sector of a circle on the rear window. as shown in the diagram below. a. What is the area, in square inches, of the entire trapezoidal rear window Show on explain low you on your answer.

The area of a trapezoid is computed as follows:

[tex]A=\frac{a+b}{2}\cdot h[/tex]where a and b are the bases, and h is the height of the trapezoid. Replacing with a = 48, b = 36, and h = 21, we get:

[tex]\begin{gathered} A=\frac{48+36}{2}\cdot21 \\ A=42\cdot21 \\ A=882in^2 \end{gathered}[/tex]**The area of the entire trapezoidal rear window is 882 square inches**

f(x)=4x+6 and g(x)=1/2 * f(x)

What is the function rule for function g?

g(x)=

**Answer: 2x + 3**

**Step-by-step explanation:**

f(x) = 4x + 6

g(x) = 1/2 * f(x)

Plug f(x) into the g(x) equation.

g(x) = 1/2 * (4x + 6)

Now simplify,

g(x) = 2x + 3

2. A new car dealership invites 500 people to a promotional event. Only 330 people attend the event. What percentage of the people attend the event?

since

[tex]550X=330[/tex]then

[tex]X=\frac{330}{500}=0.66[/tex]then it is the 100x0.66= **66%**

Based off of the diagram below, correctly categorize each of the angle pairs. Some angle pairs go to more than one category. There are a few incorrect angle pairs as well. The incorrect pairs DO NOT get categorized.For context, line CD intersects line AB at point E.Line EG is perpendicular to line AB at point E.

Vertical angles = angle AEC and angle DEB

Adjacent angles = GEF and angle CEG also GEF and FEB also DEB and BEF

AED and DEB, also AED and AEC

Complementary angles = angle GEF and angle FEB, and angle AEC and angle CEG

That's all. **None of the angles are complementary**

what is seven times negative three / 7(-3)

**-21**

1) Let's calculate this product:

7 (-3) *Multiply 7 by -3*

*-*21

2) So, seven times negative three is equal to **-21 **that is the same as adding seven times the number -3. Remember different signs in a product turns to out to a negative result.

A 220 m wire is cut into three pieces. The second piece is 2 times as long as the first. The third piece is 4 times as long as the second. How long is each piece?

Answer:

**The first piece = 20m**

**The second piece = 40m**

**The third pice = 8x = 160m**

**Given:**

Total length of wire = 220m

2nd piece = 2 times the 1st piece

3rd piece = 4 times the 2nd

**To find:**

The length of each of the piece

The wire was cut into 3:

1st piece + 2nd piece + 3rd piece = 220m

let the first length = x

2nd length = 2 (1st length) = 2(x)

2nd length = 2x

3rd length = 4(2nd piece) = 4(2x)

3rd length = 8x

[tex]\begin{gathered} x\text{ + 2x + 8x = 220} \\ simplify: \\ 11x\text{ = 220} \end{gathered}[/tex][tex]\begin{gathered} divide\text{ both sides by 11:} \\ \frac{11x}{11}=\frac{220}{11} \\ x\text{ = 20} \end{gathered}[/tex]**The first piece = 20m**

**The second piece = 2x = 2(20) = 40m**

**The third pice = 8x = 8(20) = 160m**

i just want the answers, i dont want an explanation.

**Given: **

**Required: **Evaluation

**Explanation:**

Use BODMAS rule to evaluate all

71.

[tex]\begin{gathered} 16+4(-3)-7=16-12-7 \\ =-3 \end{gathered}[/tex]72.

[tex]\begin{gathered} (-24)\div(4)+16(2)=-6+32 \\ =26 \end{gathered}[/tex]73.

[tex]\begin{gathered} -5-8+6(-3)=-13-18 \\ =-31 \end{gathered}[/tex]74.

[tex]\begin{gathered} 30-6\div3+4=30-2+4 \\ =32 \end{gathered}[/tex]75.

[tex]\begin{gathered} 21-45+8\div2=21-45+4 \\ =25-45=-20 \end{gathered}[/tex]**Final Answer: **

**71 - E**

**72 - AE**

**73 - A**

**74 - BE**

**75 - B**

Use the formula h = 16t2, where t is time in seconds and h is the distance in feet traveled by a free-falling body or object to solve the following problem.

A diver dives from a cliff that has a height of 125 feet. Determine the time of the dive.

The dive lasted approximately

seconds.

(Type an integer or decimal rounded to the nearest tenth as needed.)

If a diver dives from a cliff that has a height of 125 feet, The **dive lasted **approximately 2.80 seconds

A diver dives from a **cliff that has a height **of 125 feet

The formula h = 16t², where t is time in seconds and h is the distance in feet traveled by a free-falling body or object

125 = 16t²

125/16 = t²

t = √(125/16)

t = √125/√16

t = 5√5 /4

t = 1.25 x 2.23

t = 2.795

t = 2.80

Therefore, if a diver dives from a cliff that has a height of 125 feet,** The dive lasted** approximately 2.80 seconds

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Vector v has an initial point at (8, 4) and a terminal point at (−8, 10). What is -1/2 times vector v?

In order to find a vector multiplication by a scalar, we follow the rule:

[tex]u\ast(n_1,n_2)_\Rightarrow(un_{1,}un_2)[/tex]then, if we apply it to the vector v, we need to find the dimensions of the vector, for that we subtract the initial point from the terminal point,

[tex](-8-8,10-4)\Rightarrow(-16,6)[/tex]then, multiply by the scalar -1/2,

[tex]-\frac{1}{2}\ast(-16,6)\Rightarrow(8,-3)[/tex]Answer:

[tex](8,-3)[/tex]You are about to enter an elevator with a weight capacity of 500 pounds. There are three people already in the elevator. The weights of the passengers are 107 pounds, 172 pounds and 129 pounds. Assuming that you weigh 136 pounds, is it safe for you to enter the elevator?

**Given**

capacity of 500 pounds.

weights of the passengers are 107 pounds, 172 pounds and 129 pounds.

you weigh 136 pounds

**Find**

is it safe for you to enter the elevator?

**Explanation**

as total pounds in the elevator = 107 + 172 + 129 = 408 pounds

total pounds included my weight = 408 + 136 = 544 pounds

capacity = 500 pounds

so , extra pounds = 544 - 500 = 44 pounds

so , no it is not safe for you to enter the elevator.

**Final Answer**

Therefore , No the weigh capacity would be exceeded by 44 pounds

the ratio of students to faculty is 25 to 2. how many faculty members will be needed for a student population of 623? rounded to the nearest whole number

We have a ratio of students to faculty members is 25 to 2.

For a students population of 623, the number of faculty members will be:

[tex]623\text{ students}\cdot\frac{2\text{ faculty members}}{25\text{ students}}=49.84\text{ faculty members}\approx50\text{ faculty members}[/tex]**50 faculty members will be needed for a student population of 623.**

A rectangular safe can hold 5,184 cubic inches. Gold bars that are 3 inches by 6 inches by 2 inches fit to completely fill the safe. What is the volume of each gold bar?11 in.336 in.318 in.315 in.3

**Given:**

Rectangular safe hold 5184 cubic inches

Gold bar,

3 inches by 6 inches by 2 inches

**Find-:**

The volume of each gold bar

**Explanation-:**

The gold bar is in a rectangular shape

So volume is:

[tex]V=\text{ Length}\times\text{ Width}\times\text{ Height }[/tex]The dimension of the gold bar is 3 inches by 6 inches by 2 inches.

[tex]\begin{gathered} V=3\times6\times2 \\ \\ V=36\text{ in}^3 \end{gathered}[/tex]Volume of each gold bar is 36.

In a square box problem, the:Top number is the product of those left and rightBottom number is the sum of those at left and rightComplete this square box problem

Answer

Draw the box to complete the table.

Next,

To get the top, multiply both the left and the right = 11 x (-3)

= -33

To get the top, add both the left and the right = 11 + (-3) = 11 - 3 = 8

IXL Transversals of parallel lines: prove angle relationships 6QF for geometry, please help

4) [tex]m\angle XWY=m\angle HGY[/tex] (definition of congruent angles)

5) [tex]\angle HGY \cong \angle GTU[/tex] (corresponding angles theorem)

6) [tex]m\angle HGY=m\angle GTU[/tex] (definition of congruent angles)

7) [tex]\angle GTU[/tex] and [tex]\angle UTR[/tex] are supplementary (linear pair)

8) [tex]m\angle GTU+m\angle UTR=180^{\circ}[/tex] (definition of supplementary angles)

9) [tex]m\angle HGY+m\angle UTR=180^{\circ}[/tex] (substitution)

10) [tex]m\angle RTU+m\angle XWY=180^{\circ}[/tex] (substitution)

Evaluate (You can use which ever first step you

selected above)

[tex] \frac{3 \times 3 \times 2^{ - 4} \times 2^{0} }{(3 \times 2 ^{ - 3}) ^{2} } \\ = \frac{3^{ 1+1 } \times 2^{ - 4 + 0} }{3 \times 2 ^{ - 3 \times 2} } \\ = \frac{ {3}^{2} \times {2}^{ - 4} }{3 \times {2}^{ - 6} } \\ = 3^{2 - 1} \times 2^{ - 4 - ( - 6)} \\ = 3 \times {2}^{ - 4 + 6} \\ = 3 \times {2}^{2} \\ = 3 \times 4 \\ = 12[/tex]

**I USED THE LAWS OF EXPONENTS.**

IF YOU DO NOT KNOW THEM PLEASE TELL ME AS SOON AS POSSIBLE TO ARRANGE FOR YOU.

(calc exponential growth and decay calculus!) a principal amount of $5000 is deposited into an account paying interest at a rate of 6 percent continuously compounded. what will the account balance be after 3 years

SOLUTION

**Given:**

**The formula is given as:**

**Final answer:**

Can someone answer this question for me please, I really need the help:

**Answer:**

4x² +28x +49

**Step-by-step explanation:**

You want a **polynomial** equivalent to the **area of the figure** shown.

The polynomial can represent the sum of three areas:

blue area + green area + yellow area

= 4x² +4(7x) +7²

= **4x² +28x +49**

For j(x) = 3x − 1, find j of the quantity x plus h end quantity minus j of x all over h period a 3 to the power of the quantity x minus 1 end quantity times the quantity 3 to the power of h end quantity all over h b 3 to the power of the quantity x minus 1 end quantity times the quantity 3 to the power of h minus 1 end quantity all over h c 3 to the power of the quantity x minus 1 end quantity times the quantity 3 to the power of h plus 1 end quantity all over h d the quantity x minus 1 end quantity times the quantity 3 to the power of h plus 1 end quantity all over h

The resulting value of the function [j(x+h)-j(x)/h] is 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h

What is an exponential function?An **exponential **function is defined as a function whose **value **is a **constant **raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ in mathematics, where x is the independent **variable**

Given the **function **expressed as;

j(x) = 3⁽ˣ⁻¹⁾

Required **value **of the **function **[j(x+h)-j(x)]/h

We have to determine the function j(x+h) and j(x)

j(x+h) = [tex]3^{(x+h) -1}[/tex]

Substitute the **values**,

[j(x+h)-j(x)]/h = [ [tex]3^{(x+h) -1}[/tex] - 3⁽ˣ⁻¹⁾ ]/h

⇒ [ [tex]3^{(x-1) +h}[/tex] - 3⁽ˣ⁻¹⁾ ]/h

⇒ [ [tex]3^{(x-1)} \times3^{h}[/tex] - 3⁽ˣ⁻¹⁾ ]/h

⇒ 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h

Hence, the equivalent **value **of the **function **is 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h

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10 Millie and her gr

made this plan for a garden.

They will plant flowers in

8 square feet of the garden.

They will plant vegetables in

the rest of the garden.

10 feet

2 feet

FOR

129

FOR FOR

20 CAP

4 feet

7 feet

9 feet

6 feet

Part A

Which of these can be used

to model the area of the

vegetable garden?

A2 x 10

B6X7

©6x9

D 10 x 7

Part B

What is the total area of the

garden in square feet?

Part A) Option c is correct answer. 6 x 9 can be used to model the **area **of the vegetable garden.

Part B) Total **area **of the garden in square feet is 62 square feet.

**What do you mean by area?**

**Area **is a unit of measurement used to describe a region's size on a flat or curved surface. While a plane region or area refers to the **area **of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.

To calculate the area we first individually calculate the area of the garden with flowers and vegetables,

**Area **of the garden where flowers are planted:

**Area **= length x breadth

**Area **= 4 x 2 = 8 square feet

**Area **of garden where vegetables are planted:

**Area **= 6 x 9 = 54 square feet

Total **area **of the garden = 8 + 54

Total **area **of the garden = 62 square feet

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17. Critique Reasoning Lisa used a number line to model 2(3). Does her number line make sense? Explain why or why not. 8-7-6-5-4-3-2-1 0

Reasoning Criticism Lisa modeled 2 with a number line (3). Her **logical number line** is -6.

Therefore, Reasoning Criticism Lisa modeled 2 with a number line (3). Her **logical number line** is -6.

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Dilate the following points by each scale factor (k) provided. P(3, 4) by k=1/2 And N(4, 15) by k=2

Dilations involve multiplication, so we have that the dilation with scale factor 1/2 of the point (3,4) **is** **(1.5, 2)**

and the dilation with scale factor 2 of the point (4,15)** is (8, 30)**

Find a_10 5, 12, 19, 26, 33...

Given,

The progression is 5, 12, 19, 26, 33...

The first term of the series is, a = 5.

The common difference of the series is,

d = 12 - 5 = 7

The 10th term of the series is,

[tex]\begin{gathered} a_{10}=a+(10-1)\times d \\ =5+9\times7 \\ =5+63 \\ =68 \end{gathered}[/tex]**Hence, the 10th term of the series is 68.**

14. Write a quadratic equation that cannot be factored.

Given:

Quadratic equation

To write a quadratic equation that cannot be factored or cannot be solved by factoring, we note first that factoring is the easiest method to solve a quadratic equation as long as the equation is easily factorable. If not, we'll need alternative approaches like employing the quadratic formula.

We also note that factoring cannot always be used to solve quadratic equations.

Below is an example of an equation that can be solve by factoring:

[tex]\begin{gathered} x^2-3x-10=0 \\ (x-5)(x+2)=0 \end{gathered}[/tex]Now, the equation that cannot be factored or cannot be solved by factoring is:

[tex]x^2+x-1=0[/tex]We cannot apply factoring to the above equation. **Therefore, the answer is:**

Melissa brought 6 apples for $1.20 .if each apple cost the same amount, how much would 20 apples cost

The **cost **of 20 apples is such that the **ratio **of apples to cost **maintained **or each apple **costs** the **same **amount is $4.

The **ratio** is the **division **of the two numbers.

For example, a/b, where a will be the **numerator **and b will be the **denominator**.

As per the given,

**Melissa **brought 6 apples for $1.20.

The **ratio **of cost to apple ⇒

1.20/6

Now let's suppose the cost of 20 apples is x dollars.

The **ratio **of cost to apple ⇒

x/20

Since the **cost** of each apple is the **same**, therefore, both **ratios **must be the same.

x/20 = 1.20/6

x = 20(1.20/6)

x = 4

Hence "The **cost **of 20 apples is such that the **ratio **of apples to cost **maintained **or each apple **costs** the **same **amount is $4".

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how many cubic blocks with a side length of 1/6 cm are needed to fill the volume of this prism?The answer choices are 4,8,9,32.

Given the figure, we can deduce the following information:

Height=1/2 cm

Length=1/2 cm

Width= 1/6 cm

To determine the number of cubic blocks with a side length of 1/6 cm needed to fill the volume of the given prism, we first note that a cube has equal sides. So, the dimensions of the cube must be:

Height= 1/6 cm

Length=1/6 cm

Width=1/6 cm

Next, we get the volume of the cube by using the formula:

[tex]\begin{gathered} Volume\text{ of the cube}=(Height)(Length)(Width) \\ =(\frac{1}{6})(\frac{1}{6})(\frac{1}{6}) \\ Simplify \\ =\frac{1}{216}\text{ }cm^3\text{ } \end{gathered}[/tex]Then, we get the volume of the given prism using the same formula:

[tex]\begin{gathered} Volume\text{ of the given prism}=(He\imaginaryI ght)(Length)(W\imaginaryI dth) \\ =(\frac{1}{2})(\frac{1}{2})(\frac{1}{6}) \\ =\frac{1}{24}\text{ }cm^3\text{ } \end{gathered}[/tex]Now, we find the number cubic blocks by using the formula:

[tex]\begin{gathered} Number\text{ }of\text{ cubic blocks}=\frac{Volume\text{ of the given prism}}{Volume\text{ of the cube}} \\ =\frac{\frac{1}{24}}{\frac{1}{216}} \\ Simplify \\ =9 \end{gathered}[/tex]**Therefore, the answer is 9.**

why do you think Hoar referenced the chinese inventing gunpowder,paper,and the compass?
Examine graphs A and B. What do you notice about the difference between the Y axis for the good graph A and the Poot graph B? How is a break shown on the Y axis of graph A
How many moles are in a gas sample occupying 0.500L at 170 mmHg and 250C?Group of answer choices0.004570.006002.183.483.85
Benefits of Gaming Video games can aid in building brain functions that are important to learning. People who play video games have increased attention spans and visual recognition because they need these abilities while playing in-depth, strategy-based games. Many of these games take long periods of time to play, thus players must stay focused for longer. Developing focus can aid in learning and is an important trait for all people to have. Problem-solving, something vital for success in school and careers, is another skill that can be developed through gaming. Many games, including action and sports games, require players to solve problems quickly in order to be successful. These skills can be developed through continuous playing of video games. The multiple cognitive actions required by video games, such as those required by strategy-based games, help students develop the ability to multi-task. A recent study also suggests that those with dyslexia have improved reading and brain skills with repeated gaming experiences. With all of these benefits, there are still opponents who believe gaming is negative. Opponents believe that some games promote violence and lead to violent emotions. However, if a parent or guardian spends time discussing any violent images or situations from video games with players, these objections can be overcome. The positive benefits of perseverance and patience can become the focus of video games.3Which sentence would be the best conclusion to the essay? A. These benefits are important and overcome the negative parts of gaming. B. So, even the things people say are bad about gaming can be turned into benefits. C. Perseverance, patience, problem solving and focus are things that will help students do better. D. The lessons learned from gaming can be applied not only in school, but in everyday life as well.
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solve for B 25+ 7/9=74