[tex]\alpha^{3} -10\alpha ^{\frac{3}{2} } +25[/tex]

This is the answer right here

a fitness club leases space at a major shopping center. the club has 10,500 square feet which represents 16% of the total leasable space at the shopping center. calculate the total leasable space at the center?

The **shopping mall** has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.

According to the information provided, a fitness club occupies 10,500 **square feet** or 16% of the total leasable area at a sizable shopping mall. We can use the proportional and percentage approaches to determine the total leasable area.

Let's assume that the **variable** "x" stands for the whole amount of leasable space. Since we are aware that the area leased by the gym is 16% of the total leasable area, we can create the following equation:

10,500 = 0.16x

To solve for "x", we can divide both sides of the equation by 0.16:

10,500 / 0.16 = x

Simplifying this expression gives us:

x = 65,625

Therefore, The **shopping mall** has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.

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Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

The indicated IQ score, x, is enter your response here. (Round to one decimal place as needed.)

The indicated** IQ score** is given as 117.

The area under the **curve** is given as 0.1431

the area to the left of x = 1 - 0.1431

= 0.8569

for 0.8569 the z stat is 1.07

u = 100

sd = 15

x = u + z * sd

= 100 + 0.8569 * 15

= 116.05

approximately 117

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Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

xx

0.1431

A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the scale to the curve at labeled coordinate x, which is to the right of the curve’s center and peak. The area under the curve to the right of the vertical line is shaded and labeled 0.1431.

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Write the number for three million twenty thousand

Answer: 3,020,000

Step-by-step explanation:

three million twenty thousand

**Answer: 3,020,000**

**Step-by-step explanation: 3,000,000 + 20,000 = 3020000**

1. what is the last name of whom we honor for discovering ways to express and minimize logic though a new but similar form of algebra? 2. what does the k in k-map stand for? 3,4,5,

Boole. K-map stands for Karnaugh Map and is used to **simplify **and minimize the **expression **of logic in a similar form to algebra.

**George Boole** is the mathematician we honor for discovering ways to express and minimize logic through a new but similar form of **algebra**. The technique used to simplify and minimize these expressions is known as a Karnaugh Map, or K-map for short. A K-map is a visual representation of a Boolean **expression **using squares and circles to represent true or false variables in a table. By arranging the variables in the table, the same logic can be expressed in a simpler form with fewer variables. This allows for a simpler and more efficient form of logic expression. K-maps are used in many fields, such as digital **logic design**, where the efficiency of expression is important.

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Solve the system of equations:

**Answer:**

The solution is **(****x**** ****=**** ****6****,**** ****y**** ****=**** ****-****3****)**

**Step-by-step explanation:**

[tex]\sf \frac{x}{y + 1} = - 3 \: \: ........(1) \\ \\ \sf \frac{y}{x - 3} = - 1 \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \sf x + 3y = - 3 \: ........(1) \\ \\ \sf x + y = 3 \: \: \: \: \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \: \: \: \sf x + 3y = - 3 \: \: \: \: \: | \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf x + y = 3 \: \: \: \:\: \: \: \: | \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Tanya is renting a bounce house for a birthday party. The graph shows the time in hours (x)

compared to the total cost in dollars (y). Determine rate and initial value to write a linear equation.

=mx+b): _____

Find the rate (M). Find the initial value (B).

Equation (y=mx+b).

**the equation of the** straight line will be y = 10x+10.

What is **equation** **straight** line?

Y = mx + c is the general **equation** for a **straight** line, where m denotes the line's **slope** and c the y-**intercept**. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a **straight** **line**, including point-slope form, **slope**-**intercept** form, general form, **standard** form, etc. A **straight** **line** is a geometric object with two **dimensions** and infinite lengths at both ends. The formulas for the **equation** of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-**intercept**, standard, general, and others.

The initial value 10

slope m = 30-20/2-1

m = 10/1=10

So the equation of the straight line will be y = 10x+10.

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Tina and her friends started a project called Lemonade for Lions. Every Saturday, they sell lemonade to raise money for lion conservation. One Saturday evening, they share the day's leftover lemonade evenly among the 4 of them. Each person gets 1/8 of a gallon of lemonade.

Starting amount of lemonade: 5 gallons

Amount sold: 4 gallons

Amount left over: 5 - 4 = 1 gallon

Each person gets 1/8 of a gallon:

1 gallon / 8 = 0.125 gallons

So, each person gets 0.125 * 4 = 0.5 gallons.

Therefore, Tina and her friends were left with 1 gallon of lemonade, which they shared equally among the 4 of them, giving each person 1/2 of a gallon of lemonade.

Amount sold: 4 gallons

Amount left over: 5 - 4 = 1 gallon

Each person gets 1/8 of a gallon:

1 gallon / 8 = 0.125 gallons

So, each person gets 0.125 * 4 = 0.5 gallons.

Therefore, Tina and her friends were left with 1 gallon of lemonade, which they shared equally among the 4 of them, giving each person 1/2 of a gallon of lemonade.

The price of a gallon of unleaded gas was $2.81 yesterday. Today, the price rose to $2.88. Find the percentage increase. Round your answer to the nearest tenth of a percent.

The **percentage increase **of the **gas **would be 2.5%.

We can calculate the value of the **percentage increase **by the following formula,

percentage increase = (final value - initial value) / initial value × 100%

As per the given question, we have

**initial **value = $2.81 , and **final **value = $2.88

**Substitute **the values in the above formula, and we get

percentage increase= (2.88 - 2.81 ) / 2.81 × 100%

percentage increase = (0.07) / 2.81× 100%

percentage increase = 0.0249 × 100%

Apply the **multiplication **operation, and we get

percentage increase = 2.49%

Thus, the **percentage increase **of an item would be 2.5%.

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Someone help, please!

The appropriate response will be (A). The first equation of motion gives the link between "**velocity** and time."

Equation: A statement that two variable or **integer** expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

An equation is a mathematical representation of two equal objects, one on each side of a "equals" sign. We can solve challenges in our daily lives with the aid of equations. Most of the time, we look for help with pre algebra to resolve problems in real life. **Pre-algebra** concepts contain the fundamentals of mathematics.

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. Find the coordinates of the center and the measure of the radius for a circle whose equation is

(x-8)2 + (y+4)² =12 (3 points)

**Answer:**

Radius is 2√3 units

Center is (8,-4)

**Step-by-step explanation:**

Compared to the standard form equation of a circle, [tex](x-h)^2+(y-k)^2=r^2[/tex], then the radius would be [tex]r=\sqrt{12}=2\sqrt{3}[/tex] and the center would be [tex](h,k)\rightarrow(8,-4)[/tex].

Completing a Proof

Given: ABCD is a parallelogram.

Prove: mZA+mZB+mZC+mZD=360*

A

D

B

C

By the definition of a parallelogram, AD // BC and

AB/DC. Using, AD as a transversal, ZA and Z

are same-side interior angles, so they are

By the definition of supplementary,

mZA+mZD=180. Using side [

as a

transversal, ZB and ZC are same-side interior angles,

so they are supplementary. By the definition of

supplementary, mZB+mZC=180. So, mZA+mZD

+ m2B+mZC=180+180 by the [

property. Simplifying, we have mZA+mZB+mZC+

mZD=360°.

27

A

The required, we have **proven **that the **sum **of the measures of the **angles **in parallelogram ABCD is **360 degrees**.

Given: ABCD is a parallelogram. To prove: mZA + mZB + mZC + mZD = 360 degrees

What is parallelogram?A **parallelogram **is a **quadrilateral **consisting of pairs of **parallel sides**.

Here,

The proof you provided is correct! Here's a step-by-step explanation of the proof:

By the **definition **of a **parallelogram**, AD // BC and AB/DC.

Using AD as a transversal, ZA and ZD are same-side interior **angles**, so they are **supplementary **(meaning their measures add up to 180 degrees).

Using side AB as a transversal, ZB and ZC are same-side interior angles, so they are supplementary as well.

By the definition of supplementary angles, mZA + mZD = 180 degrees and mZB + mZC = 180 degrees.

Adding the two equations together, we get:

mZA + mZD + mZB + mZC = 180 degrees + 180 degrees

Simplifying the right side of the equation, we get:

mZA + mZB + mZC + mZD = 360 degrees

Therefore, we have proven that the **sum **of the measures of the **angles **in parallelogram ABCD is **360 degrees**.

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mr hall is doggie-paddling in the school pool at a speed of 1 m/sec when he spots his favorite rubber ducky. He increases his speed to 3m/sec over a period of 3 seconds. What is Mr. Halls acceleration?

**Answer:**

1m/sec

**Step-by-step explanation:**

Mr. Hall spent 3 seconds to increase his speed to 3m/sec increasing 1m/sec, don't over think it.

A bowling alley charges $2.00 per game and will rent a pair of shoes for $1.00 for any number of games the bowling alley has an earnings goal of $300 for that day write a linear equation that describes the problem

The **linear equation** that describes the **problem** is: 2x + y = 300.

A **linear equation** can be defined in **standard form** as Ax + By = C, where:

A, B, and C are integers

x and y are variables.

From the information given, we have the following:

number of games = x

rent for a pair of shoes for any number of games = y

total earnings goal for that day = 300

Therefore, the **linear equation** would be: 2x + y = 300

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the expression n^2 - n - 30 can be written in Factored Form as (n + 5) (n + k), where k represents a number

**Answer:**

k = -6

**Step-by-step explanation:**

Expand by substituting -6:

(n+5) (n-6) = n^2 + 5n - 6n (-6×5)

Thus, (n+5)(n-6) = n^2 -1n -30

(In a facotrised form for quadratics, the numbers need to add to 'bx', in this case -1, and multiply to form 'c' (-30). So -6×5 = -30 and k= -6)

the foreign language club is showing a four-movie marathon of subtitled movies. how many ways can they choose from the available?

The number of ways the **foreign** language club can choose 4 movies from the **available** is [tex]nC4 = n! / 4!(n-4)![/tex].

To calculate the number of ways the **foreign** language club can choose four movies from the available subtitled movies, we need to use the combination formula, which is:

[tex]nCr = n! / r!(n-r)![/tex]

Where n is the total **number** of available subtitled movies and r is the number of movies to choose (in this case, r=4).

Assuming there are at least four subtitled movies available, the number of ways to choose four movies would be:

[tex]nC4 = n! / 4!(n-4)![/tex]

Simplifying the **equation** further, we have:

[tex]nC4 = (n * (n-1) * (n-2) * (n-3)) / 4 * 3 * 2 *1[/tex]

Therefore, the number of ways the foreign language club can choose four movies from the **available **subtitled movies is given by the formula nC4.

The formula calculates the number of possible **combinations** of four movies that can be selected from the total number of available subtitled movies, without regard to the order in which they are shown.

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An athletic track is given in the figure.

The two straight parts are 80 m long.

The total length of the track is 400 m.

Find the radius of the curved part of the track

on both sides.

Subtract the length of the two straight parts

from the entire length of the track.

The radius of the curved part of the track will be **37.3m.**

Solution:

Given that

The length of straight parts = **80m each**

The total length of the track = is **400m**

So, the total length of curved parts = 400 - (80*2) = **240m**

Therefore, the radius of the curved parts =

[tex]2\pi r = 240\\r = 240/2\pi \\[/tex]

Hence, **r = 37.3m.**

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Find the slope of the line through each pair of points. ) (11, 8), (- 13, 11)

The **slope** of the **line** through each pair of **points** (11, 8), (- 13, 11) is -1/8.

The slope of a line is defined as **the change** in **y- coordinate** with respect to x - coordinate. The slope of a line represents the** direction** and **steepness** of a line. The formula for the **slope** of a line that passes through the points (x₁, y₁) and (x₂, y₂) is given by

Here we have

The pair of points (11, 8), (- 13, 11)

By the given formula,

Slope (m) = [ y₂ - y₁]/ [x₂ - x₁]

The **slope** from (11, 8) to (- 13, 11) can be calculated as follows

Slope = [ 11 - 8 ]/ [ -13 -11 ] = 3/-24 = -1/8

Therefore,

The **slope** of the **line** through each pair of **points** (11, 8), (- 13, 11) is -1/8.

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Helppppppppppp meeeeee guyssssssss

**Answer:**

2. $9.99

3. 45 tickets for $27

4. 20 cents

**Step-by-step explanation:**

**2. 79.92/8 = 9.99**

**3. 27/45 0.6 and 15/20 = 0.75 and 60 cents is less than 75 cents**

**4. 6/30 = 20**

**Answer:**

**Step-by-step explanation:**

79.92/8= 9.12 per cd

15/20= .75

27/45=.6 better deal because it is .60 cents per ticket

6/30= .20 per can

how do i do these types of problems?

**Answer:**

** 1/24.**

**Step-by-step explanation:**

There are 2 events here and they are independent, so the single probabilities are multiplied.

P(4 when die is rolled) = 1/6

P(A on the spinner) = 1/4

So, P(4 and A)

= 1/6 * 1/4

=** 1/24.**

PLEASE HELP ME WITH THESE!!!!!!!!!!!!!!!!!!!!

If I have an answer please ignore my current answer and just solve for the correct answer. Thanksssss!

The **volume **of the **rectangular prism **will be 1008 cubic inches and the volume of the pyramid is 504 cubic inches.

The **volume **of the rectangular prism is defined as the **space **in three-dimension covered by the **rectangular prism **having the sides Length, Width, and Height.

The volume of the rectangular prism will be the multiplication of the three parameters which are Length, Width, and Height of the prism.

The volume of the pyramid is the product of half of the area of the base and the height of the pyramid,

The volume of prism = 14 x 12 x 6

The volume of the prism = 1008 cubic inches

The volume of the pyramid,

Volume = 1/2 x Base area x H

Volume = 1/2 x 72 x 14

Volume = 504 cubic inches.

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Mark is buying 4 computers for his business. The table shows the prices and the advertised sales for the same type of computer at 4 computer stores. Based on the advertised sales, at which store will mark get the lowest price on 4 computers?

At a** total price** of $2720 for 4 Computers, retailer 2 delivers the best deal based on the listed specials.

Based on the stated** sales**, we need to figure out the entire cost of 4 **computers** at each retailer, accounting for any discounts or promotions, in order to determine which store will provide the lowest pricing for 4 Computers.

Let's use the following **variables** to symbolize the costs and special offers at each retailer:

P1: the price of a single computer in a store 1

P2: the price of a single computer in a store 2

P3: the price of a single computer in a store 3

P4: the price of a single computer in a store 4

D1: discount on one computer at store 1

D2: discount on one computer at store 2

D3: discount on one computer at store 3

D4: discount on one computer at store 4

Then, we may figure the total cost of four** computers** at each store using the following formulas:

Total cost at store 1 = 4(P1 - D1)

Total cost at store 2 = 4(P2 - D2)

Total cost at store 3 = 4(P3 - D3)

Total cost at store 4 = 4(P4 - D4)

The total cost at each** store** can then be calculated by plugging in the values from the table as follows:

Store 1: Total cost = 4(950 - 0.2*950) = 3040

Store 2: Total cost = 4(800 - 0.15*800) = 2720

Store 3: Total cost = 4(1100 - 0.25*1100) = 3300

Store 4: Total cost = 4(850 - 0.1*850) = 3060

Therefore, At a **total price **of $2720 for 4 Computers, retailer 2 delivers the best deal based on the listed specials.

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1/4 of the sum of 18 and 6. What does that mean? It it like converting 18 plus 6 to a fraction?

**Answer:**

See below

**Step-by-step explanation:**

Sum of 18 and 6 = 24

1/4 of the sum of 18 and 6 is asking you what is the result of dividing 24 by 4

In a way you can think of it as a fractional question but the answer is a whole number

[tex]\dfrac{1}{4} \cdot (18 + 6) = \dfrac{1}{4} \cdot 24 = \dfrac{24}{4} = 6\\[/tex]

if 5 books are picked at random from a shelf containing 8 novels, 3 books of poems, and a dictionary, what is the probability that

The **probability **that the dictionary is selected is 0.417, 3 novels and 2 books of poems are selected is 0.707. The probability that 4 novels are selected is 0.354.

The **probability **that the dictionary is selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select the dictionary and 4 other books.

The total number of ways to select 5 books from the shelf is:

C(12,5) = 12! / (5! * 7!) = 792

The number of ways to select the dictionary and 4 other books is:

C(1,1) * C(11,4) = 11! / (4! * 7!) = 330

Therefore, the probability that the **dictionary **is selected is:

P(dictionary) = 330/792 = 0.417

The **probability **that 3 novels and 2 books of poems are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 3 novels and 2 books of poems.

The total number of ways to select 5 books from the shelf is:

C(12,5) = 12! / (5! * 7!) = 792

The number of ways to select 3 novels and 2 books of poems is:

C(8,3) * C(3,2) = (8! / (3! * 5!)) * (3! / (2! * 1!)) = 560

Therefore, the probability that **3 novels** and **2 books **of poems are selected is:

P(3 novels, 2 books of poems) = 560/792 = 0.707

The** probability** that 4 novels are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 4 novels and 1 other book.

The total number of ways to select 5 books from the shelf is:

C(12,5) = 12! / (5! * 7!) = 792

The number of ways to select 4 novels and 1 other book is:

C(8,4) * C(4,1) = (8! / (4! * 4!)) * (4! / (1! * 3!)) = 280

Therefore, the probability that **4 novels** are selected is:

P(4 novels) = 280/792 = 0.354

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_____ The given question is incomplete, the complete question is given below:

If 5 books are picked at random from a shelf containing 8 novels, 3 books of poems, and a dictionary, what is the probability that a. the dictionary is selected? b. 3 novels and 2 books of poems are selected? c. 4 novels are selected?

5. A Set of Speakers costs $35 and Songs cost $195 each. The sales tax

rate is 8.25%. The expression 0.0825(35+ 195s) can be used to determine

the amount of sales tax due on the entire purchase of a set of Speakers

and S.Songs. Expand the expression and round to the nearest hundredth.

The **amount** of **sales tax **due on the **entire purchase** of a set of **speakers** and s songs is $2.89 plus $16.09 for each song **purchased**, rounded to the nearest hundredth.

**What is an expression?**

In **mathematics**, an **expression** is a **combination** of **numbers, variables**, and/or operators that represents a mathematical **quantity** or **relationship**. It can be a single number or variable, or a **combination** of multiple **numbers**, **variables**, and **operators**.

The given expression 0.0825(35+195s) represents the amount of sales tax due on the entire purchase of a set of speakers and s songs, where s is the number of songs purchased.

Expanding the expression, we get:

0.0825(35+195s) = 0.0825(35) + 0.0825(195s)

= 2.8875 + 16.0875s

Rounding this expression to the nearest hundredth, we get:

2.89 + 16.09s

Therefore, the **amount** of **sales tax **due on the **entire purchase** of a set of **speakers** and s songs is $2.89 plus $16.09 for each song **purchased**, rounded to the nearest hundredth.

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Find the measure of two complementary angles, ZA and ZB, if

mA=7x+4 and mZB=4x+9.

The **measure** of ∠A is 53.

The measure of ∠B is 37.

What is an expression?An **expression** contains one variable or more than one variable with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

∠A and ∠B are **complementary**.

This means,

∠A + ∠B = 90

Now,

∠A = 7x + 4

∠B = 4x + 9

7x + 4 + 4x + 9 = 90

11x + 13 = 90

11x = 90 - 13

11x = 77

x = 7

Now,

∠A = 7x + 4 = 7 x 7 + 4 = 49 + 4 = 53

∠B = 4x + 9 = 4 x 7 + 9 = 28 + 9 = 37

Thus,

∠A = 53

∠B = 37

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Malik just got hired for a new job and will make $96, 000 in his first year. Malik was

told that he can expect to get raises of $5,000 every year going forward. How much

money in salary would Malik make in his 11th year working at this job?

The** amount **of money Jamar will make in his 18th year working at this job is = $107,500

A **salary** is a form of periodic **payment **from an employer to an **employee**, which may be specified in an **employment **contract. It is contrasted with piece wages, where each job, hour or other unit is paid **separately**, rather than on a **periodic **basis.

here, we have,

**Calculation** of yearly salary outcome

The **amount** of money Jamar made in his first year= $48,000

The **salary** rise per year = $3,500

The **amount** of money he will make for the extra 17 years is

= 17 × $3,500

= $59,500

Therefore the **amount** he will receive as his **salary** in the 18th year working at this job = $48,000 + $59,500

= $107,500

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I NEED HELP PLEASEEEE!!!!

**Answer:**

**Step-by-step explanation:**

the answer is 420 cuase the manufatcure of math is hard i wont give an explanation.

What quantity must be added to 3-7x+4 to obtain - +4x-2?

A-4x2+3x+2

B.-412 + 11x + 2

C.-4x² + 11x-6

D. 2x²-3x+2

E. 2x²-3x+6

**Answer:**

**Step-by-step explanation: (10)(A) Add and subtract polynomials of degree one and degree two. (10)(B) Multiply polynomials of degree one and degree two. (10)(C) Determine the quotient **

**Hope it helps =}**

Answer:

b

Step-by-step explanation:

true or false: the rule of thirds is the process of dividing an image into thirds, using two horizontal lines and two vertical lines, and positioning the most important elements inside the squares the lines create.

**True.** The rule of thirds is a **photography** and visual arts guideline that involves dividing an image into thirds using two horizontal lines and two **vertical lines,** and then placing the image's most important **elements** at the intersection points or along the lines.

This aids in the creation of a balanced and visually appealing composition. This results in nine **rectangular **areas of equal size, with four **intersection** points where the lines cross.

The rule of thirds principle suggests that the points of intersection or the lines themselves are ideal places to position the composition's most important elements. The **resulting** image is more visually balanced and **pleasing** to the eye as important **elements** are placed in these areas.

It is important that, however, that the rule of thirds is not a hard** **and fast rule, and that there were times when breaking it can result in more **dynamic** and interesting **compositions**. The rule of thirds is merely a tool for artists and** photographers** to use in order to create more effective and engaging images.

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In circle M, m/NMO = 144º and the area of the shaded sector = 107. Find the

length of MN.

In **circle** M, m/NMO = 144º, and the **area** of the **shaded** **sector** = 107. then the **length** of MN is 23.19 units.

**What is the sector of the circle?**

That the **portion** (or part) of the **circular** **region** enclosed by two **radii** and the corresponding **arc** is called a **sector** of the **circle**.

The area of the shaded sector of circle M can be represented as follows:

Area of sector = (m/NMO / 360) * π * r²

We know that m/NMO = 144° and the area of the sector is 107, so we can substitute these values into the equation and solve for the radius:

107 = (144 / 360) * π * r²

Multiplying both sides of the equation by 360 / 144 gives:

360 * 107 / 144 = π * r²

Dividing both sides of the equation by pi gives:

r² = 360 * 107 / (144 * π)

Taking the square root of both sides of the equation gives:

r = √(360 * 107 / (144 * π))

Now that we know the radius, we can use it to find the length of MN.

The length of the minor arc MN is equal to the length of the central angle NMO in radians times the radius:

MN = m/NMO * π * r / 180

Substituting in the values for m/NMO and r gives:

MN = 144 * π * √(360 * 107 / (144 * π)) / 180

Hence, In **circle** M, m/NMO = 144º, and the **area** of the **shaded** **sector** = 107. then the **length** of MN is 23.19 units.

To learn more about the **sector of circle** visit,

https://brainly.com/question/30402678

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