A mall is designing an outdoor space. The available space is 127 feet by 46 feet. The
plan is for a grassy section with a width of 40 feet. Next to the grass will be a cement
sidewalk with a width of 6 feet. What is the area of the available space in square feet?

Answer:

y = -8/3x + 33

Step-by-step explanation:

y2 - y1 / x2 - x1

9 - 1 / 9 -12

8 / -3

= -8/3

y = -8/3x + b

1 = -8/3(12) + b

1 = -32 + b

33 = b

The answer is B, which is to find the common denominator.

In solving a rational equation, the first step is usually to find a common denominator for all the fractions in the equation. This allows us to combine the fractions into a single fraction and simplify the equation.

To find the common denominator, we need to identify the factors of the denominators and determine the least common multiple (LCM) of these factors. Then, we multiply each fraction by the appropriate factor(s) to get the common denominator. For example, if we have the equation:

(3/x) + (4/2x) = 1/4

The denominators are x and 2x, which have factors of x and 2. The LCM of these factors is 2x, so we need to multiply the first fraction by 2 and the second fraction by 1 to get:

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

Then we can combine the fractions and simplify the equation to get:

(10/2x) = 1/4

From here, we can continue to solve for x by cross multiplying and manipulating the equation.

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Answer: $160

Step-by-step explanation:

48 dollars for 3 shirts so she pays 16 dollars for each shirt  

if she going to buy 10 its 10 time 16

and you get 160

Answer:

brainlest maybe

Step-by-step explanation:

Nature's Best wants to combine nuts they sell for $3.60 a pound with dried fruit they sell for $2.40 a pound to create a trail mix. How much of each snack should they use to make 10 pounds of trail mix that would sell for $3.30 a pound?

--------------

Let amt. of nuts be "x" lbs ; value is 3.60x dollars

-------------

Amt of fruit is "10-x" lbs ; value is 2.4(10-x) = 24-2.4x dollars

----------------------

Amt of mix is 10 lbs ; value is 3.3*10= 33 dollars

------------------------

EQUATION:

value + value = 33 dollars

3.6x + 24-2.4x = 33

1.2x = 9

x = 7.5 lbs (amt of nuts in the mix)

10-x = 2.5 lbs (amt of fruit in the mix)

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

Answer:

A triangle.

Step-by-step explanation:

The plane would pass through opposite sloping faces of the pyramid and through the base; the shape formed is a triangle.

Step-by-step explanation:

Multiply the number outside the brackets to the numbers inside:

So,

9 * 9x = 81x

9 * 2y = 18y

9 x -6 = -54

So the simplified or equivalent expression is:

81x + 18y - 54

Answer:

Step-by-step explanation:

Evaluate the expression, given functions f and h:  

f(x) = 3x − 1,

h(x) = −2x2 + 3x − 2.

f  

7

3

− h(−2)

The probability of customers buying each insurance is 1/24.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

Total number of sales is 6.

Total number of customers is 12.

The number of customers interested only in auto insurance is 6.

The number of customers interested only in homeowners insurance is 4.

The number of customers interested only in life insurance is 2.

Now, the probability that two sales are for auto insurance is given as,

2/6 = 1/3

The probability that two sales are for homeowners insurance is given as,

2/4 = 1/2

And,  the probability that two sales are for life  insurance is given as,

2/4 = 1/2

Thus the probability of two sales for each insurance is given as the product of all the three probabilities as,

 1/3 × 1/2 × 1/2 = 1/12

And, the probability of six customers out of 12  buying the sales is,

6/12 = 1/2

Thus, the probability for the given case is,

1/2 × 1/12 = 1/24

Hence, the probability for the given problem is 1/24.

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Using the concept of probability and the combination formula, it is found that there is a 0.4444 = 44.44% probability  they get to be on the same team.

--------------------

--------------------

Combination formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

--------------------

Finding the number of desired outcomes:

\(D = 2C_{8,3} = 2\frac{8!}{3!5!} = 112\)

--------------------

Finding the number of total outcomes:

\(T = C_{10,5} = \frac{10!}{5!5!} = 252\)

--------------------

The probability is:

\(p = \frac{D}{T} = \frac{112}{252} = 0.4444\)

0.4444 = 44.44% probability  they get to be on the same team.

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The Correct answer is A. (-4,1) ordered pair generated by this model should be discarded because the values are unreasonable.

In algebra, a quadratic equation (from Latin quadratus 'rectangular') is any equation that can be rearranged in well-known form as ax²+bx+c=0 Where x represents an unknown value, and a, b, and c constitute recognized numbers.

One supposes usually that a ≠ zero; the one's equations with a = zero are taken into consideration degenerate because the equation then will become linear or even simpler. The numbers a, b, and c are the coefficients of the equation and can be prominent with the aid of calling them, respectively, the quadratic coefficient, the linear coefficient, and the consistent or loose time period.

The values of x that satisfy the equation are referred to as answers to the equation, and roots or zeros of the expression on its left-hand aspect. A quadratic equation has at most two answers. If there is handiest one solution, one says that it's miles a double root. If all the coefficients are real numbers, there are both actual solutions, a single actual double root, or two complicated answers which can be complicated conjugates of each other.

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Complete Question:

Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. which ordered pair generated by this model should be discarded because the values are unreasonable?

A radioactive substance will have a decay of A ≈ 31.1936 mg after 32 hours.

Radioactive decay (additionally referred to as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the manner with the aid of using which an volatile atomic nucleus loses electricity with the aid of using radiation. A fabric containing volatile nuclei is taken into consideration radioactive.

Every atom seeks to be as strong as possible. In the case of radioactive decay, instability happens whilst there's an imbalance withinside the quantity of protons and neutrons withinside the atomic nucleus. Basically, there's an excessive amount of electricity withinside the nucleus to preserve all of the nucleons together.

Initial Radioactive substance, A₂ = 110 mg Remains substance, A = 55 mg time, t = 22 hours

Here, radioactive substance decay. exponentially.

\(a=a_{0}e^{at} \\\\55=110*e^{22k} \\\\\frac{55}{110} = e^{22k} \\\\ \\e^{22k} =\frac{1}{2}\)

Taking lo both side, we get ln (1/2) = lne²²K

ln (1/2) = k*22

\(k=\frac{ln(1/2)}{22}\)

K = -0.03150669

Substance remains after 32 hours,

t=32 hr

\(A=110*e^{( (-0.03150669))*32} \\A=110*e^{(-1.2602676)} \\\\\)

A = 110x 0.283578131

A = 31.19359441

A ≈ 31.1936 mg

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Answer:

3x + 7 = -20

3x = -20-7

3x = -27

3x ÷ 3 = x

- 27 ÷ 3 = -9

x= -9

Answer:

10

Step-by-step explanation:

ab+c

Put a as 2, b as 3, and c as 4.

(2)(3) + (4)

Evaluate.

6 + 4

= 10

Answer:

10

Step-by-step explanation:

Plug the values in the equation

(2)(3) +4

(2)(3)=6

6+4=10

Therefore your answer is 10

Hope this helps!

Answer:

x=11

Step-by-step explanation:

2x+5-27

step 1 subtract 5 from each side

2x=22

step 2 divide each side by 2

x=11

Answer:

2x=27-5

2x=22

2x/2=22/2

x=11

Answer:

To subtract 1/2 from 7/10, we need to find a common denominator. The least common multiple of 2 and 10 is 10, so we can convert 1/2 to 5/10:

7/10 - 5/10 = (7 - 5)/10 = 2/10 = 1/5

Therefore, 7/10 - 1/2 = 1/5.

Answer:

To subtract 1/2 from 7/10, we need to find a common denominator. The least common multiple of 2 and 10 is 10, so we can convert 1/2 to 5/10:

7/10 - 5/10 = (7 - 5)/10 = 2/10 = 1/5

Therefore, 7/10 - 1/2 = 1/5.

We would expect the central 95% of autos to be found in the interval from 20 to 40 mpg.

The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, approximately 68% of the observations fall within one standard deviation of the mean, approximately 95% of the observations fall within two standard deviations of the mean, and approximately 99.7% of the observations fall within three standard deviations of the mean.

Assuming that the distribution of autos' miles per gallon (mpg) is approximately normal, we can use the empirical rule to estimate the interval in which we would expect the central 95% of autos to be found.

Then, according to the empirical rule, approximately 95% of autos should be found within 2 standard deviations of the mean. We can write:

μ - 2σ ≤ x ≤ μ + 2σ

where x represents the mpg of an individual auto.

For example, if we take a random sample of 100 autos and find that the mean mpg is 30 and the standard deviation is 5, then we can estimate the interval in which we would expect the central 95% of autos to be found as:

30 - 2(5) ≤ x ≤ 30 + 2(5)

20 ≤ x ≤ 40

Therefore, we would expect the central 95% of autos to be found in the interval from 20 to 40 mpg.

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The area of the semi-circular window in Sandra's dining room by rounding to nearest tenth is approximately 100.5 square inches.

To find the area of a semi-circle, we need to first calculate the area of a full circle and then divide it by 2. The formula for the area of a circle is

A = π * r²,  where A is the area and r is the radius.

Rounding to the nearest tenth, the area of the window in the shape of semi-circle in Sandra's dining room is approximately 100.5 square inches.

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a. The prime numbers in this list are 5 and 7. b. There are no prime numbers in this list. c. The prime numbers in this list are 31 and 17. d. The prime numbers in this list are 61 and 2.

a. In the list 5, 7, 12, 11, the prime numbers are 5, 7, and 11. Prime numbers are numbers greater than 1 that have only two factors, 1 and themselves.

b. In the list 14, 6, 3, the prime number is 3. The other numbers have more than two factors, making them not prime.

c. In the list 31, 17, 9, 15, the prime numbers are 31 and 17. The numbers 9 and 15 have more than two factors, so they are not prime.

d. In the list 782, 61, 2, the prime numbers are 61 and 2. Number 2 is the smallest prime number, and 61 has only two factors, 1 and 61. The number 782 has more than two factors, so it is not prime.

To summarize, the prime numbers in each list are: a. 5, 7, 11; b. 3; c. 31, 17; d. 61, 2.

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The number of chairs that should be removed, for there to be as few empty seats as possible but for all rows of chairs to be complete, is 33 chairs.

The number of chairs that make up a row is 11 chairs and there are to be 70 students in attendance. The number of rows that would take the students is therefore:

= Number of students / Number of rows

= 70 / 11

= 6. 36

= 7 rows rounded up

The number of rows needed is 7 rows which means the number of chairs would be:

= 7 rows x 11 chairs per row

= 77 chairs

The number of chairs to be removed is:

= Total chairs - Chairs needed

= 110 - 77

= 33 chairs

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Answer:

Step-by-step explanation:

given:

the scale from a square park to a drawing of the park is 5 m to 1 cm

the actual park has an area of 1,600 m²

find:

what is the area of the drawing of the park​

solution:

drawing scale is 5m : 1cm

1,600 m² =      5² m²      

   x                  1² cm²

cross multiply:

5² m² x = 1600 m² (1 cm²)

x = 1600 m²

      5² m²

x = 64 cm²

therefore, the area of a square park in the drawing is 64 cm²

The area of a square park in the drawing is 64 cm².

A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.

The area of a square is equal to the squared of sides or the multiplication of two sides.

Given that the scale from a square park to a drawing of the park is 5 m to 1 cm.

The area of the actual park is 1,600 m²

To determine the area of the drawing of the park​

Since 5 meters to 1 centimeter is the scale from a square park to a drawing of the park.

So the drawing scale is 5m : 1cm

Let the area of the drawing of the park​ is A

Since the area of a square is equal to the squared of sides or the multiplication of two sides.

So 1600m²/A = 5²m² / 1² cm²    

Cross multiplication in the terms

⇒ 5² m² A = 1600 m²*cm²    

⇒ A = 1600m²*cm²/ 5² m²

⇒ A = 64 cm²

Hence, the area of a square park in the drawing is 64 cm²

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Answer:

f^(-1)(x) = e^(x/3)

Step-by-step explanation:

1.  Replace 'f(x)' by 'y:'  y = 3ln x

2. Interchange x and y:  x = 3ln y => x/3 = ln y

3. Solve for y:  

   e^(x/3) = y

4.  Replace this 'y' with 'f^(-1)(x)'

    Then f^(-1)(x) = e^(x/3)

The length of each arc intercepted by each slice is 2.09 inches.

The area of each slice 18.85 square inches .

To find the length of each arc intercepted by each slice and the area of each slice of a pizza that is 12 inches in diameter, follow the steps below. Length of each arc intercepted by each slice

The formula to find the length of each arc is given by:

L = θ/360 * 2πr

WhereL = length of arc

θ = angle of arc in degrees

r = radius of circle (diameter/2)

Given, diameter of pizza = 12 inches

So, radius of pizza = 12/2 = 6 inches

Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.

Now, substituting the given values in the formula:

L = 60/360 * 2π* 6L = 1/6 * 12πL = 2π/3 ≈ 2.09 inches

The formula to find the area of each slice is given by:

A = θ/360 * πr²

Given, diameter of pizza = 12 inches

So, radius of pizza = 12/2 = 6 inches

Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.

Now, substituting the given values in the formula:

A = 60/360 * π* 6²A = 1/6 * 36π

A = 6π ≈ 18.85 square inches

Thus, the length of each arc intercepted by each slice is approximately 2.09 inches and the area of each slice is approximately 18.85 square inches.

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The eccentricity of the conic section below is: A. closer to 0 than 1.

In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.

In Mathematics, there are four (4) types of conic section and these include the following with their eccentricity:

In this context, we can reasonably infer and logically deduce that the eccentricity of the conic section is closer to zero (0) than one (1) because it represents a circle.

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Answer:

Option C, The volume of the length cube is 3 times the volume of the smaller cube

Step-by-step explanation:

21.8 / 7.8 = 2.8

the volume of the larger would be 21.8^3 = 10360.23

the volume of the larger would be 7.8^3 = 474.55

Answer:

160 iPads with built in WiFi.

Step-by-step explanation:

10% of 400 = 40, now times by 4.

Answer:

100.571inches

Step-by-step explanation:

Perimeter. =2πr

Perimeter. =2×22÷7×16

Perimeter. =704÷7

Perimeter. =100.571inches

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Answer:

\( {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \\ n = 2ab\)

Answer:

(x+7)(x+9)

Step-by-step explanation:

(x+7)(x+9)

Apply the distributive property by multiplying each term of x+7 by each term of x+9.

x^2+9x+7x+63

Combine 9x and 7x to get 16x.

x^2+16x+63

The volume of the cylindrical fish tank is given by the equation

V = 282.74 inches³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the cylinder be represented as V

Now , the radius of the cylindrical fish tank r = 3 inches

The height of the cylindrical fish tank h = 10 inches

The volume of fish tank = πr²h

Substituting the values in the equation , we get

Volume of Cylindrical fish tank V = π x ( 3 )² x 10

On simplifying the equation , we get

Volume of Cylindrical fish tank V = 90π inches ³

Volume of Cylindrical fish tank V = 282.74 inches³

Therefore , the value of V is 282.74 inches³

Hence , the volume of cylindrical fish tank is 282.74 inches³

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