How many inches long is the radius of the largest circle that can fit inside a rectangle 18 inches long and 12 inches wide

Allison's gray paint will be lighter.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol %.

percentage, a relative value indicating the hundredth parts of any quantity.

Here, number of white paint cups/ total number of cups is used to find the percentage

Allison:

Percent of white paint:

(2/3)*100= 66.67%

Alexander:

Percent of white paint:

(11/17)*100= 64.7%

Allison's Percent of white paint is more.

So, Allison's gray paint will be lighter.

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After 99 days, Karen is required to pay $14,436.63 in full, plus $139.63 in interest.

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Given, Karen obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 3.6%. Her loan is for $14,300 for 99 days.

From the formula of simple interest(SI) :

SI = P * R *  T / 100

Where p = principal amount

r = rate of interest

T = time

In our case

p = 14300

r = 3.6

time = 99/365

Simple interest = (14300* 3.6 * 99) / 36500

Simple interest = (143 * 3.6 * 99) / 365

Simple interest = 139.63

The total amount she has to pay = principal amount + SI

The total amount she has to pay = 14300 + 136.63

The total amount she has to pay = 14,436.63

therefore, Karen has to pay $139.63 interest and $14,436.63 Total amount after 99 days.

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Therefore , the solution of the given problem of coordinates comes out to be  the coordinate P = (7, 0.4).

A coordinate system is a technique used in geometry to precisely locate points or other topological objects on a continuum, such as Euclidean space, using one or more numbers or coordinates. A point or item on an a double plane is located using a pair of integers known as coordinates. The x and y positions are two integers that describe a point's location on a 2D plane.

Here,

David want to find the coordinate are a useful tool for segmenting lines into smaller units.

P's coordinate is P = (7, -0.4)

The criteria are as follows:

A = (8,0)

=> B = (3,-2) (3,-2)

m: n=1:4

Using P = mx2+nx1 my2+ny

m+n

m+n, line ratio is computed.

The result is:

P 1x3+4x8 /1x-2+4x0 = 1+4 / 7

=> P = 35, 2

=>P = (7, -0.4) (7, -0.4)

1+4

P therefore has the coordinate P = (7, 0.4).

Therefore , the solution of the given problem of coordinates comes out to be  the coordinate P = (7, 0.4).

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The volume of the combined solid formed using a cone and a hemisphere 1488.67 cm³.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

is The total height of the solid = 49 cm

The slant height of the cone l = 35 cm

The radius of the base r = 7 cm

The radius of hemisphere = height of the hemisphere = 7 cm

Then height (h) of the cone = 49 - 7 = 42 cm

Now, find the volume of the cone.

Use the formula - πrl

= (22/7) × 7 × 35

= 770 cm³

Now, find the volume of the hemisphere.

Use the formula - (2/3)πr³

= (2/3) × (22/7) × (7)³

= (2/3) × 22 × 49

= 718.67 cm³

Then to find the volume of the solid use the formula -

volume of solid= volume of cone + volume of hemisphere

volume of solid = 770 + 718.67

volume of solid = 1488.67 cm³

Therefore, the volume of the solid is obtained as 1488.67 cm³.

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Answer:

C. y=3x

Step-by-step explanation:

we have the slope intercept formula y=mx+b

where m is the slope and b is the y intercept.

in this graph the y intercept is zero

to calculate the slope we look at the rise divided by the run.

to get from the bottom point to the top point, you go up 6 and to the right 2

so the slope is 6/2 which is 3

now we have the equation y=3x+0

the zero goes away and we have

y=3x

The filling of the table to get equivalent ratios is;

3/4 : 1/3

27/8 : 2/3

3: 4/3

1: 4/9

Equivalent ratios are defined as the ratios that are the same whenever they are compared. We can say that two or more ratios can be compared with each other to find out whether they are equivalent or not. For example, 5:10 and 20:40 are equivalent ratios.

From the given table, let us complete the equivalent ratios;

1) 3/4: 1/3

This can be expressed as;

(3/4)/(1/3) = 9/4

2) Let the unknown fraction be x and as such;

x: 2/3 = 9/4

Multiply both sides by 3/2 to get;

27/8

3) Let the unknown number be x and as such, we have;

3:x = 9/4

Cross multiply to get;

(4 * 3)/9 = 4/3

4)  Let the unknown fraction be x and as such;

1 : x = 9/4

Cross multiply to get;

(4 * 1)/9 = 4/9

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The measure of angle D is 80°, angle E is 60° and angle F is 40°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

From the given triangle DEF, the two exterior angles are 140° and 120°.

Here, 140°+m∠F=180°

m∠F=40°

120°+m∠E=180°

m∠E=180°-120°

m∠E=60°

By angle sum property of a triangle, we have

m∠D+m∠E+m∠F=180°

m∠D+60°+40°=180°

m∠D=80°

Therefore, the measure of angle D is 80°, angle E is 60° and angle F is 40°.

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Answer:

2/9 + 3/9 + 4/9 = 1

Step-by-step explanation:

A number divided by itself (except 0) is equal to 1.

For example, 8/8 = 1; 21/21 = 1; 5/5 = 1.

We need to add three fractions that have the same denominator and different numerators, so that the numerators add up to the denominator.

2/9 + 3/9 + 4/9 = 9/9 = 1

Answer: 2/9 + 3/9 + 4/9 = 1

The person who is right, given the diagram and the definition of supplementary angles, is Shawn.

If two angles sum up to 180 degrees, they are referred to as supplementary angles. When combined, supplementary angles make a straight angle (180 degrees).

However, it should be emphasized that the supplementary angles do not necessarily need to be close to one another. As a result, any two angles can be supplementary if their sum is 180 degrees.

The angles given of A and B are supplementary because their positioning is such that when they are summed, they will add up to 180 degrees. Shawn was therefore correct.

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A graph which shows the relationship given in the table is: B. graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 56 through the point 1 comma 54.

In this scenario, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot while the total amount of sunglasses would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot (see attachment) which models the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 56

In conclusion, we can reasonably infer and logically deduce that the y-intercept is equal to (0, 56).

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In the word problem the statement "The sum of a negative and a positive number is a negative number" is False.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here The sum of a negative and a positive number is a negative number.

=> Because we find the difference between the numbers and assign the sign of bigger number to result.

If bigger number is negative then result will be negative.

Example., 5-1=4, which is not negative.

Hence the statement The sum of a negative and a positive number is a negative number is False.

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b= -7

Step 1: Plug in the given data using the format of y=mx+b

m (slope)=2, x=7, y=7

7=2(7)+b

Step 2: Solve for b

7=2(7)+b

7=14+b

-7=b

Answer:

d=2pir

Step-by-step explanation:

d=2pir

Answer:

To find the original price of the bicycle, we need to undo the two discounts that were applied to it.

We know that the final price of the bicycle is $315, and that it was first discounted by 50%. To undo this discount, we need to divide the final price by the percentage of the discount (in decimal form). So:

$315 / 0.50 = $630

This is the price of the bicycle after the first discount. Next, we know that there was an additional 10% discount applied. To undo this discount, we need to divide the price after the first discount by the percentage of the additional discount (in decimal form). So:

$630 / 0.90 = $700

So the original price of the bicycle was $700.

The sale price for a bicycle is $315. The original price was first discounted by 50% and then discounted an additional 10%. The correct answer is $700.

A bicycle, also called a pedal cycle, bike or cycle, is a human-powered or motor-powered assisted, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A bicycle rider is called a cyclist, or bicyclist. Bicycles were introduced in the 19th century in Europe.

Assuming that's 10% off the discounted price, x × (1 − 50 100) ×(1 − 10 100) = $315 x = $ 315 (.5)(.9) = $700

Therefore, the sale price for a bicycle is $315. The original price was first discounted by 50% and then discounted an additional 10%. The correct answer is $700.

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We should order 70 hats and 140 pairs of sunglasses to lose the least amount of money in the sales promotion.

What is linear optimization?

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

This is a linear optimization problem that can be solved using the graphic method.

To begin, we can set up the problem as follows:

Let x be the number of hats and y be the number of pairs of sunglasses.

The constraints are:

y = 2x (because for every 2 hats sold, 1 pair of sunglasses is sold)

y <= 100 (because the supplier can only provide 100 pairs of sunglasses)

x + y >= 210 (because you want to sell at least 210 items in total)

x, y >= 0 (because the number of items sold cannot be negative)

The objective function is: -3x - 2y (because you lose $3 on every hat sold and $2 on every pair of sunglasses sold)

To graph the constraints, we can start by plotting the inequality y <= 100. This creates a line that goes from the origin (0,0) to (50,100) and is shaded in below the line. Next, we can plot the inequality x+y >= 210 which creates a line that goes from (0, 210) to (210, 0) and is shaded in above the line.

Finally, we can plot the equation y = 2x, which represents the relationship between the number of hats and sunglasses sold.

The feasible solution for this problem is the point where the lines intersect and that lies within the feasible region. In this case, the point where the three lines intersect is (70, 140) which is the optimal solution.

Therefore, you should order 70 hats and 140 pairs of sunglasses to lose the least amount of money in the sales promotion.

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Answer:

let Length = x

then width = x -2  (2 inches less than length

now

A = Lw

35 = x (x -2)

35 = x2 - 2x

x2 -2x -35 = 0

(x-7)(x+5) = 0  

x-7=0

x=7      

so length = 7

width = 7 -2 = 5

Hope this helps

Step-by-step explanation:

The final statement is: The value of F(8)=21

The Fibonacci sequence is a set of integers (the Fibonacci numbers) that starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers. The sequence follows the rule that each number is equal to the sum of the preceding two numbers.

Given here: The fibonacci function is given by

F(n)=F(n-1)+F(n-2) and F(6)=8 and F(7)=13

Now option  is given by F(8)= F(7)+F(6)

                                                = 13+8

                                                =21

Hence, The F(8)=21 is the correct answer.

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The factors of the polynomial are (-3x+4)(x-2)

A factor is a number that divides another number, leaving no remainder.

Given is a polynomial, -3x²+10x-8,

On factorization, we get,

= -3x²+10x-8

= -3x²+6x+4x-8

= -3x(x-2)+4(x-2)

= (-3x+4)(x-2)

Hence, the factors of the polynomial are (-3x+4)(x-2)

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Given expression in LHS is less than the expression in RHS. So, the given inequality is false.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants .

Algebraic expressions are the idea of expressing numbers the use of letters or alphabets with out specifying their real values. The fundamentals of algebra taught us the way to express an unknown cost the usage of letters which include x, y, z, and many others. these letters are referred to as here as variables. An algebraic expression may be a mixture of each variables and constants. Any cost that is positioned before and accelerated by a variable is a coefficient.

Given expression ,

The product of 4/5 and 3 is greater than 3

so, it can be written as ,

4/5  * 3  >  3

LHS = 4/5 * 3

LHS = 12/5

LHS  = 2. 4

Where RHS = 3

So, the inequality is false.

Hence, Given expression in LHS is less than the expression in RHS. So, the given inequality is false.

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On solving the provided question, we can say that in the quadrilateral  z = 180 - 111 = 69 and y = 360 - (97 + 83 + 69) = 360 - 249 = 111

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here,

in the quadrilateral

z = 180 - 111 = 69

and y = 360 - (97 + 83 + 69) = 360 - 249 = 111

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On solving the provided question, we can say that  the linear equation z , no. of wheels = 14x +12y => z = 42 + 48 => z = 90

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, the equation

x = 14, tri cycle

y = 12 cars

z , no. of wheels = 14x +12y

z = 42 + 48

z = 90

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The value of x in the given triangle is 76.2°. The solution is obtained using trigonometry formulas.

The study of the right-angle triangle's sides, angles, and connection is the main focus of the field of mathematics known as "trigonometry." Therefore, it is helpful to use trigonometric formulas, functions, or trigonometric identities to find the unknown or missing angles or sides of a right triangle. The angles in trigonometry can either be expressed in degrees or radians. The most used trigonometric angles for computations include 0, 30, 45, 60, and 90 degrees.

In the triangle, we are given hypotenuse equal to 21 and perpendicular equal to 5.

We know that cosine(theta)= adjacent side/hypotenuse

So, cosine(theta) = 5/21

Here, theta=x

So, cosine(x) = 5/21

x= Cos inverse(5/21)

x= 76.2°

Hence, the value of x in the given triangle is 76.2°.

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Answer:

m<15 = 88°

Step-by-step explanation:

Because m and n are parallel lines, that makes m<2 and m<10 corresponding angles, meaning they're equal.

So, since we're told m<2=92°, we can then say that similarly, m<10=92°.

m<10 and m<15 form a straight line, which adds to 180°. Writing this as a mathematical expression, we get:

m<10+m<15=180°

92°+m<15=180°

m<15=180°-92°=88°

A) The solution to the system of simultaneous equations is; (1, 3)

B) The number of hours from start that both will be at the same location is; 1 hour.

The solution to a graph of two simultaneous equations will be the point at which both lines intersect each other.

Now, we see from the graph that the coordinate of the point of intersection of both lines is; (1, 3)

Now, we see that the x-axis represents hours since start while y-axis represents miles from start. Thus;

The number of hours from start that both will have be at the same location which is when their y-values will be the same is 1 hour.

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Answer: 1 hour

Step-by-step explanation:

Elijah's total earnings in a week, given the amount of sales x, is $500 + $0.30x.

Sales refers to the amount of goods or services sold by a business in a given period of time. It is often used to measure a company's revenue or performance, and is calculated by multiplying the number of units sold by the price per unit. Sales can be used to track changes in demand for a product or service over time, or to compare the sales of different products or businesses.

Elijah's earnings for a week in which he made $775 in sales would be calculated as follows:

Base salary: $500

Commission: 30% of $775 = $775 * 0.30 = $232.50

Total earnings: $500 + $232.50 = $732.50

Elijah's earnings for a week in which he made $x in sales would be calculated as follows:

Base salary: $500

Commission: 30% of $x = $x * 0.30 = $0.30x

Total earnings: $500 + $0.30x = $500 + $0.30x

So the formula for Elijah's total earnings in a week, given the amount of sales x, is:

$500 + $0.30x.

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Answer: Choosing a smaller unit of measure is more meaningful because it allows for more precise measurements. When using a smaller unit of measure, such as millimeters instead of centimeters, or seconds instead of minutes, you are able to capture more detailed information about the measurement. For example, measuring something in centimeters may give you a rough idea of the size, but measuring it in millimeters will give you more detailed information, which can be especially important in scientific or technical fields. Additionally, choosing a smaller unit of measure can be more meaningful when making comparisons or performing calculations, as it allows for greater accuracy.

Step-by-step explanation:

Hopes this helps you for Tomorrow!!

The statement "the product of a number and 27" can be modelled as 27A.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is a statement as -

"the product of a number and 27"

Let the number be {A}. We can write -

A × 27

27A

Therefore, the statement "the product of a number and 27" can be modelled as 27A.

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In two peoples, the smaller income is, $13,000

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Together two people earn $28000.

And, One earns $2000 more than other.

Let the smaller income = x

So, The larger income = x + 2000

Thus, We can formulate;

⇒ x + (x + 2000) = $28,000

⇒ 2x + $2,000 = $28,000

⇒ 2x = 28,000 - 2,000

⇒ 2x = 26,000

⇒ x = 26,000/2

⇒ x = 13,000

Thus, The smaller income = $13,000

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Answer:

$4,620

Step-by-step explanation:

Since he made $28 for one hour, (28)(1) =28, you would multiply 28 and 165 to find out how much he made in 165 hours

(28)(165) = $4,620

The Surface region of the cylinder that has a 3 cm radius is 8.4π cm²

The area or region that an object’s surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has. There are numerous shapes and dimensions in geometry, including spheres, cubes, cuboids, cones, cylinders, etc. Each form has its own volume and surface area.

Given, The surface area of a right cylinder with a diameter of 8 cm is 60π cm².

From the general formula for the Surface area of the cylinder

Area = 2πrh + 2πr²

or

Area = 2πr²(h/r + 1)

Where

r = radius of the base

h = height of the Cylinder

in our case

r = 8/2 = 4 cm

Thus,

60π = 2πrh + 2πr²

60π = 2πr²(h/r + 1)

(h/r + 1 ) = 60π/ 2π4²

(h/r + 1) = 15/8

Also given there is another similar Cylinder that has a radius of 1.5 cm or a diameter of 3 cm.

Since it's similar to the First cylinder thus "h/r" would be the same for both of them.

Thus,

The surface area of the second cylinder = 2πr²(h/r + 1)

The surface area of the second cylinder = 2π *  1.5² * 15/8

The surface area of the second cylinder = 8.4π

Therefore, the Surface area of the cylinder that has a 3 cm radius is 8.4π cm².

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