Find the GCF: 12,24,36​

The new diameter of the sphere after the air is added is 32.6cm

A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the centre.The Surface Area of Sphere is 4πr², where r is the radius of sphere.

The original surface area when air is not added. is :

A = 4×3.14×15²

A = 2826cm²

When air is added, the surface area increased by 500cm². Therefore the new surface area = 2826+500 =3326cm²

To find the new radius of the sphere

3326 = 4×3.14× r²

r² = 3326/12.56

r² = 265

r = √265

r = 16.3

the diameter of the balloon after the air is added = 2r = 2× 16.3 = 32.6 cm

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In triangle ABC and triangle PQR , DC IS PROPORTION TO SR.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices.

Hence, In triangle ABC and triangle PQR , DC IS PROPORTION TO SR.

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ΔABC is the required triangle in which AB = 4 cm, BC = 7 cm and AC = 5 cm.

To see the attachment.

Now, According to the question:

Let us assume that given sides are :

BC = 7 cm, AB = 4 cm and AC = 5 cm

Steps of construction

Step I Draw a line BC = 7 cm.

Step II With center B and radius 4 cm draw an arc.

Step III With center C and radius 5 cm, draw an arc which cuts the previous arc at A.

Step IV Join AB and AC.

Hence, ΔABC is the required triangle in which AB = 4 cm, BC = 7 cm and AC = 5 cm.

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Therefore , the solution to the given problem of expression comes out to be 5 is the exponent of the variable z.

Math allows for the conceivable operations of multiplication, division, addition, and subtraction. The structure of the expression is as follows: Calculator, expression, and a number or variable A mathematical expression is made up of variables, numbers, and operations (such as addition, subtraction, multiplication, or division, etc.). You can contrast two statements or expressions.

Here,

The following expression (27x2)z/3x2)(z6) can be simplified as follows:

If your base is the same, you can subtract the exponents using the properties of powers.

Then:

=(27x^2)z/(-3x^2)(z^6)

=-9z/z^6 You can see that x2-2=x0=1

=-9/z^5 (Thereafter, z6-1=z5)

Consequently, the response is: 5 is the exponent of the variable z.

Therefore , the solution to the given problem of expression comes out to be 5 is the exponent of the variable z.

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The equivalent expression to 3/4 of 2 1/5 is 3/4 × 11/5

Caleb:

Length of rope = 2 1/5 yards

Length used for dog leash = 3/4 of 2 1/5

= 3/4 × 11/5

Manny:

Distance hiked = 6 2/5 miles

Distance he stopped to climb a lookout tower = 1/4 of 6 2/5 miles

Number of miles Manny hiked before he stopped to climb a lookout tower = 1/4 of 6 2/5 miles

= 1/4 × 6 2/5

= 1/4 × 32/5

= 32/20

= 1 12/20

= 1 3/5 miles

Dante and friends:

Length of the poster = 1 1/2 yards

Width of the poster = 3/4 yard

Area of the poster = Length × width

= 1 1/2 yards × 3/4 yard

= 3/2 × 3/4

= 9/8

= 1 1/8 square yards

Therefore, the area of the poster can be calculated by multiplying length by width and written in square units.

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1. The expression to illustrate the fact that Caleb has 2 1/5 yards and then used 3/4 of the rope is B. 3/4 × 11/5.

2. The number of miles that Manny hiked before he stopped is D. 1 3/5 miles.

3. The fraction of the writing area is D. 1 1/8 square yards.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Caleb has 2 1/5 yards and then used 3/4 of the rope. The expression to illustrate this will be:

= 3/4 × 2 1/5

= 3/4 × 11 / 5

The number of miles that Manny hiked before he stopped is;

= 1 /4 × 6 2/5

= 1/4 × 32/5

= 32 / 20

= 8 / 5

= 1 3/5 miles.

The fraction of the writing area is:

= 1 1/2 × 3/4

= 3/2 × 3/4

= 9/8

= 1 1/8 square yards.

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Answer:

1 inch

Step-by-step explanation:

It's 1 inch because you minus 20 inch by 19 inch and get 1 inch

Note that the line is a horizontal line, passing through the point (0, 1) in the y-axis.

All points of this line have 1 as their y-coordinate. That is, this line contains points like (-3, 1), (-1, 1), (5, 1), (17, 1)... etc.

Thus, this is the line where y is always 1, this is the line y=1.

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Each and every point along this line has a y-coordinate of 1. This line has points like (-3, 1), (-1, 1), and (5, 1), for example (17, 1).

The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept.

A sleeping line is a line that is horizontal. From left to right or right to left, it is a straight line. The word "horizon," which refers to the line where it appears that the earth and sky are meeting in the distance, is the ancestor of the word "horizontal." A horizontal line is a straight line that is perpendicular to the x-axis and contains points with identical y-coordinates throughout.

Vertical lines are straight lines that are mapped from top to bottom, whereas horizontal lines are straight lines that are mapped from left to right. In coordinate geometry, the horizontal line is the line parallel to the x-axis, while the vertical line is the line parallel to the y-axis.

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There are three vectors in three-dimensional space, namely the X-axis, the Y-axis, and the Z-axis.

Vector is a term used to describe a mathematical quantity that has both magnitude and direction, such as velocity, force, and acceleration. A vector can be represented by an arrow, with its length representing the magnitude and its direction indicating the direction. Vectors can be added together or scaled to create new vectors. Vector operations are essential in physics, engineering, and other fields of mathematics.

Each of these vectors has a magnitude and direction and can be used to represent any point in 3D space. All three axes intersect at the origin, which is the point (0,0,0). Vector algebra can be used to describe and calculate the relationships between these vectors in 3D space.

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The probability of 0 < z < 2.18 is 0.9945, rounded to four decimal places.

1. To find the probability, we first need to calculate the area under the standard normal distribution curve to the left of z = 1.34 and to the right of z = 2.13.

2. To do this, we can use the graphing calculator to plot the standard normal distribution curve.

3. Then, we can calculate the area under the curve to the left of z = 1.34 by subtracting the area under the curve to the left of z = 2.13 from the total area under the curve.

4. Finally, we can round the answer to four decimal places to get the probability of 0.9945.

The probability of 0 < z < 2.18 is 0.9945, rounded to four decimal places.

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Answer: 5 or -5

Step-by-step explanation:

Since a^2+b^2=c^2 is the Pythagorean theorem, you need to plug in a=3 and b=4 into the equation. 3^2+4^2=c^2. Simplify the left side of the equation first. 3^2 is 9 and 4^2 is 16. 9+16=25. So, 25=c^2. Take the root of this and the square root of 25 is -5 or 5 interchangeably.

Answer:

I think it's (4,4) but I could be wrong

Step-by-step explanation:

Brayden's total earning by walking lap around a track is $35, if he walks 2+1/2 = 5/2 laps per day for 7 days.

Per day walking of brayden = 5/2 laps

7 days walking of brayden = 5/2 × 7 = 35/2 laps

As per the question statement he earns $1 per lap if he walk less than 16 laps and $2 per lap if hi walks 16 or more lap. Since the total walking of brayden is more than 16 laps, so he will earn at the rate of $2 per lap. So total earning will be,

= 2× 35/2

= $35

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The range of a function is the set of all possible outputs (y-values) for a given input (x-value).

Given the function f(x) = [x+3]-5, we can see that the function first adds 3 to x and then subtracts 5. The square bracket notation around (x+3) indicates that the function is taking the greatest integer less than or equal to (x+3).

For any input x, the output of the function will always be the greatest integer less than or equal to (x+3) - 5. Therefore, the output of the function is always an integer less than or equal to -2.

So the range of the function is [-5, -2] U (-2, ∞)

Option A) [-5,∞) is incorrect as the range starts with -5 but the function output is always less than or equal to -2.

Option B) (-5,∞) is incorrect as the function output is always less than or equal to -2.

Option C) [3,∞) is incorrect as the function output is always less than or equal to -2.

Option D) (3,∞) is incorrect as the function output is always less than or equal to -2.

The correct answer is (-2, ∞)

The expression's coefficients have values of 3 and -5, and the constant term has a value of 2.

The formula is 0 = 2 + 3x² - 5x.

We obtain = 3x² - 5x + 2 = 0 by arranging the equation in the form of the general equation ax2 + bx + c = 0.

The leading coefficient is a, the intermediate term's coefficient is b, and the constant term is c.

We may locate the equation's roots or the parabola's vertex by knowing the values of a, b, and c.

After comparing the equation to the general equation, the coefficient and constant term values are as follows.

A = 3

B = -5

C = 2

So, now both the polynomial and the coefficients are available.

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The slope of line y  = 10 is zero.

We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.

It describes the steepness of a line.

The slope of x - axis.

m = 0

As for x-axis the change in y-coordinate is zero.

So, by definition of slope,

m = 0/(change in x coordinate)

m = 0

We know that the slopes of parallel lines are equal.

A line y = 10 is parallel to x-axis

So, the slope of line y = 10 is zero.

i.e., the line y = 10 has zero steepness.

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On solving the provided question we can say that the value of multiplication is x^34.

A math problem is a problem or question that requires the application of mathematical concepts and skills to solve.It is an extension of repeated addition. The operation is symbolized by the multiplication sign "x" or an asterisk (*), a dot (•) or the letter "m" . .

For example, if we multiply 4 and 5, the product will be 20 (4x5 = 20).

In addition, multiplication can also be represented using the distributive property, which states that for any three numbers a, b and c, a(b+c) = ab + ac.

In Multiplication, order of numbers doesn't matter, meaning a x b = b x a.

It's also commutative, meaning the order of numbers doesn't change the result.

Multiplication is the foundation for many other mathematical concepts, including algebra and geometry. It's an essential operation in many fields such as science, engineering, and finance.

And answer for above question is given by,

If each of the 5 students in a class has 3 apples, the total number of apples among the students is 3 apples/student * 5 students = 15 apples.

To find the product of the number of apples and the number of students, we multiply the number of apples (15) by the number of students (5) which is 15*5 = 75

So the product of the number of apples and the number of students is 75.

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Using simultaneous equations, the cost of each pecan cheesecake and chocolate marble cheesecake is as follows:

Simultaneous equations are a system of equations (two or more equations) solved concurrently or simultaneously.

                                  Pecan    Chocolate   Total Revenue

Adam's sales                8                6                   $182

Daniel's sales               7               12                  $274

Let sales units of Pecan = p and sales units of chocolate = c

Equation 1: 8p + 6c = 182

Equation 2: 7P + 12C = 274

Multiply Equation 1 by 2:

Equation 3: 16p + 12c = 364

Subtract Equation 2 from Equation 3:

16p + 12c = 364

-

7P + 12C = 274

9p = 90

p = 10

= $10

Substitute, p = 10, in Equation 1:

8p + 6c = 182

8(10) + 6c = 182

80 + 6c = 182

6c = 102

c = 17

= $17

Check:

8p + 6c = 182

8(10) + 6(17) = 182

80 + 102 = 182

Thus, based on a system of equations, the pecan cheesecake costs $10 per unit while the chocolate marble cheesecake costs $17 per unit.

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Answer:1280

Step-by-step explanation:

75% of something is 960 you can use trial and error to find the amount by just doing 75% of a number a little higher than what you got

The 4:5 ratio in terms of pixels is nothing but the measure of 1080×1350 pixels in an image of the video.

A colon separates two numbers that represent the width-to-height proportion of an image or video. This proportion or ratio is referred to as the aspect ratio. In terms of height and width, it shows how wide the size is. It makes sure the videos or images are presented without stretching or resolution loss.

The resolution in pixels for the aspect ratio 4x5 or 4:5 is 864 x 1080 or 1080 x 1350 pixels. This establishes how many pixels are present in an image's or video's width and height. The most popular pixel ratio is this one.

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Answer: To find the area that 1.6 litres of paint will cover, we can use the unit rate. The unit rate is a way to compare different quantities by finding how much of one quantity corresponds to one unit of another quantity.

We know that 750ml of paint covers an area of 12 m2, this means that the unit rate of paint:area is 750ml:12m^2

We can use this to find the area that 1.6 litres of paint will cover.

First we should convert the 1.6 litres of paint to milliliters, since we have the unit rate in ml:

1.6 litres = 1.6*1000 ml = 1600 ml

Now we can use the unit rate to find the area that 1.6 litres of paint will cover:

Area = (1600 ml paint) * (12 m2/750ml paint) = 21.333 m2

So, 1.6 litres of paint will cover approximately 21.333 m^2

Note that you could also use the proportion (750ml/12m^2) = (1600ml/x) to find the value of x.

Step-by-step explanation:

There are two triangles, triangle abc and triangle def. Side ab is congruent to side de, side ac is congruent to side df. Angle cab is congruent to angle fde. The length of the side bc is (x-4).  The value of x is 23.

The value of x can be calculate as follows:

Given that the triangles are congruent and moreover

Considering that

AB = DE

AC = DF

so,

The third will be compatible as well.

so,

BC = AE

x - 4 = 19

x = 19 + 4

x = 23

Therefore , the value of x is 23. When there are two triangles, triangle abc and triangle def. Side ab is congruent to side de, side ac is congruent to side df. Angle cab is congruent to angle fde. The length of the side bc is (x-4).

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Answer:

Step-by-step explanation:

9)

60/40 =                             divide both side by 10

6/4 =                                  divide both side by 2

3/2

10)

28/63 =                            divide both side by 7

4/9

11)

45/120 =                             divide both side by 15      

3/8          

The 4 (four) quadrants in order are: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV.

A coordinate plane is divided into four sections called quadrants. These quadrants are numbered I, II, III, and IV in a counterclockwise direction, starting with the top right.

Quadrant I is the top right section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are positive.

Quadrant II is the top left section of the coordinate plane, and it contains all the points where the x-coordinate is negative and the y-coordinate is positive.

Quadrant III is the bottom left section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are negative.

Quadrant IV is the bottom right section of the coordinate plane, and it contains all the points where the x-coordinate is positive and the y-coordinate is negative.

Understanding this concept is important for solving mathematical problems, especially in algebra and geometry.

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Answer:

Use direct variation method of mathematics

Answer:

4 (8+r)

Step-by-step explanation:

So, the probability that the two biscuits are not the same type is 0.15 or 15%.

To find the probability that the two biscuits are not the same type, we need to calculate the probability that Sue takes one biscuit of each type.

First, we will calculate the probability that Sue takes one plain biscuit, one chocolate biscuit, and one currant biscuit.

The probability of Sue taking one plain biscuit is 12/20, since there are 12 plain biscuits out of a total of 20.

The probability of Sue taking one chocolate biscuit after taking a plain biscuit is 5/19, since there are now 5 chocolate biscuits out of 19 remaining.

The probability of Sue taking one currant biscuit after taking a plain and chocolate biscuit is 3/18, since there are now 3 currant biscuits out of 18 remaining.

To find the overall probability that Sue takes one biscuit of each type, we multiply the individual probabilities together:

P = (12/20) * (5/19) * (3/18) = 0.15

So, the probability that the two biscuits are not the same type is 0.15 or 15%.

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The reflection in the line y = x, followed by a reflection in the x-axis transformation that maps the preimage to the image.

What is the transformation?

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection, or translation. A function, f, that maps to itself are called the transformation, i.e., f: X → X. The pre-image X becomes the image X after the transformation. This transformation can be any or combination of operations like translation, rotation, reflection, and dilation.

In geometry, transformation involves changing the position and/or size of a shape.

The transformation that maps the pre-image to the image is dilation

From the given diagram

We can see that the size of and are not the same.

When the No change in size or shape or orientation and Flips the pre-image and produces the mirror-image, then the transformation type is Reflection.

Hence, the reflection in the line y = x, followed by a reflection in the x-axis transformation that maps the preimage to the image.

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When a number has an exponent of 0, it means that the number is being multiplied by itself 0 times. In other words, it is multiplied by 1.

To determine this:

In the case of 3 with an exponent of 0, it would be represented as 3^0. To calculate the value, we would take 3 and multiply it by 0 times.

3 x 1 = 3

So, 3 with an exponent of 0 is equal to 3.

It is important to note that any number with an exponent of 0 will always equal 1, except for 0 which will always be 0. This is because any number multiplied by 1 is itself, and 0 multiplied by any number is always 0.

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The area of a rectangle is found by multiplying the length and width.The area of a triangle is found by taking half the base multiplied by the height.  

The formula for this is A = lw, where A is the area, l is the length, and w is the width. For example, if the length of the rectangle is 10 cm and the width is 5 cm, then the area of the rectangle is A = 10 * 5 = 50 cm2.

The area of a triangle is found by taking half the base multiplied by the height. The formula for this is A = 1/2bh, where A is the area, b is the base, and h is the height. For example, if the base of the triangle is 10 cm and the height is 5 cm, then the area of the triangle is A = 1/2 * 10 * 5 = 25 cm2.

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