Solve on your own by canceling zeros: 250 divided by 50

With the concept of proportion and time unit conversion from minutes to seconds, The answer is 1980 feet is travelled in one minute.

Proportion refers to the relationship between two or more quantities or values, often represented as a ratio or fraction. It can also refer to the relative size or scale of something in relation to something else. In mathematics, a proportion is an equation that states that two ratios are equal. For example, "the ratio of apples to oranges is 2:3" can be written as the proportion "2/3 = x/y," where x and y represent the number of apples and oranges. In statistics, a proportion is a measure of the frequency with which an event occurs, often expressed as a decimal or percentage.

Speed is a scalar quantity that measures how fast an object is moving. It is often represented by the symbol "v" and is typically measured in units of distance per time, such as meters per second (m/s) or miles per hour (mph). Speed is defined as the magnitude of an object's velocity, which is a vector quantity that also includes information about the direction of motion. For example, an object that is moving at a constant speed of 50 miles per hour to the north has a velocity of 50 mph to the north. Speed can also be calculated by dividing the distance traveled by the time it took to travel that distance, such as speed = distance / time.

car travels 66feet in 2 seconds.

car travels 66/2 feet in 1 seconds.

1 minute = 60 seconds

in 1 minute, car travels 33*60 = 1980 feet.

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The standard form for two-variable linear equations is Ax + By = C. For example, 2x + 3y = 5 is a standard linear equation.

A linear equation is one in which the highest power of the variable is always 1. It is also known as a one-degree equation.

A linear equation with one variable has the standard form Ax + B = 0. Here, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables takes the standard form Ax + By = C.

A linear equation is one with the highest degree of 1. This means that no variable in a linear equation has an exponent greater than 1. The graph of a linear equation is always a straight line.

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The correct graph that represents the given compound inequality -2x + 5 < 7 and 5x - 4 ≤ 6 is: graph D.

In Mathematics, it is very important for students to note that they do not flip the inequality symbol (sign) when you are solving an inequality by multiplication or division with a positive numerical value (number).

Next, we would simplify each of the compound inequality as follows;

-2x + 5 < 7

Subtracting 5 from both sides of the inequality, we have the following:

-2x + 5 - 5 < 7 - 5

-2x < 2

Dividing both sides of the inequality by -2, we have the following:

-2x/-2 < -2/2

x < -1

Next, we would flip the inequality symbol (sign) because it was divided by a negative numerical value (number);

x > -1

Simplifying 5x - 4 ≤ 6, we have;

5x - 4 + 4 ≤ 6 + 4

5x ≤ 10

x ≤ 10/5

x ≤ 2

Therefore, the compound inequality {x > -1 and x < 2} can be re-written as follows;

-1 < x ≤ 2

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Answer:

40

Step-by-step explanation:

Let x=how old Myra is.

3x + 10 = x

x + 3x + 10 = 40

4x + 10 = 40

4x = 40 - 10

4x = 30

x = 30/4

x = 7.5

3x + 10= 32.5

x + 3x + 10= 40

7.5 + 32.5 = 40

40 = 40

Answer: 40

Step-by-step explanation:

The right order of the statements and reasons thaty prove that ΔABC is congruent to ΔDEC is presented as follows;

Two triangles are congruent, if the three sides in both triangles are congruent, or if two angles and an included side in one triangle are congruent to two angles and an included side in the second triangle.

The details of thereasons used to prove the congruency of the trisngles are as follows;

Alternate interior angles theorem

The alternate interor angles theorem states that the alternate interior angles formed by two parallel lines and a common transversal are congruent.

Altternate interior angles are the angles formed by the transversal and two parallel lines, on the inside area in between the parallel lines, and on opposite sides of the transversal

ASA ≅

The ASA ≅ (acronym for Angle-Side-Angle congruency), postulate states that, if two angles in one triangle ABC are congruent to two angles in another triangle CDE, and the included side, between the angles, are congruent in both triangles, then triangle ABC is congruent to triangle CDE

ΔABC ≅ ΔCDE

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Answer:Therefore the surface area of the solid formed is about 598.33 in²

Step-by-step explanation:If the height of a right triangular prism is 1 5/6 inches. The surface area of the solid formed is: 598.33 in².

Surface area

First step

Right triangular prism=1 5/6 inches= 11/6 inches

Height of the base=8 2/3 inches = 26/3 inches

Second step

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

You begin with 400 bacteria, approximately 21839 of the bacteria can you expect after 100 hours.

If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.

The given equation is [tex]A=P_0(2.71828)^{0.04t}[/tex].

Begin with 400 bacteria, approximately how many of the bacteria can you expect after 100 hours.

Here, [tex]P_0=400[/tex] and t=100

Now, [tex]A=400\times(2.71828)^{0.04\times100}[/tex]

A=400×2.71828⁴

A=400×54.598

A=21839

Therefore, the option D is the correct answer.

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The compound interest rate is 3.9%.

We know that when we talk about the compound interest, we mean the kind of interest that is going to accrue both on the principal and on the interest.

In this case we know that;

A = P(1 + r)^n

A = amount

P = principal

r = rate

n = number of years

710.89  = 658.20(1 + r)^2

710.89/658.20 = (1 + r)^2

1.08 = (1 + r)^2

ln(1.08) =ln (1 + r)^2

0.077 = 2ln(1 + r)

0.077/2 = ln(1 + r)

ln(1 + r) = 0.0385

1 + r = 1.039

r = 1.039 - 1

r = 0.039

r = 3.9%

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The solutions for the given Cubic equation y = x³ - x² - 41 x + 105 are x = -7 and x = 5.

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. Polynomials are referred to as cubic polynomials if they have a degree of three.

Given, a polynomial y = x³ - x² - 41x + 105

The difference between the remainder theorem and the factor theorem:

The remaining factor theorem really consists of two theorems that link a polynomial's roots to its linear factors. The theorem is frequently applied to avoid using long division while factoring polynomials. This gives us a strong tool to factor polynomials, especially when coupled with the rational root theorem.

Use the factor theorem to find the roots of a cubic equation.

possible roots are factors of the constant theorem.

Once you get one root then you can use synthetic division to get the other roots.

For instance,

x³ - x² - 41x + 105 = 0,

use synthetic division

3    1     -1     -41    105    

           1     2     -35

    1         2      -35       0   (1, 2, -35 are co-efficient of the quadratic equation)

So now we have

x³ - x² - 41x + 105 = (x-3 )( x² + 2x - 35)

(x-3 )( x² + 2x - 35)

(x-3)(x(x+7)-5(x+7))

(x- 3)(x +7) (x - 5)

Solution means that at values 3, -7, and 5 of x, y will be zero.

Therefore, all X intercepts of the given Polynomial function are 3, -7, and 5.

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The new lengths triangle that is formed after the given dilation is; Height = 4 and base = 2

Dilation is defined as a transformation that is used to resize an object. This means that dilation is used to make the objects larger or smaller. When the objects get larger, it is called an enlargement but when the object becomes smaller, it is called a reduction.

Now, we want to dilate the given triangle by the scale factor 2/3. Since the factor of dilation is less than 1, then we can call it a reduction of shape.

Thus, we multiply each side of the given triangle by 2/3 to get;

Height = 6 * 2/3 = 4

Base = 2/3 * 3 = 2

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The value of the inequalities will be:

a. x > 6

b. x ≤ 24

c. x ≥ 6

d. x < 6

e. x ≥ 24

It should be noted that inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

x + 28 > 34

Collect the like terms

x > 34 - 28

x > 6

x/2 ≤ 12

Cross multiply

x ≤ 12 × 2

x ≤ 24.

7x ≥ 42

Divide

x ≥ 42/7

x ≥ 6

x - 2 < 4

x < 4 + 2

x < 6.

3x ≥ 72

Divide

x ≥ 72/3

x ≥ 24

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The area of a rectangle ABCD is 60 square inches and the area of triangle ACD is 30 square inches.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

In the given rectangle ABCD, AD= 5 in. and DC=12 in.

a) Now, area of rectangle ABCD =DC×AD

= 12×5

= 60 square inches

b) By joining vertices A and C, we get triangle ACD.

c) Now, the area of triangle ADC is

Area =1/2 ×Base×Height

= 1/2 ×12×5

= 30 square inches

Therefore, the area of a rectangle ABCD is 60 square inches.

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The person who pays more after each additional day d after day 0 is Patricia.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Emily:

P = 2d - 1

After 3 days, the price for renting the book.

P = 2 x 3 - 1 = 6 - 1 = $5

Patricia:

After 3 days, the price for renting the book.

= $20

Thus,

Patricia pays more for each additional day.

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The solution to the inequality equations are

a) 15 pt < 2 gal , True

b)  1 gal < 5 qt , True

c) 12 fl oz > 2 c , False

d) 2 qt 1 cup > 2 c , False

e) 20 pints = 10 quarts , True

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

a)

The inequality equation is 15 pt < 2 gal

Now , 15 pints = 1.875 gallons

So , 15 pt < 2 gal is True

b)

The inequality equation is 1 gal < 5 qt

Now , 1 gallon = 4 quarts

So , 1 gal < 5 qt is True

c)

The inequality equation is 12 fl oz > 2 c

Now , 2 c = 16 fl oz

So , 12 fl oz > 2 c is False

d)

The inequality equation is 2 qt 1 cup > 2 c

Now , 2 c = 16 fl oz

So ,  2 qt 1 cup > 2 c is False

e)

The inequality equation is 20 pints = 10 quarts

Now , 10 pints = 5 quarts

So ,  20 pints = 10 quarts is True

Hence , the inequality equations are solved

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volume of cone is  =1/3 x³.

The formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the cone.

here, given that,

The base diameter and the height of a cone are both equal to x units.

Volume =  ⅓ r²h

              =1/3 x²x

              =1/3 x³

Hence, volume of cone is  =1/3 x³.

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There are 23% more 41+ year olds have a preference for Enterprise Content Management in comparison to 18-25 year olds

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We are given that the table shows the Technology career types for different ages groups.

The 41+ year olds have a preference for Enterprise Content Management = 3215

The percent become

3215 / (3215 + 4673 + 5822) x 100

3215 / (3215 + 4673 + 5822) x 100

3215 / 13710 x 100

23.45

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Answer:

8 [tex]\frac{2}{3}[/tex] cups of dough

Step-by-step explanation:

2/3 cup for every dumpling

13 dumplings

x = dough

x = 2/3 * 13

x = 26/3

x = 8 [tex]\frac{2}{3}[/tex] = 8.667

The volume of the pyramid, in cubic meters, given the length of each side and the height, is 2, 592, 100 meters ³

The Volume of a pyramid can be found by the formula :

= ( Base length x Base width x Height ) / 3

Base length = 230 meters

Base width = 230 meters as this is a square base

Height = 147 meters

The volume is therefore:

= ( 230 x 230 x 147 ) / 3

= 2, 592, 100 meters ³

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Answer:

the nearest thousandth is 241.006.

The correct solution set for the given graph include the following: C. {point in Quadrant II}.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, or cross each other, which is typically represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

By critically observing the graph of lines a and b, we can reasonably infer and logically deduce the correct solution set lies in Quadrant II because both lines would eventually intersect as they increase.

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Answer:

P(not brown)

Step-by-step explanation:

Blue, Red, and Green are all the same!

It couldn't be red or yellow, because yellow has only 1

There is no brown, so most likely you won't get brown

Answer:

x=7

Step-by-step explanation:

hope this helps :)

Answer:

  x ≈ 8.9

Step-by-step explanation:

You want the value of x in the diagram showing two right triangles.

The Pythagorean theorem tells you the relationship between legs 'a' and 'b' and hypotenuse 'c' in a right triangle is ...

  a² +b² = c²

For the smaller triangle, this tells you the square of the length of its hypotenuse is ...

  c² = 2² +4² = 4 +16 = 20

That square can be used directly in the equation for the larger triangle:

  20 +x² = 10²

 x² = 100 -20 = 80

 x = √80 ≈ 8.9

The value of x is about 8.9 units.

The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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The probability that the selected pupil studied both Russian and Spanish is 0.24%.

For the stated question-

Thus,

P(E) = P(R) + P(S) - P(R∩S) + P(R'∩S')

0.80  = 0.50 + 0.31 - P(R∩S) + 0.23

P(R∩S) = 0.24

Thus, the probability that the selected pupil studied both Russian and Spanish is 0.24%.

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Answer: (0,0) (4, -3) (8, -6)

Step-by-step explanation:

It is correct.

The value of the equation g ( x ) = -x + 4 , when g ( x ) = 0 , is x = 4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

g ( x ) = -x + 4   be equation (1)

On simplifying the equation , we get

when g ( x ) = 0

Substitute the values in the equation , we get

0 = -x + 4

Adding x on both sides of the equation , we get

x = 4

Therefore , the value of x = 4

Hence , the value of the equation is x = 4

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Answer:

To compare the length of the plankton to the length of the jellyfish, we can express the length of the plankton as a percentage of the length of the jellyfish.

First, we need to convert the length of the jellyfish from inches to centimeters so that we can compare the two measurements in the same unit.

12 inches = 12*2.54 = 30.48 cm

Next, we divide the length of the plankton by the length of the jellyfish and multiply by 100 to get the percentage.

0.08 inches / 30.48 cm * 100 = 0.00262 * 100 = 0.262%

So, the length of the plankton is 0.262% of the length of the jellyfish.

The required least number is n - p and the highest number is p - n.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

here,
The given numbers that are to be plotted on the number line are,
n - p, n + p, p -n

Since on the number line n comes former and p comes later it tends that p > n.

So the least number would be n - p because it will be negative,
And the height number would be p - n because
n is negative and in the operation, it becomes more than n + p.

Thus, the required least number is n - p and the highest number is p - n.

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