Three friends are sharing 4 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?

Answer:

To find out how long it will take for the police car to catch up to the speeding car, you can use the following formula:

t = d / v

Where t is the time it takes to catch up, d is the distance between the police car and the speeding car, and v is the relative speed of the police car compared to the speeding car.

In this case, the distance between the police car and the speeding car is given by the Pythagorean theorem:

d = sqrt((650 ft)^2 + (60 ft/s * 5 s)^2) = 674.22 ft

The relative speed of the police car compared to the speeding car is given by:

v = 80 ft/s - 60 ft/s = 20 ft/s

Plugging these values into the formula, we get:

t = d / v = 674.22 ft / 20 ft/s = 33.71 s

So it will take the police car approximately 33.71 seconds to catch up to the speeding car.

Note: This is just an approximation and the actual time required may vary depending on the exact positions and speeds of the two cars

Answer: it will take the police car 25 seconds and 2000 feet to catch up with the speeding car.

Step-by-step explanation: To determine the distance and time that the police car needs to catch up with the speeding car, we can set up the following system of equations:

Let x be the time it takes for the police car to catch up with the speeding car

Let y be the distance the police car needs to travel to catch up with the speeding car

The distance the speeding car travels in x seconds is given by the equation:

60x = distance

The distance the police car travels in x seconds is given by the equation:

80x = y

The distance between the two cars at the start is given by the equation:

(y - 650)^2 + 650^2 = x^2

We can solve this system of equations by substituting the second equation into the third equation, resulting in:

(80x - 650)^2 + 650^2 = x^2

Expanding and rearranging the terms, we get:

6400x^2 - 19600x + 422500 = x^2

Solving for x, we get:

x = 25 seconds

Substituting this value back into the equation for the distance the police car travels, we get:

y = 80 * 25 = 2000 ft

Answer:

7

Step-by-step explanation:

index of root = 2

exponent = 2

divide both by 2

2:2 = 1 (the root expires)

2:2 = 1 (the exponent expires)

7

The parent function of a parabola is y = x².

A function is said to be a parent function if it is expressed in the simplest form and satisfies the definition of a particular type of function.

The simplest function that satisfies the definition of a parabola is given by y = x². It is also called quadratic function.

Its graph passes through the origin (0,0) and lies in first and second quadrant.

One or more parabolas can be easily obtained by transforming the parent function of the parabola.

Therefore, the parent function of parabola is given by y = x².

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All the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12 are 3/4 and -4/5.

We have the given polynomial:

f(x) = 20x4 + x3 + 8x2 + x - 12

All potential polynomial roots are represented by rational numbers, according to the Rational Root Theorem:

x = a/b

Where a is a factor of a constant term

b is the factor of coefficient of leading term

From the given polynomial:

-12 is the constant term and 20 is the coefficient of leading term

The possible factors of -12 are ±1, ±2, ±3, ±4, ±6, ±12

The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20

So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)

Solve for x when the given function is equal to zero

20x4 + x3 + 8x2 + x - 12 = 0

(4x - 3)(5x + 4)(x2 + 1) = 0

So we get:

4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0

x = 3/4, x = -4/5, x =1, x = -1

Hence, the rational roots are x = 3/4, x = -4/5.

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We have the given polynomial:

f(x) = 20x4 + x3 + 8x2 + x - 12

x = a/b

b is the factor of coefficient of leading term

-12 is the constant term and 20 is the coefficient of leading term

The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20

So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)

Solve for x when the given function is equal to zero

20x4 + x3 + 8x2 + x - 12 = 0

(4x - 3)(5x + 4)(x2 + 1) = 0

4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0

x = 3/4, x = -4/5, x =1, x = -1

Side-Side-Side (SSS) Theorem; Two triangles are congruent if three sides of one are equal respectively to three sides of the other (SSS=SSS).

Side-Side-Side or SSS is a kind of triangle congruence rule where it states that if all three sides of one triangle are equal to all three corresponding sides of another triangle, the two triangles are considered to be congruent. Two or more triangles are said to be congruent when the measurements of the corresponding sides and the corresponding angles are equal. Let us learn more about the SSS congruence rule, SSS theorem, the formula, and solve a few examples.

The SSS postulate applies to triangles that have the same measurements for corresponding sides. An example would be a triangle that has side lengths 3, 4, and 5 and a triangle that has side lengths 4, 3, and 5

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The option 1 "Triangles ABD and CBD are congruent by the SSS Congruence Postulate." is correct.

In the given question, DB is a median of ∆ADC.

We have to find which statement best describes the relationship between triangles ABD and CBD.

From the diagram we can see that

AD = CD

Since DB is median so it divide AC into two equal parts

So AB = CB

DB = DB (Common)

So, ∆ABD ≅ ∆CBD by SSS Congruence Postulate.

So, the option 1 "Triangles ABD and CBD are congruent by the SSS Congruence Postulate." is correct.

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The complete question is:

DB is a median of ∆ADC. Which statement best describes the relationship between triangles ABD and CBD?

(1) Triangles ABD and CBD are congruent by the SSS Congruence Postulate.

(2) Triangles ABD and CBD are similar by the SSS Similarity Postulate.

(3) Triangles ABD and CBD are congruent by the SAS Congruence Postulate.

(4) Triangles ABD and CBD are similar by the SAS Similarity Postulate.

Answer:

B, D

Step-by-step explanation:

To change a fraction to a decimal, divide the numerator (number on top) by the denominator (number on the bottom).

To change a decimal number to a percent, multiply the number by 100%.

A. 40/1000 = 0.04 = 4%

No

B. 6/5 = 1.2 = 120%

Yes

C. 50/33 = 1.5151... = 151.51...%
No

D. 1/8 = 0.125 = 12.5%

Yes

E. 1/3 = 0.333... = 33.333...%

No

Answer: B, D

The equation x² + 4x - 7 can be written in the form (x + a)² - b as (x + 2)² - 11

x² + 4x - 7 in the form (x + a)² - b

Where,

b = constant

x² + 4x - 7

= (x + 2)² - 11

Hence,

x² + 4x - 7 = (x + 2)² - 11

Check:

(x + 2)² - 7

= (x + 2) (x + 2) - 7

= x² + 2x + 2x + 4 - 11

= x² + 4x - 7

Therefore, (x + 2)² - 11 is another form the equation x² + 4x - 7 can be written.

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To convert an area measured in square inches to square centimeters, we need to multiply the area in square inches by the conversion factor that converts square inches to square centimeters. In this case, the conversion factor is 6.5 square centimeters per square inch. So, to convert the paper's area of 96 square inches to square centimeters, we multiply 96 square inches by 6.5 square centimeters per square inch, giving us 96 * 6.5 = 624 square centimeters. Thus, the paper's area in square centimeters is 624 square centimeters.

If a function f offers a means of successfully generating a single value y while using a value for x to that end, then that selected x-value is said to belong to the domain of f.

A function's domain is the collection of permitted values. Included in this collection are the x values for a function, such as f. (x). Such values are gathered together to demonstrate the variety of values that can be utilized as function input. Inputting an x value causes the function to return this set of values.

here

Take into account the relationship (0,7,0,8,(2,6),(1,6),(1,7),(2,9).

The relation is shown in this case as a set of sorted pairs. The range is the set of y -coordinates, which are (6 ,7 ,8 ,9), and the domain is the set of x -coordinates (0, 1, 2) .

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A triangle's area is 1/2(b*h), where b is the base and h is the height. A triangle's base can be any of its sides, and its height is the length of the altitude from the opposite vertex to that base.

The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

The area of a triangle is 1/2(b*h), where b is the base and h is the height. A triangle's base is any one of its sides, and its height is the length of the altitude from the opposite vertex to that base.

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The exact length of the curve for the function y = ln(1 - x²) is log(5/4) - 1/9

The general formula for the arc length of the curve y on the interval [a, b] is written as,

[tex]s=\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^2 } } \, dx[/tex]

Here we have given that the function is y = ln(1 - x²)

And the limit is 0 ≤ x ≤ 1/9

When we differentiate the function, then we get the value of y' as,

y' =  1/(1 - x²) × (-2x) = -2x/(1 - x²)

Now, we have to apply the values on the arc length formula, then we get,

[tex]s=\int\limits^{1/9}_0 {\sqrt{1+(\frac{-2x}{1-x^2} )^2 } } \, dx[/tex]

When we simplify this one then we get,

[tex]s=\int\limits^{1/9}_0 {\sqrt{\frac{1+x^4-2x^2+4x^2}{(1-x^2)^2} } } \, dx[/tex]

Now, we have to divide numerator by denominator and expressing using

the rule Dividend/Divisor = Quotient + (Remainder/Divisor)

Then we get the resulting equation as,

[tex]s=\int\limits^{1/9}_0 {-1 + \frac{2}{1-x^2} } \, dx[/tex]

When we apply the limit value, then we get

s = −1/9 + log∣10/8∣−log(1)

When we simplify this one then we get,

s = log(5/4) - 1/9

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A linear equation y = 3x+5 with two variables hence has an infinite number of solutions.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given linear equation:

y = 3x+5

In this equation,

there are two variables, x and y.

And equation is one.

That means,

the number of unknowns > the number of equation

2>1.

The line y=3x+5 is a linear equation in two variables.

For every value of x, there is a unique value of y

Put x=0 ⇒ y=5

Hence, (0,5) is a solution

Put x=1, ⇒ y=8

Hence, (1,8) is a solution.

Put x=−1,⇒y=2

Hence, (−1,2) is a solution.

We so obtain varied values of y when preserving distinct values of x.

Therefore, infinitely many solutions are possible.

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There are four terms in the expression. Two are numbers and the remaining are variables.

It is a mathematical statement express the relationship between two or more mathematical terms.  In an expression there will be one or more mathematical symbols or operator such as addition, multiplication, division or subtraction sign. Beside this there are many other signs such as equal or inequal sign, integration sign, square root or cubic root sign etc.

Terms can be numbers, variables or variables with coefficient.

In the above question, we have four terms, and one symbol.

5 × 3xy

5 is number and it is called constant

3 is number but it acts as the coefficient of the variables x and y.

x and y are two variables.

there is a multiplication sign among these terms.

the above expression can be described as 5 is multiplied by 3xy.

hence, we have four terms.

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The answer is B). "the probability of rolling a die eight times and getting an odd number or a prime number four times."

A binomial distribution is a statistical distribution that describes the probability of a certain number of successful outcomes in a fixed number of independent trials. In order for a situation to be a binomial distribution, the following conditions must be met:

There must be a fixed number of trials.

Each trial must have only two possible outcomes (e.g., success or failure).

The probability of success must be the same for each trial.

The first three answer choices all involve situations that meet these conditions and are therefore examples of binomial distributions. The fourth answer choice, however, involves rolling a die, which has more than two possible outcomes (1, 2, 3, 4, 5, or 6). This means that it is not a binomial distribution.

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The quotient (x3 - 3x2 + 5x - 3) ÷ (x - 1) is x2 - 2x + 3 and remainder becomes zero

What means quotient in math?

Definition of Quotient

The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.

x^3 - 3x^2 +5x -3 / x-1 = x^2 -2x +3

x^3 -+ x^2

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

0   2x^2 +5x

     2x^2 +2x

  ----------------

       0      3x +3

               3x +3

              ---------

               0    0

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Thus, ( 6 , 8 ) is the other endpoint.

What is Midpoint Formula?

Suppose the endpoints of a line segment are ( x 2 , y 2 ) and ( x 1 , y 1 ) . Also, suppose that the midpoint is ( x m , y m ) . To get ( x 2 , y 2 ) provided that the values of ( x m , y m ) and ( x 1 , y 1 ) are known, we can use the formula: ( x 2 , y 2 ) = ( 2 x m − x 1 , 2 y m − y 1 )

First, we have to determine the given values:

[tex]$$\begin{aligned}& \left(x_1, y_1\right)=(6, -4) \\& \left(x_m, y_m\right)=(5,-1)\end{aligned}$$[/tex]

Applying these points to determine the other endpoint:

[tex]$$\begin{aligned}& \left(x_2, y_2\right)=\left(2 x_m-x_1, 2 y_m-y_1\right) \\& \left(x_2, y_2\right)=(2(5)-4,2(1)-(-6)) \\& \left(x_2, y_2\right)=(6,8)\end{aligned}$$[/tex]

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Measuring tools are necessary because its improve the quality and quantity of life while also making our lives easier and safer. It is debatable if the capacity for precise measurement of physical attributes has a significant survival value that gives humans an adaptive, evolutionary advantage honed over many years of natural selection.

A measuring instrument is a tool used to quantify anything tangible. Measurement is a key activity in the physical sciences, engineering, and quality control.

Measurement equipment that is frequently used includes thermometers, rulers, yardsticks, scales, beakers, protractors, clocks, and measuring tape. Understanding the proper way to use each instrument can make measurement more accurate , enjoyable. Each tool has a unique purpose.

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Answer:

Step-by-step explanation:

correct answer is 6 marbles, no doubt.

Answer:

15-11=4ans

123-23=100ans

The candle has burned down  [tex]3 \frac{3}{4}[/tex]  inches after 6.5 hours.

To calculate this, we first need to determine the rate at which the candle burns by dividing the total burn time (11 hours) by the total length of the candle ( [tex]5 \frac{1}{2}[/tex]  inches). This gives us a burn rate of 2 hours per inch.

Next, we can multiply the burn rate by the time the candle has been burning (6.5 hours) to determine how far the candle has burned. This gives us a result of 13 inches, which is equal to [tex]3 \frac{3}{4}[/tex] inches in standard units. Therefore, the candle has burned down  [tex]3 \frac{3}{4}[/tex]  inches after 6.5 hours.

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There are 19 such integers with 4 as a digit between 1 and 100, including 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, and 94.

An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 3.14 and 1*(1/2) are two examples of numbers that are not integers. The collection of whole numbers and their antipodes is known as the integers. The set of integers does not include fractions or decimals. Integers include, for instance, 2,5,0,12,244,15, and 8.

4-digit numbers are ones with only four digits, the first of which must be one or higher and the remaining three of which may be any number between zero and nine. Four-digit numerals include 5693, 1023, and 9825 as examples. The INTEGER data-type stores whole numbers with a precision of 9 or 10 digits, ranging from -2,147,483,647 to 2,147,483,647. Because it is a reserved value, the number 2,147,483,648 cannot be utilized. The INTEGER value is generally used to store counts, amounts, and other data since it is stored as a signed binary integer.

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Relationship between the volume of the pyramid is one third the volume of the prism with the same base and equal height.

As given in the question,

Formula used to find the volume of the pyramid and prism is given by :

Volume of the pyramid = (1/3) × base area × height

Volume of the prism = Base area × height

If the base of the pyramid and prism is same and height of both pyramid and prism are equal then

Volume of the pyramid = ( 1/3) × Volume of the prism

Therefore, the volume of the pyramid is one third the volume of the prism with same base and equal height.

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Step-by-step explanation:

4. 5 Million

5. 6:10

Not sure about 3 tho I'm sorry !

Answer:

espero te sirva siuuuuuuuuuuu

Sales is a term used to describe the activities that lead to the selling of goods or services.

Let x represent the number of eggs that she uses for one batch of brownies.

Let y represent the number of eggs that she uses for one batch of cookies.

Last month, she made 2 batches of brownies and 3 batches of cookies. This means that

2x + 3y = 16 - - - - - - - - - -1

The month before, she baked 1 batch of brownies and 1 batch of cookies, which required a total of 6 eggs. This means that

x + y = 6 - - - - - - - - - - - - - 2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

2x + 3y = 16

2x + 2y = 12

Subtracting, it becomes

y = 4

Substituting y = 4 into equation 2, it becomes

x + 4 = 6

x = 6 - 4 = 2

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The group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

The correct inequality is B. 1.4x + 0.75y ≥ 150. This inequality states that the group must sell at least $150 worth of items in order to make a profit. The cost of a granola bar is $1.40, and the cost of a bottle of water is $0.75. Therefore, the total cost of the items must be greater than or equal to $150. The formula for this inequality is 1.4x + 0.75y ≥ 150, where x represents the number of granola bars sold and y represents the number of bottles of water sold.

To solve this inequality, we can first multiply both sides of the inequality by 100. This will give us 140x + 75y ≥ 15000. Next, we can subtract 75y from both sides to get 140x ≥ 14250. Finally, we can divide both sides of the equation by 140 to get x ≥ 102.86. This means that the group needs to sell at least 103 granola bars in order to make a profit of at least $150. This can be further simplified by rounding up the granola bars sold to 104. Therefore, the group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

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5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.

What equation contains an expression?

The equal to sign (=) is the best indicator of whether a given problem is an equation or an expression because it indicates that the problem is an equation.

                It is only an expression if there isn't an equal to (=) sign present. It contains data that is used to demonstrate value, such as numbers, variables, and operators.

5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.

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Answer:

$8.50

Step-by-step explanation:

To find Ryan's hourly rate, we need to first determine the total amount of money he made from commission. Since Ryan was paid 17% commission for all the products he sold, and he sold $1700 worth of products, he made 17/100 * $1700 = $289 in commission.

Next, we need to subtract this amount from his total pay to find the amount he was paid for working. Since Ryan was paid a total of $459, and made $289 in commission, he was paid $459 - $289 = $170 for working.

Finally, we can use this amount to calculate his hourly rate by dividing it by the number of hours he worked. Since Ryan was paid $170 for working 20 hours, his hourly rate is $170 / 20 = $8.50 per hour.

Therefore, Ryan's hourly rate is $8.50.

To find Ryan's hourly rate, we need to first calculate how much money he made from commissions. We can do this by multiplying his total sales by the commission rate: $1700 * 0.17 = $289.

Next, we need to subtract the commission from his total pay to find his base pay: $459 - $289 = $170.

Finally, we can divide his base pay by the number of hours he worked to find his hourly rate: $170 / 20 hours = $<<170/20=8.50>>8.50 per hour.

Thus, total amount of children tickets bought =30 tickets

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics.

Here,

The total adults and children ticket bought  = 50

The cost of one children ticket= 10$

The cost of one  adult ticket= 20$

The total spent amount = 700$

let adult be y and children be x

Thus,

equation => x+y=50 and 10x+20y=700

=>x=50-y

=>10(50-y)+20y=700

=>500 -10y +20y =700

=>500+10y =700

=>10y=500-700

=>y=200/10

=>y=20

=>x=50-20=30

=>x=30

Thus, total amount of children tickets bought =30 tickets

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