When ringing up a customer, a cashier needs 25 seconds to process payment as well as 1
second to scan each item being purchased. How long does it take to ring up a customer
with 13 items?

Answer:

The same number of tickets was sold on the fourth day and tenth day.

Step-by-step explanation:

Given, T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was  released.

The average rate of change in a function with respect to the independent variable gives the value of change in a particular period.

If average rate of change in T(d) for the interval d = 4 and d = 10 is  is 0 , that means nothing has been changed in the number of tickets sold on 4th day and 10th day after the film release.

Hence, the correct statement is "The same number of tickets was sold on the fourth day and tenth day."

Answer:

In simpler terms, for the edge answer;

A. The same number of tickets was sold on the fourth day and tenth day.

- _ -   long answers scare me...

Step-by-step explanation:

edg- answers ;p

Answer:

3.714

Step-by-step explanation:

26 x ⅐ = 26 / 7

= 3.714 or \( 3 \frac{5}{7} \)

The 19  tykes  given away by the Shelter, that have room for only 4  tykes  per family.        

The number of different canine families that could be created from the 19  tykes  given away by the  sanctum, we need to calculate the number of combinations. room for only 4  tykes , we need to choose 4  tykes  from the aggregate of 19  tykes . The order of the  tykes  in the family doesn't count, as long as we choose different  tykes  for each family.  The number of combinations can be calculated using the formula for combinations  C( n, r) =  n!/( r!( n- r)!)  Where C( n, r) represents the number of combinations of choosing r  particulars from a set of n  particulars.  In this case, we've n =  19( total number of  tykes ) and r =  4( number of  tykes  per family).  Plugging these values into the formula, we get  C( 19, 4) =  19!/( 4!( 19- 4)!)  Calculating the factorial values  19! =  19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =  ! =  4 × 3 × 2 × 1 =  24  15! =  15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =   Substituting these values into the formula  C( 19, 4) = /( 24 ×)  ≈ 91,390  The 19  tykes  given away by the  sanctum, considering that you have room for only 4  tykes  per family.

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True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Answer:

x > -5

Step-by-step explanation:

\( - 6x > 30 \\\( 6x < - 30 \\ \frac{ 6x}{ 6} < \frac{- 30}{ 6} \\ x < - 5\)

Answer:

4, 10, 23, 46, 58

Step-by-step explanation:

this is easy stuff bro, did u rlly have to look this up

Step-by-step explanation:

70 ÷ 3 = 23  1/3

The statement about the linear equation 3a + 1/3(6a −9) = 1/2(10a − 6) that is true is: "The equation has an infinite number of solutions." (Option B)

A linear equation is defined as an equation with a maximum of one degree. A nonlinear equation is one with a degree greater than or equal to two.

On the graph, a linear equation looks like a straight line. On the graph, a nonlinear equation creates a curve.

To justify the above answer, we state the linear equation above:


3a + 1/3(6a −9) = 1/2(10a − 6) ; Simplified by opening the brackets, we have

3a + 2a − 3 = 5a − 3; collecting like terms on the left side, we have

5a -3 = 5a -3

Because 5a -3 = 5a -3, the expression holds true regardless of what integer or value a represents. Hence, it has an infinite number of solutions.

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Answer:

 the first and last are 3 and 10

Step-by-step explanation:

Answer:

10.7 yd

Step-by-step explanation:

Both the right triangles would be similar by AA Postulate.

Since, corresponding sides of similar triangles are proportional.

\( \therefore \: \frac{M}{4} = \frac{5 + 3}{3} \\ \\ \therefore \: \frac{M}{4} = \frac{8}{3} \\ \\ \therefore \: M = \frac{8 \times 4}{3} \\ \\\therefore \: M = \frac{32}{3} \\ \\\therefore \: M =10.7 \: yd \\ \\\)

Answer:

Fraction = \(\frac{19}{50}\)

Decimal = 0.38

Percent = 38%

Step-by-step explanation:

Number of shaded rectangles = 38

Total number of rectangles = 100

Fraction represented by the shaded area = \(\frac{\text{Number of blocks shaded}}{\text{Total number of blocks}}\)

                                                                     = \(\frac{38}{100}\)

                                                                     = \(\frac{19\times 2}{50\times 2}\)

                                                                     = \(\frac{19}{50}\)

Decimal form of the shaded area = \(\frac{38}{100}\) =  0.38

Percent of the shaded area = \(\frac{38}{100}\) = 38%

Answer:

Fraction =

Decimal = 0.38

Percent = 38%

Step-by-step explanation:

Number of shaded rectangles = 38

Total number of rectangles = 100

Fraction represented by the shaded area =

                                                                    =

                                                                    =

                                                                    =

The decimal form of the shaded area =  =  0.38

Percent of the shaded area =  = 38%

Answer:

$16.5

Step-by-step explanation:

25 % of 22 is 5.5

22 - 5.5 = 16.5

The sale price of the DVD in this week on sale for 25% off on the original price is $16.5.

Given that  the original price of a DVD  is $22, that means the cost of the DVD is $22.

This week the sale on the original  price of  a DVD. The sale is that 25% off on the original price of a DVD, that is 25% off on $22.

Here, calculate the discount on the original price of a DVD.

\(Discount=22\times25 \%\\Discount=22\times\frac{25}{100}\\Discount=\frac{22}{4} \\Discount=\$5.5\)

The discount is $5.5  on the original  price of  a DVD.

Therefore, the sale price of a DVD on this week after the discount:

\(Sale\ price= \$22-$5.5\\Sale\ price=\$16.5\)

Thus, the sale price of a DVD is $16.5.

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It will be easier for you to see if you first write it as a rational number, then as a decimal number.

\(10^{-6}\) means we take \(6th\)  power of \(10\) , then take the reciprocal of it.

\(6th\)  power of \(10\) is \(1000000\) , and reciprocal of it is \(\frac{1}{1000000}\)

If we write it as a decimal number, the answer would be 0.000004272

Answer:

Step-by-step explanation:

10^-6 = a millionth of 1 = 0.000001

Change 4.272 into 4272

replace the last 4 digits to 4272

We get

0.004272

The most convincing explanation I can give for why a = c is supplementary property a+ b

= 180° and b+c = 180° and substraction operation and also one more reason is a = c is also true because they are vertically opposite angles.

A supplementary angle is an angle that sums to 180 degrees. For example, the 130° and 50° angles are complementary because the sum of 130° and 50° is 180°.

We know that, supplementary angles are angles whose sum is 180°. From the above figure, using the property that linear pairs are supplementary , we have b+c = 180° , c+d = 180° , d+a = 180° ,

a+b = 180°

Therefore, consider a+b = 180° and b+c = 180°

Using subtraction property of equality, we have

180°- b = a .........(1)

180°-b = c ..........(2)

Substitute 180°- b = a in equation (2) , we get

=> a = c

Hence, we get the required results.

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B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

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The given equation have only one solution, x = 1.75

Given,

The equation; 5x + 3x - 4 = 10

We have to find the number of solutions for this equation;

Solve the equation first;

That is,

5x + 3x - 4 = 10

8x - 4 = 10

Add 4 to both sides

8x - 4 + 4 = 10 + 4

We get,

8x = 14

Now divide with 8 on both sides

8x/8 = 14/8

We get,

x = 1.75

That is,

The equation 5x + 3x - 4 = 10 has only one solution.

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The values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.

The code is 2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).

1.given that

\( x^4 . x^a = {x}^{12}\)

we know the formula

\( a^m . a^n = {a}^{m+n}\)

so, \( {x}^{(4+a)} = {x}^{12}\)

if bases are equal then Powers will be equals.

then 4 + a = 12

a = 12 - 4

a = 8.

2. given that.

\( (y^b)/(y^5)= y^2\)

we know the formula

\( a^m/a^n = {a}^{(m-n)}\)

so, \( {y}^{(b-5)} = y^2\)

when bases are equal then Powers will be equal.

b - 5 = 2

b = 2 + 5

b = 7

3.given that

\( 3^c = (1)/(27)\)

so, \( 3^c = ( 1/3)^3 \)

\( 3^c = {( 3/1)}^{-3} \)

if bases are equal then Powers will be equals.

then c = -3.

4.given that

\( (m^3)^2 = m^d\)

we know the formula

\( (a^m)^n = {a}^{m.n}\)

\( m^6 = m^d\)

if bases are equal then Powers will be equals.

then d = 6

5. given that

\( 7^0 = e\)

e = 1

6. given that

\( {4}^{(-2) }. {4}^{9}. {4}^{(-5)} = 4^f\)

we know the formula

\( a^m . a^n = {a}^{(m+n)}\)

so, \( {4}^{(-2+9-5)} = 4^f\)

if bases are equal then Powers will be equals.

then -7+9 = f

f = 2.

Hence, the values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.

The code is

f ( b + d ) + a ( e - c )

2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).

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x = (12 ± √(-16)) / 4,The solutions would be complex numbers.

To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.

The quadratic formula is:

x = (-b ± √\((b^2 - 4ac)\)) / 2a

Plugging in the values for a, b, and c, we get:

x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)

Simplifying the expression inside the square root:

x = (12 ± √\((144 - 160)\)) / 4

x = (12 ± √(-16)) / 4

Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.

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The solutions to the systems of equations are:

1. (2, 3) (see attachment below). [one solution]

2. no solution

3. (3, 13) [one solution]

The solution to a system of equations is the x-value and y-value that will make both equations true. It can be found either using a graph, by elimination method, or substitution method as explained below.

1. Using graph to solve y = 2x - 1 and y = 4x - 5:

The solution is the point where both lines intersect which is: (2, 3) (see attachment below). [one solution]

2. Solving using substitution method:

x = -5y + 4 ---> eqn. 1

3x + 15y = -1 ---> eqn. 2

Substitute x = -5y + 4 into eqn. 2

3(-5y + 4) + 15y = -1

-15y + 12 + 15y = -1

-15y + 15y = -1 - 12

0 = -13 (this shows that there is no solution)

3. Using elimination method:

14x = 2y + 16 ---> eqn. 1

5x = y + 2 ---> eqn. 2

1(14x = 2y + 16)

2(5x = y + 2)

14x = 2y + 16 ----> eqn. 3

10x = 2y + 4 -----> eqn. 4

Subtract

4x = 12

x = 12/4

x = 3

Substitute x = 3 into eqn. 2

5(3) = y + 2

15 = y + 2

15 - 2 = y

13 = y

y = 13

The solution is: (3, 13).

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The area of the region bounded by the line y =3x -6 and line y=-2x+8 is  12/5 units

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

2x = 8

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

A = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

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Answer:

9.52

Step-by-step explanation:

If Andre had $6 + $3.52 is 9.52

Answer:

Step-by-step explanation:

\(2) y^{\frac{3}{2}}=y^{3*\frac{1}{2}}\\\\=(y^{3}}^{\frac{1}{2}}\\\\=\sqrt{y^{3}}\)

b

\(3)a^{\frac{2}{3}}=a^{2*\frac{1}{3}}\\\\=(a^{2})^{\frac{1}{3}}\\\\=\sqrt[3]{a^{2}}\)

c

Answer:

Factored form:

\(y=\left(-\dfrac14x+\dfrac12 \right)(x-4)\)

Standard form:

\(y=-\dfrac14x^2+\dfrac32x-2\)

when x = 1, \(y=-\dfrac34\)

Step-by-step explanation:

Part (a)

The zeros are where the curve intersects the x-axis (where y = 0)

From inspection of the graph, the points of intersection with the x-axis are (2, 0) and (4, 0)

\(x=2 \implies x-2=0\)

\(x=4 \implies x-4=0\)

Therefore, we can write the equation as:

\(y=a(x-2)(x-4)\)

(where a is some constant to be determined)

The y-intercept is when x=0 .

From inspection of the graph, the point of intersection with the y-axis is (0, -2)

Therefore, substitute x = 0 into the equation, set it to -2 and solve for a:

\(\implies a(0-2)(0-4)=-2\)

\(\implies a(-2)(-4)=-2\)

\(\implies 8a=-2\)

\(\implies a=-\dfrac14\)

Therefore, the final equation of the parabola is:

\(y=-\dfrac14(x-2)(x-4)\)

\(\implies y=\left(-\dfrac14x+\dfrac12 \right)(x-4)\)

Standard form of a quadratic equation:  \(y=ax^2+bx+c\)

To express the equation in standard form, simply expand:

\(\implies y=-\dfrac14x^2+x+\dfrac12x-2\)

\(\implies y=-\dfrac14x^2+\dfrac32x-2\)

Part (b)

Substitute x = 1 into the equation and solve for y:

\(\implies y=-\dfrac14(1)^2+\dfrac32(1)-2\)

\(\implies y=-\dfrac14+\dfrac32-2\)

\(\implies y=-\dfrac14+\dfrac64-\dfrac84\)

\(\implies y=-\dfrac34\)

Answer:

Step-by-step explanation:

R=21

The expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters is A = 33.45

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.

The mean of probability distribution is also known as expected value. It is denoted by E ( X ). E(X), or mean μ of a discrete random variable X is calculated by multiplying each value of the random variable by its probability and taking the sum of the values.

E ( X ) = μ = ∑x P ( x )

Given data ,

To find the expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters, we need to calculate the expected count for that cell using the formula:

Expected Count = (row total * column total) / grand total

The row total for cities with more than 250,000 residents is 99, and the column total for names with less than 8 characters is 100. The grand total is 296

Expected Count = (99 * 100) / 296

Expected Count ≈ 33.45

Therefore , the expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters is approximately 26.67

Hence , the distribution is 33.45

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The complete question is attached below :

Judson collected information about the name length and the population of a random sample of 296 American cities. Here are the results:

Judson wants to perform a X2 test of independence between name length and population. What is the expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters?

The length of the altitude to EM in triangle GEM is 25 units.

Note that if the altitude of the triangle is at most 10, then the maximum area of the intersection of the triangle and the square is 5 * 10=50. This implies that vertex G must be located outside of square AIME.

Now, suppose GE meet AI at X and let GM meet AI at Y.

Clearly, XY=6 since the area of trapezoid XYME is 80. Also, triangle GXY is similar to triangle GEM.

Let the height of GXY be h.

By the similarity, h/6 = {h + 10}/10,

we get h = 15.

Thus, the height of GEM is

h + 10 = 15 + 10

h = 25 units

So the length of altitude is of triangle GEM is 25 units.

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____The given question is incorrect, the correct question is given below:

Square AIME has sides of length 10 units. Isosceles triangle GEM has

base EM, and the area common to triangle GEM and square AIME is 80

square units. Find the length of the altitude to EM in triangle GEM.

Answer:

$0.50

Step-by-step explanation:

.

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.