a classroom has two rows with nine seats in each row. there are 15 students named s1, . . . , s15, where s1, . . . , s4 always sit in the front row and s5, . . . , s10 always sit in the back row. (the students s11, . . . s15 may sit in either row). in how many ways can the students be seated?

Answer:

The axis of symmetry is x = -3.

If you draw a line at x = -3, the graph is reflected over it.

The length of PT is 3 units. The solution has been obtained using the concept of transformation.

What is transformation?

A transformation is an operation that moves a polygon or other two-dimensional object on a plane or coordinate system.

The term "pre-image" or "inverse image" refers to the shape in two dimensions prior to any modification. The image is the shape after transformation.

Transformation can be done by translation, rotation, reflection and dilation.

We are given two rectangles ABCD and PRQT

AB = DC = 3 units

AD = BC = 10 units

It can be observed that the rectangles PRQT and ABCD are same but PRQT is rotated.

Since, they are same so,

AB = PT = 3 units

Hence, the length of PT is 3 units.

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If the growth rate of bacterial culture is 150% each hour , then the correct exponential function is b(t) = 10(2.5)^t instead of b(t) = 10(1.5)^t , and after 8 hours there are about 15259 bacteria in culture .

The percent growth in the bacterial culture is = 150% = 1.5  ;

the initial amount of bacteria present is = 10  ;

the exponential function used to denote this situation is written as :

⇒ b(t) = 10(1 + 1.5)^t

⇒ b(t) = 10(2.5)^t

to find number of bacteria after 8 hours ,

we substitute t = 8 in b(t) ;

we get ;

⇒ b(8) = 10(2.5)⁸ ;

⇒ b(8) = 15258.789 ≈ 15259

Therefore , there will be 15259 bacteria present after 8 hours .

The given question is incomplete , the complete question is

The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe the error in the data below, in finding the number of bacteria in the culture after 8 hours. Correct the error and find, to the nearest whole number,

"The number of bacteria in the culture after 8 hours. The exponential function is b(t) = 10(1.5)^t ,  b(8) = 10(1.5)⁸ . After 8 hours, there are about 256 bacteria in the culture ."

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A graph that represents the overall equation represented by this scenario is shown in the image attached below.

Based on the information provided about this company with respect to its same-day delivery and total number of miles to be covered, we would assign variables to the parameters as follows:

Next, we would translate the word problem into an algebraic equation by using an inequality:

Half the total number of miles = x/2.

y > x/2 - 3

Furthermore, we would determine the x- and y-intercepts as follows:

When x = 0, we have;

y = 0/2 - 3

y = -3.

Therefore, y-intercept = (0, -3).

For the x-intercept (y = 0), we have:

0 = x/2 - 3

x/2 = 3

x = 6.

Therefore, x-intercept = (6, 0).

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Macy had 3 appointments.

Logan had 5 appointments.

What is the quadratic equation?

A quadratic equation is a type of polynomial equation of degree 2, which is written in the form of "ax^2 + bx + c = 0", where x is the variable and a, b, and c are constants. The solutions to a quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac))/2a.

Part A:

Let x be the number of appointments Macy had.

We know that the total income (60x + 40) must equal 220.

Therefore, the equation representing the situation is:

60x + 40 = 220

To solve for x, we can subtract 40 from both sides:

60x = 180

Finally, we divide both sides by 60 to get:

x = 3

Macy had 3 appointments.

Part B:

Let y be the number of appointments Logan had.

We know that the total profit (70y + 50 - 20y) must equal 300.

Therefore, the equation representing the situation is:

50y + 50 = 300

To solve for y, we can subtract 50 from both sides:

50y = 250

Finally, we divide both sides by 50 to get:

y = 5

Logan had 5 appointments.

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For the given function H(t) = -12cos( πt/45 ) + 18 the maximum height is  30 units.

Function to modeled the height 'H' of the Ferries wheel is given by:

H(t) = -12cos( πt/45 ) + 18

Where 't' represents the time in seconds.

For cosine trigonometric function,

-1 ≤ cosα ≤ 1

Here cos function lies between two values -1 and 1.

Substitute cos( πt/45 ) = 1 or -1

When cos( πt/45 ) = 1

H(t) = -12(1) + 18

⇒H(t) = 6 units

When cos( πt/45 ) = -1

H(t) = -12(-1) + 18

⇒H(t) = 30 units

Maximum height of a required cabin is equals to 30 units.

Therefore, the maximum height of given cabin represented by the function

H(t) = -12cos( πt/45 ) + 18 is equal to 30 units.

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The value of x is x > 2.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Any number can be expressed as fractions.

The given expression is [tex]\frac{5}{6}[/tex]x - [tex]\frac{1}{3}[/tex] > 1 [tex]\frac{1}{3}[/tex]

We have to rewrite the expression with x on one side.

[tex]\frac{5}{6}[/tex]x - [tex]\frac{1}{3}[/tex] > 1 [tex]\frac{1}{3}[/tex]

[tex]\frac{5}{6}[/tex]x > 1 [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{3}[/tex]

[tex]\frac{5}{6}[/tex]x > [tex]\frac{4}{3}[/tex] + [tex]\frac{1}{3}[/tex]

[tex]\frac{5}{6}[/tex]x > [tex]\frac{5}{3}[/tex]

x > [tex]\frac{5}{3}[/tex] × [tex]\frac{6}{5}[/tex]

x > 2

So the value of x is greater than 2.

Hence the correct option is x > 2.

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The equation of the model is (b) 2x = 5

From the question, we have the following parameters that can be used in our computation:

Left = x x

Right hand side = 1 1 1 1 1

The above parameters mean that

Left = 2x

Right = 5

When represented as an equation, we have

2x = 5

Hence, the equation is (b)

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Answer:

Step-by-step explanation:

The probability of adults using smartphones in meetings or classes as per the randomly selected adults is equal to 0.3375.

Percent of randomly selected adults use smartphones in meetings or classes represents the probability of success 'p' = 37%

                                                                                 = 0.37

1 - p = 1 - 0.37

       = 0.63

Number of randomly selected adults use smartphone in meetings or classes represents sample size 'n'  = 30

Exactly 19 adults use smartphone represented by x

x = 19

Using binomial distribution :

Required probability is :

P(x) = ⁿCₓ× pˣ × ( 1 - p )ⁿ⁻ˣ

⇒P(x) = [ n! / x! (n - x)! ] × pˣ × ( 1 - p )ⁿ⁻ˣ

Substitute the values

⇒P(19) = [ 30! / 19! (30 - 19)! ] × 0.37¹⁹× ( 0.63 )³⁰⁻¹⁹

⇒P(19) = ( 30!/19! ×11! )  × 0.37¹⁹× ( 0.63 )¹¹

⇒P(19 ) = 0.3375

Therefore, the required probability of selecting exactly 19 adults who use their smartphones in meetings or classes is equal to 0.3375.

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The height of the new prism so that its surface area is doubled will be 26.31 cm.

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

A right rectangular prism measures 12 cm tall, 3 cm long, and 10 cm wide. A manufacturer would like to double the surface area of this prism.

Then the height of the new prism so that its surface area is doubled will be given as,

2 x 2 x (12 x 3 + 3 x 10 + 10 x 12) = 2(3h + 3 x 10 + 10h)

2(36 + 30 + 120) = 13h + 30

372 = 13h + 30

13h = 342

h = 26.31 cm

The height of the new prism so that its surface area is doubled will be 26.31 cm.

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Answer:

A

Step-by-step explanation:

R = sqrt((7-4)^2+(14-15)^2)=sqrt(10)

The answer is A since that's the only answer with the proper radius, using the formula for a circle.

Considering that the leading digit is never zero , then the number of 9 digit integers that can contain exactly 5 zeroes are 367416 numbers   .

the number of digits in the number is = 9 digits ;

the number should have exactly five zeroes  ,

the number of ways to pick five of the digit positions for the zeroes, since the first digit can’t be zero is  = ⁸C₅ ,

There are 9 possible digits for each of other 4 positions as  other positions are occupied by 0 ,

So, the total number of possibilities is = ⁸C₅ × 9⁹⁻⁵

Simplifying further ,

we have ,

= ⁸C₅ × 9⁴

= 56 × 6561

= 367416 numbers .

Therefore , there can be 367416 numbers of 9 digits having 5 zeros .

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Starch and protein levels are checked for In order to present the idea of chemical compound variety, it is necessary to test for the presence of starches and protein macromolecules.

Hypothesis: It is a negative result if the biuret reagent remains blue after a test for protein since the reagent itself is blue. The test for protein is positive if a solution is pinkish purple or purple. The starch test solution is a yellowish brown color. We utilized iodine to test for starch in some solutions if any ingredient produced a mixture that was yellowish brown in color. Polysaccharides, monosaccharides, and disaccharides are separated from starch by iodine. Iodine interacts with molecules, changing the color of the molecules, while starch is a coiled polymer of glucose.

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The lateral surface area of the cylinder is 51.22 cm2.
What is surface area?
Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.

The cylinder shown below has a diameter of 5.2 cm on the base and a height of 7.1 cm. The diameter of the base is referred to as 'd' and the height of the cylinder is referred to as 'h'. The lateral surface area of the cylinder can be found by using the formula LSA = 2πrh, where 'r' is the radius of the base. The radius of the base of this cylinder is half of the diameter, or 2.6 cm. Therefore, the lateral surface area of the cylinder is: 2π x 2.6 x 7.1 = 51.22 cm2.

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Answer:

He only accepts jobs that last 4 or more hours.

Step-by-step explanation:

He only accepts jobs that last 4 or more hours.

He only accepts jobs that last 5 or more hours.

He only accepts jobs that last 8 or more hours.

He only accepts jobs that last 9 or more hours.

30 + 15x ≥ 90

15x ≥ 60

x ≥ 4

Answer: He only accepts jobs that last 4 or more hours.

A letter to a student who will be taking this math class next year to give them some advice about this class has been written below.

(Sender's address)

20/01/2023

Dearest,

I was happy to see your letter, and I hope this letter finds you in the best of health. I have wanted to go on a trip with you for a long time but I guess that would happen later since you have to start attending classes soon.

I have a list of things to keep in mind when you start your classes. I was always too scared of mathematics, and I know you are too, but I have always wanted to tell you how fruitful it is to learn a subject that will help you in every field you want to go in. Let me know what you think about it after you finish reading this letter. I know it is no secret that maths is a difficult subject but you can master it if you keep what I am going to tell you in mind. Practice your concepts daily. Keep brushing up on whatever your teacher teaches you. Remember the formulas and you will know how to answer any question.  I know for sure that it is going to be worth it too.

I will make sure that I meet you next weekend so that we can meet before you begin the classes. If you try hard, you can make this work. See you soon.

Love,

(Sender's name)

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True, free bilirubin is transported by the blood to the liver.

Macrophages begin the disposal of hemoglobin by separating the heme from the globin. They hydrolyze the globin into free amino acids, which can be used for energy-releasing catabolism or recycled for protein synthesis.

Bilirubin

Bilirubin is a red-orange compound that occurs in the normal catabolic pathway that breaks down heme in vertebrates. This catabolism is a necessary process in the body's clearance of waste products that arise from the destruction of aged or abnormal red blood cells.

Hemoglobin

Hemoglobin is a protein in your red blood cells that carries oxygen to your body's organs and tissues and transports carbon dioxide from your organs and tissues back to your lungs.

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The following two methods can be used for eliminating the damage to the laundry (l).

The factory and the local resident must decide whether to install the scrubber or the clothesline, depending on which option will result in the lowest cost. The best option for each party depends on their own willingness to pay for the damage reduction and their ability to pay for the solution.

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Answer:

Answers are in bold

Data set A:

Mean: 7

Median: 7

Mode: 7

Range: 11

Data set B:

Mean: 78

Median: 95

Mode: No mode or all the numbers (85, 105, 95, 90, 115)

Range: 30

Data set C:

Mean: 13

Median: 13

Mode: 11 and 16

Range: 7

Step-by-step explanation:

You're welcome.

The remaining rope he left is 495cm

Now, According to the question:

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Jacob has 6. 15 meters of rope.

He is going to use 1. 2 meters of rope to tie up his boat.

When you do the subtraction, whatever is left (the decimal part) is the length in cm when multiplied by 100.

Remaining rope = starting length - what was used.

Remaining rope = 6.15 - 1.2

Remaining rope = 4.95 meters

Hence, The remaining rope he left  = 4.95 × 100 = 495 cm

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12.2 % of the area painted blue of the figure representing a square with attached triangle on one side with perpendicular height 4cm is equal to 4.27 cm² .

Figure having square attached with triangle on one side.

Side length of the square = 5 cm

Area of the square = ( side-length )²

                                = 5²

                                = 25 cm²

Triangle attached on one side of the square with height = 4cm

Area of the triangle = ( 1/2) × base × height

                                = ( 1/2) × 5 × 4

                                = 10 cm²

Total area of the figure = 25 + 10

                                      = 35 cm²

Percent of area painted blue = 12.2% of total area

                                               = ( 12.2 / 100 ) × 35

                                               = 4.27 cm²

Therefore, for the given figure made up of square and triangle area to be painted blue is equal to 4.27 cm².

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An equation for the situation described above is h = 2m + 500.

In order to write an algebraic equation that model this situation, we would assign a variable to the number of minutes after an airplane takes off from the airport and the plane’s height respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that after 2 minutes the plane is at 500 feet as follows;

h = 2m + 500.

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A graph which represent the function g(x) = 3∛x – 1 is: graph A.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis  and y-axis respectively.

Based on the information about this graph, it represents the following function:

Function, g(x) = 3∛x – 1

By rewriting the cube root in the above function, we have the following:

Function, g(x) = 3∛x – 1

Function, g(x) = 3(x^{1/3}) – 1.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

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The time to calculate her rate along the summit Rate = 1.5 mph

Rate = Distance / Time

To solve this problem, we will first need to calculate the time it took Jane to reach the peak. Since she rode 40 miles uphill, we can use the rate of 5 mph slower than when she reached the peak to calculate this time.

Time = Distance / Rate

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5)

Time = 8 hours

Since Jane spent 2 hours exploring the mountain, the total time it took her to reach the peak was 8 hours. We can now use this time to calculate her rate along the summit.

Rate = Distance / Time

Rate = 12 miles / 8 hours

Rate = 1.5 mph

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Answer:

Part A.) 153 Boxes

Part B.) 394 Boxes (395 if rounding up)

Step-by-step explanation:

The inequality used in this situation would be:

3.74x + 25 < 600

3.74 is the price of each box

x is the number of boxes

25 is that deposit

and < 600 is not making $600 in sales

What we need to do is get X alone. First we will subtract 25 from both sides since that's the opposite of +25.

Doing that will get you

3.74x = 575

Next step is to divide 3.74 on both sides since 3.74 is being multiplied by x and division is the opposite.

That will give you X = 153.74. We round down to stay under and we end up with 153.

For part B, we would do the same process, but instead of < 600, we would do >= 1500. Just typing the same steps out.

3.74x >= 1475 since we subtract 25 from both sides

x = 394.38 since we divide 3.74 on both sides. Rounding would get us 394

Using Quadratic formula, the roots of the equation are -11 + √217/6, -11 - √217/6 .

Equations involving quadratics The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0.

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).

Using Quadratic formula,

3x² + 11x - 8

(-b±√(b²-4ac))/(2a)

⇒ (-11 ± √11² - 4(3)(-8)/2(3))

⇒ -11 ± √217 / 6

⇒ -11 + √217/6, -11 - √217/6

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Answer:

Option B

Domain: all real numbers

Range [tex]f(x) \le -8[/tex]

Step-by-step explanation:

Given function is:
[tex]f\left(x\right)=-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]

The domain is the set of all x values that result in a real and defined value for f(x).

The function has no undefined points and x is free to range from -∞ to +∞

So the domain is -∞ < x <∞ which is
All real numbers

The range is the set of all possible values for f(x) given a specific domain. In order to determine the range without too much hard work, let's first examine the function f(x)

The above function is the equation for a parabola.

Some things to note about a parabola equation:

Let us compare the general vertex form equation of the parabola with the specific f(x) equation given

General Equation:    [tex]a (x - h)^2 + k[/tex]

This example:           [tex]-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]

Comparing the similarity between the two equations we easily see that

[tex]\boxed{a = -\dfrac{5}{6}}[/tex]
This means the parabola opens downward and (h, k) represents a max point in the parabola

[tex]x - h = x + 2\\\\-h = 2\\\\h = -2\\[/tex]

[tex]k = -8[/tex]

So the vertex is at (-2, -8)

Since -8 is the maximum value for f(x), and the parabola extends to infinity on both sides, the range is :

[tex]\boxed{f(x) \le -8}[/tex]

The attached graph may help you understand better

Answer:

I got 0.6

Step-by-step explanation:

plug in c and d

0.5(15) - 2.3(3)

multiply them

7.5 - 6.9 = 0.6