Units needed 90 units per case 8

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Answer:

Height of the object is 68.6 cm.

Step-by-step explanation:

The height of the object can be determined by:

\(\frac{object distance from pinhole}{image distance from pinhole}\) = \(\frac{object height}{image height}\)

From the given question;

object distance from pinhole = 3.6 m = 360 cm

image distance from pinhole = 4.2 cm

height of image = 0.8 cm

So that;

\(\frac{360}{4.2}\) = \(\frac{object height}{0.8}\)

⇒ object height = \(\frac{360*0.8}{4.2}\)

                           = \(\frac{288}{4.2}\)

                           = 68.571

object height = 68.6 cm

Thus, the height of the object is 68.6 cm.

Answer:

6666

Step-by-step explanation:

Formula for the concentration after n steps is \(C(n) = C(0) * (0.86)^n\) and

after 11 steps, the mixture contains less than 9% vinegar.

What is concentration?

Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.

a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:

\(C(1) = C(0) * \frac{1 - 0.14}{1}\)

where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:

C(2) = C(1) * \(\frac{1 - 0.14}{1}\)

Substituting the formula for C(1), we get:

C(2) = C(0) * \((\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})\)

or, more generally:

\(C(n) = C(0) * (0.86)^n\)

b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:

\(C(0) * (0.86)^n < 0.09\)

Dividing both sides by C(0), we get:

\((0.86)^n < 0.09\)

Taking the natural logarithm of both sides, we get:

n * ln(0.86) < ln(0.09)

Dividing both sides by ln(0.86), we get:

n > ln(0.09) / ln(0.86)

Using a calculator, we get:

n > 10.7

Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.

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The value of the given expression when simplified is equal to 318.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified using the PEMDAS as shown below.

-7 + 5 - 40 × -8

As per the PEMDAS multiplication should be solved first,

= -7 + 5 + 320

Further, solve addition,

= -7 + 5 + 320

= -7 +325

= 318

Hence, the value of the given expression when simplified is equal to 318.

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Answer:

If donovan wants to get dem grades up he has to stop talking out of turn, stop passing notes to his friends, stop fighting, stop trying to kiss the girls, stop cussing, mind his own bussiness, and do his work

Step-by-step explanation:

Answer:

Answer is C) Angle G is congruent to Angle L

Phil would need to save for at least 6 weeks to have enough money to buy the bike.

Phil saves one-quarter of his pay each week, which is:

1/4 x £240 = £60

Let's assume it takes him n weeks to save enough to buy the bike. Then, the amount he saves in n weeks is:

n x £60 = £349

We can solve for n by dividing both sides by £60:

n = £349 / £60

n ≈ 5.82

Since we can't have a fraction of a week, Phil would need to save for 6 weeks to have enough money to buy the bike.

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Answer:

50 - 8 = 42

Step-by-step explanation: 42 is the awnser

Answer:

8p <= 50

Step-by-step explanation:

Explanation:

Definition or rational roots theorem:

Rational root theorem is used to find the set of all possible rational zeros of a polynomial function (or) It is used to find the rational roots (solutions) of a polynomial equation

We can actually use the Zeros Theorem and the Conjugate Zeros Theorem together to conclude that an odd-degree polynomial with real coefficients must have atleast one real root (since the non-real roots must come in conjugate algebra Use the rational zeros theorem to find all the real zeros of the polynomial function.

Rational Zero Theorem. If a polynomial function, written in descending order of the exponents, has integer coefficients, then any rational zero must be of the form ± p / q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Hence,

The final answer is TRUE

The dilation transformation of the triangle ABC by a scale factor of 3, with the point P as the center of dilation indicates;

Side A'B' will be parallel to side AB

Side A'C' will be parallel to side AC

Side BC will lie on the same line as side BC

A dilation transformation is one in which the dimensions of a geometric figure are changed but the shape of the figure is preserved.

The possible options, from a similar question on the internet are;

Be parallel to

Be perpendicular to
Lie on the same line as

The location of the point P, which is the center of dilation, and the lines PC and PA of dilation and the scale factor of dilation indicates that we get;

PB' = 3 × PB

PA' = 3 × PA

PC' = 3 × PC

Therefore; The side B'C' will be on the same line as the side BC

The Thales theorem, also known as the triangle proportionality theorem indicates that;

The side A'C' will be parallel to the side AC

The side A'B', will be parallel to the side AB

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Answer:

the percent error in the student's measurement is 4.65%.

Step-by-step explanation:

The percent error can be calculated using the formula:

| (measured value - actual value) / actual value | * 100%

In this case, the measured value is 2.7 grams and the actual value is 2.58 grams. Substituting these values into the formula, we get:

| (2.7 - 2.58) / 2.58 | * 100% = 4.65%

Rounding this to the nearest hundredth of a percent, we get a percent error of 4.65%.

Therefore, the percent error in the student's measurement is 4.65%.

The value of A(2,2) is not 4, but rather 65536, which is obtained by using the recursive definition of the function.

The given inductive definition of Ackermann's function is used to calculate the values of the function for given input values of m and n. The definition uses recursive steps to define the function for different values of m and n. To find the value of A(2,2), we start with the base cases, which are given by the first two lines of the definition. Here, since m=2 and n=2, we use the third line of the definition, which gives the value 2n=2x2=4. Now, we use the fourth line of the definition to compute A(2,1) by using the value of A(2,2) that we just found. This gives us A(2,1)=\(2^4\)=16. Finally, we use the fourth line of the definition once again to compute A(2,0) by using the value of A(2,1) that we just found. This gives us A(2,0)=\(2^{16}\)=65536. Therefore, the value of A(2,2) is not 4, but rather 65536, which is obtained by using the recursive definition of the function.

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A≈175.93yd²

A=2πrh+2πr2=2·π·4·3+2·π·42≈175.92919yd²

Therfore the surface area of the cylinder with height 3 yd and radius 4 yd is 175.93

The limit of the given sum as n approaches infinity is 0.

We have the limit as n approaches infinity of the sum from i = 1 to n of 1/(n+i). We can rewrite this sum using the hint provided as:

\(\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}\)(1/ n + i) = \(\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}\) (1/n) * (1 + i/n)

To find the limit, we need to take the limit of the Riemann sum as n approaches infinity. This is equivalent to taking the limit of the area of n rectangles under the curve y=1/x as n approaches infinity.

As n becomes very large, the width of each rectangle becomes very small, and the height of each rectangle approaches 1/n. Therefore, the area of each rectangle approaches zero.

We can then express the limit as an integral:

\(\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}\)(1/ n + i) =\(\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}\) (1/n) * (1 + i/n) =\(\lim_{n \to \infty} \int ^1 _{1+1/n}\) 1/x dx

Evaluating this integral gives:

\(\lim_{n \to \infty} \int ^1 _{1+1/n}\) 1/x dx = \(\lim_{n \to \infty}\) ln(1+1/n) = ln(1+0) = 0

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(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Step-by-step explanation:

1. The given expression is, \(A=lw\)

We need to solve it for w.

\(w=\dfrac{A}{l}\)

2. The given expression is, \(C=\pi D\)

We need to solve it for D.

\(D=\dfrac{C}{\pi}\)

3. The given expression is, \(v=s+gt\)

We need to solve it for s.

\(s=v-gt\)

4. The given expression is, \(5x-2y=11\)

We need to solve it for y.

\(D=\dfrac{5x-11}{2}\)

5. The given expression is, \(P_1V_1=P_2V_2\)

We need to solve it for P₂. So,

\(P_2=\dfrac{P_1V1}{V_2}\)

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

perpindicular

Step-by-step explanation:

The line a and line d are perpendicular to each other.

A perpendicular line is a line that intersect another line at 90 degrees. Perpendicular lines are also called normal lines.

After constructing the two lines; line a and line intersect or meet each other at 90 degrees to the horizontal.

Thus, we can conclude that the line a and line d are perpendicular to each other.

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The most appropriate scale for graphing this data set. is (a) t ones and a fitties

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

The table of values

From the table of values, we have

x-values = t: This values are in units

y-values = a: These values can be approximated to fifties

Hence, the most appropriate scale is (a)

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Answer:

115.42 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

If I were to estimate it I would have to say at least 110 to 115

Step-by-step explanation:

Now that I calculated the answer it actual is 115.42 and rounded down 115.4

Hope this helps have a great day:)

The perimeter of the figure described in the question is 42.84cm

The figure is defined by a half circle is joined to an equilateral triangle with side lengths of 12 units.

So the perimeter of the figure will be equal to half of the circumference of the triangle plus the length of the two exposed sides of the triangle.

The diameter of the circle will also be 12 units, remember that the circumference of a circle of diameter D is:

C = 3.14*D

In this case, the circumference of half circle is:

C = 3.14*D/2

Replacing the value of the diameter:

C = 3.14*12cm/2 = 18.84cm

Adding the two sides of the triangle we get the perimeter.

P = 18.84cm + 2*12cm = 42.84cm

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Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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Answer: 14x,4+4x ^2-3x

Step-by-step explanation:

1. Simplify  6x\times 26x×2  to  12x12x.

2x+12x,10+4{x}^{2}-3x-6

2x+12x,10+4x  

2

−3x−6

2 Simplify  2x+12x2x+12x  to  14x14x.

14x,10+4{x}^{2}-3x-6

14x,10+4x  

2

−3x−6

3 Collect like terms.

14x,((10-6)+4{x}^{2}-3x)

14x,((10−6)+4x  

2

−3x)

4 Simplify  (10-6)+4{x}^{2}-3x(10−6)+4x  

2

−3x  to  4+4{x}^{2}-3x4+4x  

2

−3x) Hope that helps

The following phrases are used in place of supply chain:

Supply network ; Demand chain ; Extended enterprise ; Supply web.

The supply chain is a networked system of businesses, people, information, and assets created to locate, produce, and transport items from their point of origin to their final destination, which is often from the a supplier to a customer.

Modern supply chains sometimes span several nations and involve numerous processes, making them exceedingly complicated.

The fundamental steps in such a supply chain are as follows:

Thus, the following phrases are used in place of supply chain:

Supply network ; Demand chain ; Extended enterprise ; Supply web.

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Answer:

The right equation will be "\(x^2+15x-54 =0\)".

Step-by-step explanation:

According to the question,

Border around the photograph on the top is:

= 3 cm

The remaining sides,

= 4 cm

Area,

= 10 square cm

Let the length of sides be "x".

Since,

The paper's dimensions will be:

⇒ \((x+3+4)\)

    \((x+7)\)

and

⇒ \((x+4+4)\)

    \((x+8)\)

now,

⇒ \((x+7)(x+8)=110\)

⇒ \(x^2+7x+8x+56=110\)

⇒         \(x^2+15+56=110\)

On subtracting "56" from both sides, we get

⇒       \(x^2+15x-56=110-56\)  

⇒               \(x^2+15x=54\)

Or,

⇒       \(x^2+15x-54=0\)

Answer:

y=x^4 is a function

Explanation:

A function is defined as given an equation, there should be only one corresponding, y value for any x value. In the table from the picture you attached, it is shown as for each x value, there is one corresponding y value. Therefore, x^4 is a function.

The given expression y = x⁴ is a function.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

A function is defined as given an equation, there should be only one corresponding, y value for any x value. In the table from the picture you attached, it is shown as for each x value, there is one corresponding y value.

Therefore, the given expression y = x⁴ is a function.

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Answer: 3.0 minutes

Step-by-step explanation:

The solution to the equations are b = 15, b = 22, c = 21 and n = 28

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

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Next, we collect the like terms in each of the equation

This gives

b = 31 - 16

b = 50 - 28

c = 54 - 33

n = 52 - 24

Lastly, we evaluate the like terms

b = 15

b = 22

c = 21

n = 28

The above are the solutions to the equations

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Question

Solve the following equations:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24