Create an
equation that has -13 and 12
as solutions.

Answer:

5, 6, 7, 8

Step-by-step explanation:

substitute the values of x from the table into f(x)

f(1) = 1 + 4 = 5

f(2) = 2 + 4 = 6

f(3) = 3 + 4 = 7

f(4) = 4 + 4 = 8

the values of f(x) are 5, 6, 7, 8

Answer:

attached in the file

The equation that represents the sentence "28 is the quotient of a number and 4" is 28 = n/4.

In the given sentence, "28 is the quotient of a number and 4," we can break down the sentence into mathematical terms. The term "quotient" refers to the result of division, and "a number" can be represented by the variable "n." The divisor is 4.

1) Define the variable.

Let's assign the variable "n" to represent "a number."

2) Write the equation.

Since the sentence states that "28 is the quotient of a number and 4," we can write this as an equation: 28 = n/4.

The equation 28 = n/4 represents the fact that the number 28 is the result of dividing "a number" (n) by 4. The left side of the equation represents 28, and the right side represents "a number" divided by 4.

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Cryptography is - "The study of encoding data so that confidentiality of communications can be maintained between two parties." (Option A)

Cryptography involves techniques and methods used to secure and protect information by transforming it into an unreadable format (ciphertext) using encryption algorithms.

It ensures   the confidentiality, integrity,and authenticity of data during transmission and storage.

It also encompasses   the study of cryptographic protocols, algorithms, and systems to design securecommunication systems and protect sensitive information from unauthorized access or tampering.

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The graph for the data indicates that the domain, range, value of the function and the piecewise function are;

a. Domain; [0, 9]

Range; [0, 8,000]

b. f(1) = 4,000 (The volume of water in the tank after an hour is 4,000 gallons)

c. 0 gallons per hour

d. The piecewise function for the graph can be presented as follows;

\(f(x) = \begin{cases} & 4000\cdot x\text{ if } 0\leq x\leq 2 \\ &8000 \text{ if } 2 \leq x \leq 6\\ & 2666\frac{2}{3}\cdot x - 24,000\text{ if } 6 \leq x \leq 9\end{cases}\)

A piecewise function is a function that is defined based on the specified interval on the domain of the function.

a. The domain and the range of the function are the possible x-values and the set of possible y-values of the function.

The graph of the function indicates that the domain is; [0, 9]

The domain is the duration in which the tank contained water

The range is the set of the possible y-values on the graph, which is from the following values; Minimum 0 gallons, maximum value; 8,000 gallons, therefore, the range is; [0, 8,000]

The range is the amount of water in the tank at each period on the domain

b. The graph indicates that f(1) = 4,000 gallons

The meaning of f(1) = 4,000 gallons, is that after 1 hour, the volume of the water in the tank was 4,000 gallons

c. The interval [4, 6], are located on the horizontal part of the graph, therefore, the slope of the graph in the specified interval is 0, and the average rate of change is 0, which means that the volume remain the same in the tank in the interval [4, 6]

d. The piecewise function for the graph can be presented as follows;

Slope in the interval [0, 2] is, m = (8,000 - 0)/(2 - 0) = 4,000

The equation is therefore, f(x) = 4,000·x

The equation in the interval [2, 6] is f(x) = 8,000

The slope in the interval [6, 9] is; m = (8000 - 0)/(6 - 9) = 8000/3 = 2666 2/3

The equation is; f(x) - 0 = 2666 2/3 × (x - 9) = (8000/3)·x - 24,000

The function in the interval [6, 9] is; f(x) = (8000/3)·x - 24,000

The piecewise function is therefore;

\(f(x) = \begin{cases}4000\cdot x & \text{ if } 0 \leq x \leq 2 \\ 8000 & \text{ if } 2 \leq x \leq 6 \\2666\frac{2}{3} & \text{ if } 6\leq x \leq 9 \end{cases}\)

Please find attached the possible graph of the function, obtained from a similar question on the internet;

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Answer:

84 or 66

hole it helps...

The moment of inertia (I) is a measure of an object's resistance to rotational motion around an axis. The moment of inertia of a cylinder can be calculated using the following formula:

I = (1/2) × m × r²

where:

I is the moment of inertia of the cylinder

m is the mass of the cylinder

r is the radius of the cylinder.

Here are the steps to calculate the moment of inertia for a cylinder:

Determine the mass of the cylinder. This can be done by weighing the cylinder on a scale or by using its density and volume. The formula for the mass of a cylinder is:

m = density × volume

Measure the radius of the cylinder. This is the distance from the center of the cylinder to its outer edge.

Substitute the values of m and r into the moment of inertia formula:

I = (1/2) × m × r²

Calculate the moment of inertia using a calculator.

Note that the moment of inertia of a hollow cylinder is different from that of a solid cylinder. To calculate the moment of inertia of a hollow cylinder, you need to subtract the moment of inertia of the hollow space from the moment of inertia of the solid cylinder using the parallel axis theorem.

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Answer:

16n + 41

Step-by-step explanation:

2(-n - 3) - 7(5 + 2n) (Given)

-2n - 6 - 35 - 14n (Distribute)

-16n - 41 (Add like terms)

16n + 41 (Divide by a factor of -1)

Answer:

B. -16n - 41

Step-by-step explanation:

Use the distributive property:

2(-n - 3) - 7(5 + 2n)

-2n - 6 - 35 - 14n

Combine like terms:

(-2n - 14n) + (-6 - 35)

-16n - 41

Answer:

\(\displaystyle y = 4x\)

Explanation:

Take a look at the endpoint of \(\displaystyle [10, 40].\) If you would just simply divide forty by ten, you will get your rate of change [slope] of four, leading you to the equation of \(\displaystyle y = 4x,\) especially because we are dealing with “direct variation”.

I am joyous to assist you at any time.

According to the figure the value of B is

The value of B is solved using the principles of segments of chords secants and tangents

The principle is such that

10^2 = 5 * (5 + b)

100 = 25 + 5b

gathering like terms

5b = 100 - 25

5b = 75

isolating b

b = 75 / 5

b = 15

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Answer:

No

Step-by-step explanation:

480 fruits/3 hours=160 fruits/hour average

550 fruits/5 hours=110 fruits/hour average

The equation of red graph is \(F(x) = 2 -x^{2}\).

The general equation of parabola is \(y = a(x-h)^{2} + k\).

Where,

(h, k) are the vertices of the parabola.

According to the given question.

We have two graph.

The blue and red graph both represents the equation of downward parabola.

Since, blue graph represents the equation of downward parabola.

Whose equation is given

\(G(x) = 5 - x^{2}..(i)\)

The general equation of a parabola is \(y = a(x-h)^{2} + k..(ii)\)

Where, (h, k) are the vertices of the parabola.

Compare the equation (i) with (ii)

We get

(h, k) = (0, 5) and a = -1.

Now, the red graph which also represents the downward parabola whose vertices are (0, 2)

Therefore, the equation red graph is given by

\(F(x) = a(x-0)^{2} + 2\)

⇒ \(F(x) = -1(x-0)^{2} + 2\)

⇒ \(F(x) = 2 - x^{2}\)

Hence, the equation of red graph is \(F(x) = 2 -x^{2}\).

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Answer:

awd

Step-by-step explanation:

The given conditions can be satisfied by the numbers 16 and 61.

The foundation of our entire number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number.

Given, The sum of the digits of two numbers is 7. The product the number and its reverse number are formed by Interchanging the digits is 976.

Let "xy" be the given two-digit number.

Thus,

x +y =7....(1)

and (10x+y)(10y + x) = 976

100xy + 10y² + 10x² + xy = 976

101xy + 10y² + 10x² = 976

From equation 1

707x - 101x² + 490 +10x² - 140x + 10x² = 976

-81x² + 567x = 486

x² - 7x + 6 = 0

Thus x = 1, 6

y = 6,1

Therefore, The number that satisfies the given conditions is 16 or 61.

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Answer. I think is A

Step-by-step explanation:

Answer:

75 and 76

Step-by-step explanation:

We can say that a's reduced row echelon form will have no zero rows.

Systems of linear equations can be solved using a type of matrix called reduced row echelon form.

If Ax = b has a unique solution for every b, then A must have full row rank, meaning that its reduced row echelon form will have no zero rows. This means that the reduced row echelon form of A will have a leading 1 in every non-zero row and will be in the form of an identity matrix. Therefore, the reduced row echelon form of A is the invertible matrix and A has a unique solution for every b.

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The value of x in the isosceles trapezoid ABCD is 7.

To find the value of x in the isosceles trapezoid ABCD, we can use the properties of isosceles trapezoids. In an isosceles trapezoid, the bases are parallel, and the legs (non-parallel sides) are congruent.

In this case, let's consider the legs of the trapezoid, AC and BD. Since the trapezoid is isosceles, AC is congruent to BD.

From the given information, we know that AD = 5x + 9 and BC = 8x - 12.

Since the legs of an isosceles trapezoid are congruent, we can set up the equation:

AD = BC

5x + 9 = 8x - 12

Now we can solve for x:

5x - 8x = -12 - 9

-3x = -21

Dividing both sides of the equation by -3, we get:

x = (-21) / (-3)

x = 7

Therefore, the value of x in the isosceles trapezoid ABCD is 7.

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Answer:

Step-by-step explanation:

Hello again

Step 1

12(5y+4)  Equation/Question

Step 2

12(5y+4)  Simplify

12(5y)+12(4)

Step 3

12(5y)+12(4)  Solve

answer

60y+48

Hope this helps

Answer:

55.83

Step-by-step explanation:

Divide the number of pounds by 2.2046 to use the standard equation.

Answer:

55.34 kg

Step-by-step explanation:

1 kg = 2.204 lbs

then

\(122 lbs\times \frac{1 \: kg}{2.204 \: lbs} \)

because lbs from the numerator will goes with lbs in the denominator the only unit remains is kg

so

122 ÷ 2.204 kg = 55.34 kg

Answer:

Step-by-step explanation:

Let H stand for the total number of Helen's coins and I for the total number of Ivan's coins.

We are told that H = I

We also know that Helen has 64 20-cent coins.  The total mass of her coins, H, is 1.134kg.

Ivan has 104 20-cent coins.  

We are told that both have a non-defined number of 50-cent coins.

(a) Who has more money in coins and by how much?

Since both have an equal number of coins, but Ivan has more 20-cent coins than Helen, Helen must therefore have a greater number of 50-cent coins, making her the richest of the two.

Helen has (H - 64) 50-cent coins

I has (I - 104) 50-cent coins

Since H=I, the ratio of Helen's to Ivan's 50-cent coins is (H-64)/(H-104)

But it is here that I don't know how to calculate the total value of coins, without more information.  All I know is that both have a known number of 20-cent coins, but I don't see an upper limit to the number of 50-cent coins.

Let's assume both had 200 coins.  The breakdown is shown in the attachment.

Sorry, I may see the answer tomorrow, but I need to leave now.

Answer:

(a) Helen, $12

(b) 1.026kg

Step-by-step explanation:

(a) Both have same no. of coins.

H [64x20cents] [40x50cents] [Ivan's 50cents]

   ↓SAME        ↓WEIGHT DIFF    ↓SAME

I   [64x20cents] [40x20cents] [Ivan's 50cents]

40x$0.50=$20

40x$0.20=$8

$20-$8=$12

(b) Helen's coins' mass = 1.134kg

                                       =1134g

Weight of the 40 of 50cents = 40x2.7g

                                                = 108g

Ivan's coin's mass = 1134g-108g

                              = 1026g

                              = 1.026kg

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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Answer:

\(7x^{2} - 2x\)

Step-by-step explanation:

combine like terms. not trying to be mean, but that all you have to do.

Answer:

14-2x

Step-by-step explanation:

collect like terms

3×2+4×2-2x-x-x

6+8-2x

=14-2x

The probability that there are no counts in a 30 second interval is 0.284

What is probability ?

Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Before we can determine the probability that a particular event will occur, we must first know the total number of outcomes.

Given that,

Assume that a Geiger counter records counts using a poisson process, with an average rate of 2 counts per minute.

0.284

P(X < 10 Seconds)  = P(X<1/6 minutes) = F(1/6) = 1-e-2*1/6 = 1-e-1/3 = 0.284

Therefore, the  probability that there will be no counts in a 30-second period is 0.284.

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The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

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Jen simulated her net income over 5 years assuming sales vary based on a normal distribution $100,000 and operating costs 60% and 65% of sales. keeping the loan payment be fixed at $13,000. The probability of making at least $12,000 each year is the number of successful simulations divided by 100. and at least $60,000 total over 5 years based as the number of successful simulations divided by 100.

To simulate Jen's annual net income over the next 5 years, a spreadsheet model can be created with columns for year, sales, operating costs, loan payment, and net income.

For each year, the sales can be generated from a normal distribution with mean $100,000 and standard deviation $10,000, and the operating costs can be generated from a uniform distribution between 60% and 65% of sales.

The loan payment can be fixed at $13,000, and the net income can be calculated as the difference between the sales, operating costs, loan payment, and taxes (28% of net income).

To find the probability that Jen will make at least $12,000 in each of the next five years, 100 simulations can be run using the model created in part a. For each simulation, the net income for each of the next five years can be calculated, and if the minimum net income is at least $12,000 for each year, then the simulation is counted as a success.

The probability of success can be calculated as the number of successful simulations divided by 100.

To find the probability that Jen will make at least $60,000 total over the next five years, 100 simulations can be run using the model created in part a. For each simulation, the total net income over the next five years can be calculated, and if it is at least $60,000, then the simulation is counted as a success.

The probability of success can be calculated as the number of successful simulations divided by 100.

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Let m be a fixed number in n. Then the function f(x) = xm is defined on all of r. To show that f(x) is continuous on r, we need to show that it is continuous at every point a in r.

Consider a fixed point a in r, and let ε > 0 be given. We want to find a δ > 0 such that if |x - a| < δ, then |f(x) - f(a)| < ε.

Since f(x) = xm, we have

f(x) - f(a)| = |xm - ma| = |m||x-a||x^(m-1) + am^(m-1)|.

Now, since m^(m-1) is a constant, we have that |x-a| < δ implies

|m||x-a||x^(m-1) + am^(m-1)| ≤ |m|(|x-a|)δ^(m-1) + |am^(m-1)|.

Therefore, if we choose δ such that

δ < ε / (|m|(δ^(m-1)) + |am^(m-1)|),

then we have

|f(x) - f(a)| < ε,

and hence f(x) is continuous at a. Since a was arbitrary, we conclude that f(x) is continuous on r.

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a) The expected winning probability for a single game defined is: $3.59

b) The standard deviation of winning is: $10.11

a) If the game costs $5 to play, the expected winnings are: - $0.79

If the game costs $5 to play, the standard deviation of winning is $11.33.

Because the projected winning value is negative, the game should not be played with a -$5 playtime charge.

The total number of hearts in a deck is 13.

The probability of drawing three hearts is:

P(drawing 3 Hearts)

13 ÷ 52 × 12 ÷ 51 × 11 ÷ 50 = 0.0129

The probability of selecting three black cards is:

A deck of black cards has 26 cards.

P (drew three black cards):

26 ÷ 52 × 25 ÷ 51 × 24 ÷ 50 = 0.1176

Any other draw probability: P(3 hearts) + P(3 blacks) + P(any other draw) = 1.

858 ÷ 66300 + 7800 ÷ 66300 + P(any other draw) = 1

P(any other draw) = 57642 ÷ 66300

For only one game,

E(X) = Σ[ X × p(X)]

E(X) =Σ[(50 × 858 ÷ 66300) + (25 × 7800 ÷ 66300)+0]

E(X) = $3.588

b) The standard deviation is equal to √Var(X)

Var(X) = Σ[ X² × p(X)] - E(X)

Σ[ X² × p(X)] = Σ[(50² × 858 ÷ 66300) + (25² × 7800 ÷ 66300) + 0] = 105.88235

Var(X) = 105.88235 - 3.588 = 102.29435

Winning standard deviation = √102.29435 = $10.114

If the game cost $5 to play :

The total sum won if and only if:

Three sketched hearts = $50 - $5 = $45

Three blacks are drawn for a total of $25 - $5 = $20.

Any other combination drawn = $0 - $5 = -$5

The distribution is as follows:

E(X) = Σ[ X × p(X)]

E(X) =Σ[(50 × 858 ÷ 66300) + (25 × 7800 ÷ 66300) + (-5 × 57642 ÷ 66300)]

E(X) = - $0.7588

The winning standard deviation is:

The standard deviation is equal to √Var(X)

Var(X) = Σ[ X² × p(X)] - E(X)

Σ[ X²×p(X)] = Σ[(50² × 858 ÷ 66300) + (25² × 7800 ÷ 66300) + (-5² × 57642 ÷ 66300)] = 127.61764

Var(X) = 127.61764 - (-0.7588) = 128.37644

The winning standard deviation is:

Std(X) = √Var(X) = √128.37644 = $11.330

With a game cost of - $5, the predicted winnings for a single game are negative, hence you should avoid playing the game.

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Answer:

Red balls =  84     Blue balls =  140

Step-by-step explanation:

Ok so there are 225 marbles

And ratio here is Red : Blue = 3 : 5

So Red marbles = 3x whereas Blue marbles = 5x

Therefore,

3x + 5x = 225

8x = 225

x = 28.125 = 28

Red balls = 28*3 = 84     Blue balls = 28*5 = 140

(Pls check whether total no of balls is 224)

The slant height of the cone is 24 cm. 

We are given that the surface area of the cone is 252.58 cm' with the radius of 6 cm.

The surface area of the cone is calculated through the equation as;

                   A = πr² + πrl

where r is the radius and l is the slant height.

Now Substituting the known values to the equation,

             252.58 = π(6 cm)² + π(6 cm)(l)

l = 24 cm.

Thus, the slant height of the cone is 24 cm. 

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Answer:

The answer is 28y + 63

Step-by-step explanation:

7(4y+9)

=28y+63