Write an expression to represent: 1 more than the quotient of x and 4.

The only ordered pair that is a solution to the given system of inequalities is (0, -1).

Inequalities are mathematical statements that describe a relationship between two values or expressions that are not necessarily equal. In an inequality, the symbols "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to) are used to indicate the relationship between the expressions.

In the given questions,

To determine if an ordered pair is a solution to a system of inequalities, we must check if the pair satisfies all the inequalities in the system.

For the given system of inequalities:

y < -x² + x

y > x² - 4

Checking each of the given ordered pairs:

(0, -1):

-1 < -0² + 0 is true

-1 > 0² - 4 is true

So, (0, -1) is a solution to the system of inequalities.

(1, 1):

1 < -1² + 1 is false

1 > 1² - 4 is true

So, (1, 1) is not a solution to the system of inequalities.

(2, -3):

-3 < -2² + 2 is true

-3 > 2² - 4 is false

So, (2, -3) is not a solution to the system of inequalities.

(3, -6):

-6 < -3² + 3 is false

-6 > 3² - 4 is false

So, (3, -6) is not a solution to the system of inequalities.

Therefore, the only ordered pair that is a solution to the given system of inequalities is (0, -1).

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The values of the trigonometry ratios are sin(21) = √(1 -  k²), cos(201) = -k,  cos(42) = 2k² + 1 and cos(51) = k√3/2 - 1/2√(1 -  k²)

Given that cos 21° =k

Next, we calculate the trigonometry ratios as follows

(1) sin 21°

Here, we use

sin²(x) + cos²(x) = 1

So, we have

sin²(21) + cos²(21) = 1

This gives

sin²(21) + k² = 1

By subtraction, we have

sin²(21) = 1 -  k²

Take the square roots

sin(21) = √(1 -  k²)

(2) cos 201⁰

This is calculated using

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

So, we have

cos(180 + 21) = cos(180)cos(21) - sin(180)sin(21)

Evaluate the ratios

cos(201) = -1 * k - 0 * √(1 -  k²)

So, we have

cos(201) = -k

(3) cos 42°

Here, we have

cos(a + a) = cos²(a) - sin²(a)

So, we have

cos(21 + 21) = cos²(21) - sin²(21)

Evaluate the ratios

cos(42) = k² + 1 +  k²

So, we have

cos(42) = 2k² + 1

(4) cos 51°

This is calculated using

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

So, we have

cos(30 + 21) = cos(30)cos(21) - sin(30)sin(21)

Evaluate the ratios

cos(51) = √3/2 * k - 1/2 * √(1 -  k²)

So, we have

cos(51) = k√3/2 - 1/2√(1 -  k²)

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Answer:

271.17 is the answer

Step-by-step explanation:

we know that the housing and fixed expenses of $813.52/month.

6 months emergency funds 

= 813.52 × 6 = 4881.82

We know that you want to have it funded in 18 months

put it fraction will solve the problem:

[tex]\frac{4881.12}{18}[/tex] = 271.17

271.71 being the answer

According to the data, Alondra would have to save $275 each month if she wants to have $7,000 after two years.

To calculate the savings that Alondra must make to have $7,000 after 2 years we must carry out the following procedure:

First, we must subtract $400 from her initial contribution to your savings.

$7,000 - $400 = $6,600

Then we must divide $6,600 into the number of months that are 2 years (24 months).

$6,600 / 24 = $275

Based on the above, if she saves $275 of her salary each month, she will have $7,000 after 2 years. This is possible because her monthly payment is $358.41

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Lily will need to invest $16,483.29 in the account now to have $40,000 in 18 years.

The two types of interest computations utilised in finance are simple interest and compound interest.

Simple interest is just computed on the principal, or the initial amount borrowed or invested. For a specific amount of time, the interest rate is applied to the principal sum, and each period's interest earned or charged is the same.

On the other hand, compound interest is calculated using both the original principal and any prior interest payments. The principal is increased by the interest generated in each month, and the new sum serves as the foundation for computing interest in the following period.

The compound interest is given by the formula:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

Isolating the value of P we have:

[tex]P = A/(1 + r/n)^{(nt)}[/tex]

Now, substituting the values A = $40,000, r = 0.06 (6% as a decimal), n = 2 (compounded semi-annually), and t = 18 years:

[tex]P = $40,000/(1 + 0.06/2)^{(2*18)}\\P = $40,000/(1.03)^{36}[/tex]

P = $40,000/2.4271

P = $16,483.29

Hence, Lily will need to invest $16,483.29 in the account now to have $40,000 in 18 years.

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Step-by-step explanation:

the first one appears to be exponential

the second one cuadratic

the last one, cuadratic aswell

a) The range of values that the game operator can use to represent a winner getting a stuffed animal is given as follows:

1 to 45.

b) The percentage of the 10 simulated winners who got a stuffed animal is of: 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There is a 45% theoretical probability of getting a stuffed animal, hence the range of values can be given as follows:

1 to 45.

From the table, out of 10 winners, 4 have numbers ranging from 1 to 45, hence the percentage is given as follows:

p = 4/10 x 100%

p = 40%.

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The equation of the graph is y = 2sin(πx) with  a period of 2 and an amplitude of 2

The general equation for a sine function is:

y = A × sin(Bx)

Where A represents the amplitude and B represents the frequency, which is related to the period of the function.

In this case, the given period is 2, which means the frequency (B) can be calculated as:

B = 2π / period = 2π / 2 = π

The given amplitude is 2 (A = 2).

Therefore, the equation of the graph is y = 2sin(πx)

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Answer:

B) Permutation.

Answer:8

Step-by-step explanation:2*1+3*2=8

Answer:

h

Step-by-step explanation:

From the table, we can see that the probability of selecting exactly 8 girls is 0.183.

Therefore, the answer is:

P(x=8) = 0.183

The probability of selecting exactly 8 girls out of a sample of 14 newborn babies is 0.183 or approximately 18.3%.

It is a branch of mathematics that deals with the occurrence of a random event.

The given table shows the probabilities of selecting different numbers of girls (x) out of a sample of 14 newborn babies.

The probability of selecting exactly 5 girls is 0.122, which means that in a large number of random samples of 14 newborn babies

We would expect to find approximately 0.122 × (total number of samples) with exactly 5 girls.

To find the probability of selecting exactly 8 girls, we look at the value in the table for x = 8, which is 0.183.

Therefore, the probability of selecting exactly 8 girls out of a sample of 14 newborn babies is 0.183 or approximately 18.3%.

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Answer:

294

Step-by-step explanation:

First, we can find the area of one of the cube's sides.

A = length × width

A(side) = 7 × 7

A(side) = 49

We know that a cube has 6 sides. Therefore, to get the surface area of the cube, we can multiply the area of 1 side by 6.

SA = A(side) × 6

SA = 49 × 6

SA = 294

The estimated values of a and b are given below:

The probability of Type I error (false positive) is denoted by a.

The probability of Type II error (false negative) is denoted by b.

Data provided:

In 6,500 computer sessions with no intrusions, only 13 resulted in a false alarm.

Hence, the probability of a false alarm is 13/6,500 = 0.002.

Therefore, the estimated value of a = 0.002

Only 500 were detected out of 2,000 intrusions.

Hence, the probability of a missed detection is (2,000 - 500)/2,000 = 0.75.

The probability of true positive is 500/2,000 = 0.25

The estimated value of b will be 1 - true positive rate = 1 - 0.25

b = 0.75

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The length of the missing leg is √29 units

Given that c=5 km and b=2 km

We have to find the value of a

The length of the missing leg is a which is hypotenuse which we have to find.

c²+b²=a²

5² + 2² =a²

25+4=a²

29=a²

Square root on both sides

a=√29 units

Hence, the length of the missing leg is √29 units

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The other two angle of rotation that connect A and B are 3π/4 radians and -13π/4 radians

To rotate point A to point B, we are rotating -5π/4 radians counterclockwise from the positive x-axis. To find two other angles of rotation that take A to B, we can add or subtract multiples of 2π radians, since this will result in a full revolution around the unit circle.

First, to find a negative angle of rotation that takes A to B, we can subtract 2π radians from -5π/4 radians:

-5π/4 - 2π = -13π/4

This tells us that rotating point A -13π/4 radians (or 3π/4 radians clockwise) will take it to point B.

Next, to find a positive angle of rotation that takes A to B, we can add 2π radians to -5π/4 radians:

-5π/4 + 2π = 3π/4

This tells us that rotating point A 3π/4 radians counterclockwise will take it to point B.

Therefore, the other two angle of rotation that connect A and B are 3π/4 radians and -13π/4 radians

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The amount of annuity is $56,935.

the amount of annuity can be calculated by the use following the formulation:

[tex]A = R * ((1 + r)^n - 1) / r[/tex]

Wherein:

In this case, we've:

R = $1000

r = 6.2% = 0.062

n = 18

So, plugging in the values, then we will get the value as:

[tex]A = $1000 * ((1 + 0.062)^{18 }- 1) / 0.062[/tex]

A = $1000 * (4.238 - 1) / 0.062

A = $1000 * 56.935

A = $56,935

Consequently, the amount of annuity is $56,935.

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Answer:

Step-by-step explanation:

Let's use the given information to set up two equations involving the number of minutes and the number of miles, and then solve for those variables.

First, we know that the total cost of the ride is the sum of the flat fee, the cost per minute times the number of minutes, and the cost per mile times the number of miles. So we have:

$18.70 = 4 + 0.20x + 1.50y$

We also know that the number of minutes is three times the number of miles, so we have:

$x = 3y$

Now we can substitute the second equation into the first equation and solve for y:

$18.70 = 4 + 0.20(3y) + 1.50y$

$18.70 = 4 + 0.60y + 1.50y$

$18.70 = 4 + 2.10y$

$14.70 = 2.10y$

$y = 7$

So the number of miles for this trip is 7. Using the second equation, we can find the number of minutes:

$x = 3y = 3(7) = 21$

Therefore, the number of minutes for this trip is 21.

Answer:

Step-by-step explanation:

You want the minutes and miles for a trip that had a total cost of $18.70, which included a $4 flat fee, and $1.50 per mile plus $0.20 per minute. The number of minutes was 3 times the number of miles.

If each mile had a charge of $1.50 plus a charge for 3 minutes at $0.20 per minute, the effective travel charge per mile was ...

  $1.50 +3(0.20) = $2.10 per mile

The total cost of the trip included a fixed $4 fee plus the travel charge, so the travel charge was ...

  travel charge = total - fixed fee = $18.70 -4.00 = $14.70

The number of miles that result in this travel charge is ...

  $14.70 / ($2.10/mile) = 7 miles

The number of minutes is 3 times this, or ...

  (7 miles)·(3 minutes/mile) = 21 minutes

The charge was for 21 minutes and 7 miles.

__

Additional comment

Often, when there is a fixed relationship between elements of a problem, it is convenient to combine them in a group. The equation for the number of groups is often much simpler, even to the point of allowing you to solve the problem mentally. Here, our "group" was 1 mile and 3 minutes.

This can be a useful strategy even when there is an excess. For example, if there are 3 more nickels than quarters, we know those 3 nickels add 15¢ to the value of the 30¢ groups that consist of 1 quarter and 1 nickel. When you find the number of groups, you immediately know the number of quarters. You have to add 3 to get the number of nickels.

The scientific notation of the given number is 1.24×10⁻⁶.

The given number is 0.00000124.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Here, 0.00000124=1.24×10⁻⁶.

Therefore, the Scientific notation of the given number is 1.24×10⁻⁶.

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Check the picture below.

[tex]\tan(48.8^o )=\cfrac{\stackrel{opposite}{1.6}}{\underset{adjacent}{b}} \implies b=\cfrac{1.6}{\tan(48.8^o)}\implies b\approx 1.4 \\\\[-0.35em] ~\dotfill\\\\ \sin(48.8^o )=\cfrac{\stackrel{opposite}{1.6}}{\underset{hypotenuse}{c}} \implies c=\cfrac{1.6}{\sin(48.8^o)}\implies c\approx 2.1[/tex]

Make sure your calculator is in Degree mode.

1. The transformation here is the vertical transformation

2. This is a horizontal transfprmation

3. This is a 90 degree clockwise rotation

In mathematics, 'transformation' signifys a performance or executable that modifies the positioning, orientation, magnitude, or silhouette of a geometric shape or set of coordinates while preserving specific features.

Transformations are a prevalent idea in various sections of math, including geometry, linear algebra and functional appraisals. Below are some of the generality popular metamorphoses:

Translation: A transformation that migrates each point of an item by the equivalent length in the equivalent direction. This does not adjust the subject's scale or facing.

Rotation: A conversion that rotates a subject round a pin-point termed the center of rotation, by a distinct angle.

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Answer:

Ok, let's follow the steps:

1 million + 257 million = 258 million

258 million - 1090 million = -832 million

Now, I'm not sure what you mean by "add the remainder", since we don't have any remainder to add. However, if you meant "add the absolute value of the remainder", we can do that. The absolute value of -832 million is 832 million. So, adding that to our result, we get:

-832 million + 832 million = 0

Therefore, the final result is 0.

The inequality that represents the number line given in the image above is: D. x > -1.

A number line is a straight line that represents the set of real numbers, with each point on the line corresponding to a unique real number, as shown in the given diagram above.

There's an unshaded or open circle on the number -1, and an arrow extending from zero to your right. This means that -1 is not included in the possible values of x. It also means the x is greater than -1.

Therefore, the inequality is: D. x > -1.

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Answer: The possible length of the third side is probably 23cm.

All I did was add 9cm and 15cm which equaled 24cm and you could give that answer or any other number below 24.

Answer:

  7 ≤ s ≤ 23; any number of centimeters between 7 and 23 cm.

Step-by-step explanation:

You want to know possible lengths of the third side of a triangle with side lengths 9 cm and 15 cm.

The triangle inequality requires the sum of the two shorter side exceed the longest side. When two sides are given, this means the length of the third side lies between their difference and their sum.

The third side s must satisfy ...

  15 -9 < s < 15 +9

  6 < s < 24

The third side can have any whole number value between 7 cm and 23 cm, inclusive. For example, it might be 7 cm or it might be 20 cm.

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The degree of each vertex is 4, 1, 2, 3, and 2.

To find the degree of each vertex in a graph, you need to count the number of edges that are incident on that vertex.

The degree of a vertex is the number of edges connected to it. Here are the steps you can follow to find the degree of each vertex in a graph:

1. Identify all the vertices in the graph.

2. For each vertex, count the number of edges that are incident on it. To do this, you can follow the edges that are connected to the vertex and count them.

3. Record the degree of each vertex.

Here we have a graph

The number of vertices in the graph is 5

Let's name each vertex as shown in the figure  

To vertice A, 4 edges are connected

Hence, the degree of vertice A is 4

To Vertice B, 1 edge is connected

Hence, the degree of vertice B is 1

Similarly

Degree of Vertice C is 2

Degree of vertice D is 3

Dergree of vertice E is 2

Therefore,

The degree of each vertex is 4, 1, 2, 3, and 2.

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The within-treatments sum of squares is sometimes referred to as the "error sum of squares" because it represents the amount of variability in the data that is not accounted for by the treatment effect. In other words, it represents the variability that is due to random error or chance factors that are not related to the treatment. The error sum of squares is used to estimate the variance of the population from which the samples were drawn. The F-ratio is then calculated by comparing the treatment mean square to the error mean square. If the treatment effect is significant, then the treatment mean square will be larger than the error mean square, resulting in a larger F-ratio and a rejection of the null hypothesis. Therefore, the error sum of squares is an important component of the ANOVA table as it helps to determine whether the treatment effect is significant or not.

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Answer:

1. Let’s assume that the original garden was a rectangle with width w and length l. After extending it by equal length on two sides, we get a new rectangle with width w+2x and length l+2x. The area of the new rectangle is (w+2x)(l+2x). To find the area of the extended area only, we need to subtract the area of the original garden from the area of the new rectangle. The area of the original garden is wl. Therefore, the polynomial that represents how much square foot of soil you need to cover the extended area only is:

(w+2x)(l+2x) - wl

which can be simplified as:

wl + 2lx + 2wx + 4x^2 - wl

The polynomial can be further simplified as:

4x^2 + 2lx + 2wx

2. If the original garden was extended by 6 ft on each side, then the new garden will be extended by 175% 1.

To calculate this percentage, we can use the formula:

% increase = (new value - old value) / old value * 100%

The original garden has an area of 64 square feet (8 feet x 8 feet). If we extend each side by 6 feet, then the new garden will have an area of 196 square feet (14 feet x 14 feet).

So, using the formula above:

% increase = (196 - 64) / 64 * 100%

% increase = 132 / 64 * 100%

% increase = 206.25%

Therefore, if the original garden was extended by 6 ft on each side, then the new garden will be extended by 206.25% 1.

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

The transformations that would lead to ABCD being carried onto itself would be:

For shapes to be transformed such that they are carried into themselves, a reflection can be used if the line of reflection is at the midpoint of the shape. That way, when reflected, it is reflected into itself.

Looking at ABCD, we see that y = 2 would be the midpoint horizontally. This transformation would therefore carry it into itself. The same is true for x = 3.

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The calculated value of the tangent of J is tan(J) = √35/√79 or tan(J) = √2765/79

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

Opposite = √35

Adjacent = √79

The tangent of J is calculated as

tan(J) = Opposite/Adjacent

Substitute the known values in the above equation, so, we have the following representation

tan(J) = √35/√79

So, we have

tan(J) = √2765/79

Hence, the solution is √2765/79

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The slope of the line is given as follows:

m = -1/8.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

From the table, we have that when x increases by 8, from x = -16 to x = -8, y decays by one, from y = 8 to y = 7, hence the slope m is given as follows:

m = -1/8.

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