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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 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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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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The volume Colton store inside the new shed is 640 cubic feet.

We are given that;

length=10, width=8, height=6

Now, we can calculate the volumes of each part:

Volume of base prism = lwh Volume of base prism = (10)(8)(6) Volume of base prism = 480 cubic feet

Volume of roof prism = Bh Volume of roof prism = (0.5)(8)(4)(10) Volume of roof prism = 160 cubic feet

Volume of shed = Volume of base prism + Volume of roof prism Volume of shed = 480 + 160 Volume of shed = 640 cubic feet

Therefore, by the given prism the answer will be 640 cubic feet.

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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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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 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 value mean of variable 1 is approximately 170.42 and the median is 153.75.

We are given that;

Variable 1 = 190,187,186,183,182,182,181,181,180,164,161,160,140,158,156,155,152.5,151

Now,

To Find the mean by adding up all the values and dividing by the number of values

Mean = (190 + 187 + 186 + 183 + 182 + 182 + 181 + 181 + 180 + 164 + 161 + 160 + 140 + 158 + 156 + 155 + 152.5 + 151) / 18 Mean = (3067.5) / 18 Mean ≈ 170.42

Find the median by arranging the values in ascending order and locating the middle value

Median = (140 ,151 ,152.5 ,155 ,156 ,158 ,160 ,161 ,164 ,180 ,181 ,181 ,182 ,182 ,183 ,186 ,187 ,190) Median = (152.5 + 155) / 2 Median = (307.5) / 2 Median = 153.75

Therefore, by mean and median answer will be 170.42 and 153.75.

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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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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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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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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.

Consider the function f(x) = (x² - 4)/(x - 2).

For x gives us x = -2 and x = 2 which are the x-intercepts of f(x) and we have f(0) = -4/2 = -2 which is the y-intercept of f(x)

What is meant by function?

A function is a mathematical rule that assigns a unique output value for each input value in a specified domain. It is a relationship between two or more variables that describes how one variable depends on the others.

What is meant by the x-intercept?

The x-intercept of a function is the point where the graph of the function intersects the x-axis. It is the value of the input variable (usually denoted as x) that makes the output of the function equal to zero.

According to the given information

Consider the function f(x) = (x² - 4)/(x - 2). To find the x-intercept, we set f(x) = 0 and solve for x. We get (x² - 4)/(x - 2) = 0 which means that x² - 4 = 0 since division by zero is undefined. Solving for x gives us x = -2 and x = 2 which are the x-intercepts of f(x). To find the y-intercept, we set x = 0 and solve for y. We get f(0) = -4/2 = -2 which is the y-intercept of f(x)

The complete question is:

For this rational function, Use algebra to find the x-intercepts and

y-intercepts. The given function is f(x) = (x² - 4)/(x - 2)

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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

Answer:8

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

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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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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For the given figure the measurement or lengths are:

AB = 4.5 cm.

ED = 9 cm.

DF = cannot be determined since it is a chord and it needs more information.

CA = 4.5 cm.

We have the radius of the given circle is 4.5 cm.

Now we have to find the lengths of the mentioned line segment from the circle figure.

A is the center of the circle and B is a point on circumference of circle.

So, AB is a radius of the circle. So, AB = 4.5 cm.

Now, E and D are two points on circumference of circle and segment ED passes through the center A.

So, ED is a diameter for the circle.

We know that Diameter = 2*Radius

So, ED = 2*4.5 = 9 cm.

F and D are two points on circumference of circle but segment DF does not pass through the center A. So it is not diameter it is a general chord.

So we cannot determine this due to inadequate information.

A is the center of the circle and C is a point on circumference of circle.

So, CA is a radius of the circle. So, CA = 4.5 cm.

Hence, AB = 4.5 cm.; ED = 9 cm.; DF = cannot be determined; CA = 4.5 cm.

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The question is incomplete. The complete question will be -

"The circle below has a center at point A and a radius of 4.5 cm.

Find the measurement of the line segments that you can determine. For anyone you cannot determine, explain your reasoning why.

Segment AB

Segment ED

Segment DF

Segment CA"

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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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

Answer:

For this question you can use simultaneous equation, both elimination method or substitution method. In math when you are trying to solve for something but you don't have the answer to it, you can always use x.

soooo
5x + 3y = 27 (equation 1)

7x + 9y = 51 (equation 2)

soo im using substitution method

From equation 1, we can solve for y in terms of x:

y = (27 - 5x) / 3

Substitute this expression for y into equation 2 and solve for x:

7x + 9[(27 - 5x) / 3] = 51

Multiplying both sides by 3 to eliminate the fraction:

21x + 27 - 15x = 153

Simplifying and solving for x:

6x = 126

x = 21

Now, we can substitute this value for x into either equation 1 or equation 2 to solve for y:

5(21) + 3y = 27

105 + 3y = 27

3y = -78

y = -26

Since a negative cost doesn't make sense, we need to double-check our work. We made an error by switching the signs of the cost variables in our equations. So, the correct answers are:

The cost per pound of almonds is $21.

The cost per pound of jelly beans is $26.

Answer:

h

Step-by-step explanation:

Answer:

Step-by-step explanation:

Based on the expression, the answer to the question is, and the condensed expression is 1/(25k²).

A value is represented by an expression, which is made up of symbols, variables, constants, and operators. Expressions are used in computer programming to alter data and carry out calculations. Expressions may be straightforward or intricate, and they may contain arithmetic, logical, or conditional assertions. Expressions in mathematics can stand in for equations, functions, and other abstract ideas. Expressions can be used to describe actual phenomena, such as how things move or how systems behave.

To simplify the expression (1/5k)², we square the numerator and denominator separately, as follows:

(1/5k)² = (1²) / (5k)²

= 1 / (25k²)

Therefore, the simplified expression is 1/(25k²).

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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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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 complete statement is -

There have been two especially important shifts in how markets are defined in recent decades: one involves technology  and the other involves globalization.

Given is that there have been two especially important shifts in how markets are defined in recent decades. It is asked to fill in the blanks with correct values.

We can fill the statement as -

There have been two especially important shifts in how markets are defined in recent decades: one involves technology  and the other involves globalization.

Therefore, the complete statement is -

There have been two especially important shifts in how markets are defined in recent decades: one involves technology  and the other involves globalization.

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The probability that a student randomly chooses to play drums is  34.29%

The total number of students in seventh grade = 35

The number of students who choose drums in seventh grade is 14

The total number of students in eighth grade = 35

The number of students who choose drums in eighth grade is 10

Total number of students who play drums = 14 + 10 = 24

Total number of students = 35 + 35 = 70

The probability that a student randomly chooses to play drums is:

Probability = Total number of students who play drums / Total number of students

Probability = 24 / 70

Probability = 0.342857 (rounded to 6 decimal places)

probability = 34.29%

Hence,  the probability that a student randomly chooses to play drums is  34.29%

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