matching question match the sets on the left with a true statement about the cartesian product of those sets on the right. {1, 2} x {3, 4} = {1, 2, 3, 4} x {3, 4, 5, 6} = {4, 5, 6, 7} x {4, 5, 6, 7} = {a, e, i, o, u} x {b, g, t, d} =
{1, 2, 3} x {1, 2, 4} =
Choose:
(5, 5) is a member.
its cardinality is 4. (2, 2) is a member. its cardinality is 20.
(4, 3) is a member.

Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.

The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.

Exponential decay equation is one of the two exponential functions.  The other is the exponential growth equation.

The annual decrease in the number of employees = 5%

The current number of employees in the company = 860

The expected time = 10 years.

The exponential decay equation is as follows, y = 860 x 0.95^10.

y = 860 x 0.95^10 = 515

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Answer:

[tex]5x {}^{3} - x + 5x + 2[/tex]

Step-by-step explanation:

Greetings!!!

So to find the sum of (f+g)(x) just simply add these two functions

Add like terms together

If you have any questions tag it on comments

Hope it helps!!!

The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.

To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.

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Answer:

Step-by-step explanation:

(a) Dataset with mean substantially less than median:

9, 10, 11, 12, 90

The mean of this dataset is (9+10+11+12+90)/5 = 26.4, while the median is 11, which is substantially greater than the mean. The last data value is 90, which is a positive integer less than 100.

(b) Dataset with mean substantially more than median:

98, 99, 100, 101, 200

The mean of this dataset is (98+99+100+101+200)/5 = 119.6, while the median is 100, which is substantially less than the mean. The last data value is 200, which is a positive integer less than 100.

(c) Dataset with mean equal to median:

2, 3, 4, 4, 5

The mean of this dataset is (2+3+4+4+5)/5 = 3.6, which is equal to the median (the middle value of the dataset). The last data value is 5, which is a positive integer less than 100.

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As a result, the percentage of adults who selected math is different from the percentage of kids who did.

As a number out of 100, a percentage is a method to express a proportion or a fraction. It is symbolized by the number %. If there are 25 boys in a class of 100 pupils, for instance, then there are 25% of boys in the class. It is a helpful method to compare quantities and to express changes in values over time.

given

120 80

Total    200

Women Overall Party A Party B

70 60

Overall    130

Therefore, there are 130 ladies in the group.

b) The chart indicates that 70 women plan to support Party A.

Thus, the percentage of adults who selected English was 40% of 48, which is equal to 0.4 times 48 and 19.2 when rounded to the closest whole number.

b) Reeshma is not accurate. The percentage of adults who selected math is 35%, while for children it is 40%, according to the pie chart.

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The complete question is:-   complete the two-way table, which shows the voting intentions of a group of men and women. a How many women are in the group?

Men

Party A Party B 120

Total    200

Women   130

Total       380

b How many women intend to vote for Party A?

2 A group of 48 adults are asked what their favourite subject was at school. They can choose from

maths, English and science.

A group of 32 school children are asked the

same question.

None of the available options match the parabola's equation.

To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.

A parabola's vertex form is given by:

[tex]y = a(x-h)^2 + k[/tex]

where (h,k) is the parabola's vertex.

[tex]y = a(x-5)^2 - 3[/tex]

These values are substituted into the equation to produce:

[tex]-15 = a(2-5)^2 - 3[/tex]

[tex]-15 = 9a - 3[/tex]

[tex]-12 = 9a[/tex]

[tex]a = -4/3[/tex]

[tex]y = (-4/3)(x-5)^2 - 3[/tex]

This equation is expanded and simplified to produce:

[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]

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The perimeter of the figure is 16p + 10.

The whole length of a two-dimensional or three-dimensional shape's sides or edges is known as its perimeter. It is frequently referred to as the shape's perimeter or circumference. It is possible to determine the perimeter of many geometric forms with accuracy. The perimeter is a key idea in geometry and has several practical uses, such as determining the radius of a circular racetrack or determining the length of fencing required for a certain property.

The perimeter of a figure is the sum of the lengths of all its sides.

Thus,

Perimeter = (p - 9) + (7p + 5) + (p - 9) + (7p + 5)

Perimeter = 2p + 2(7p) + 2(5)

Perimeter = 16p + 10

Hence, the perimeter of the figure is 16p + 10.

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A patient weighing 220 pounds needs 293 milligrams of medicine.

We have given that,

patient weighing 162

pounds requires 216 milligrams of medicine

We have to calculate the amount of medicine required by a patient weighing 220 pounds

Consider the value of amount of medicine is x.

Set up a proportion.

pounds / milligrams of medicine

What is the proportion we get?

[tex]162/216=220/x[/tex]

So,

[tex]162/216=220/x[/tex]

[tex]162x=216\times220[/tex]

[tex]162x=47,520[/tex]

[tex]x=47,520/162[/tex]

[tex]x=293[/tex]

A patient weighing 220 pounds needs 293 milligrams of medicine.

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The height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000 cm² is equals to the 159.24 cm.

The area obtained after substracting the circular area from the total area of the cylinder is called as curved surface area. Curved surface area is calculated by formula, 2πrh

where r --> radius of cylinder

h --> height of cylinder

π --> math special constant

We have an open cylinder with the following dimensions,

Radius of cylinder, r = 8 cm

Curved surface area of cylinder, A = 1000 cm². We have to calculate the height of this open cylinder. Let the height of an open cylinder be 'h cm' . Using the above formula, height of cylinder, h = curved Area/ 2πr

=> h = A/2π

=> h = 1000/2 ( 3.14)

=> h = 1000/6.28

=> h = 159.24

Hence, required value of height is 159.24 cm.

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To understand why b = d = 0 if the function is even, we need to consider the definition of an even function.Therefore If P(x) is an even function, then b = d = 0.

A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. It can have one or more terms and can be of any degree.

An even function is a function that satisfies the condition f(x) = f(-x) for all x in the domain of the function.

If P(x) is an even function, then we have P(x) = P(-x) for all x. Substituting -x for x in the expression for P(x), we get:

P(-x) = a(-x)⁴ + b(-x)³ + c(-x)² + d(-x) + e

= a(x⁴) - b(x³) + c(x²) - d(x) + e

Since P(x) = P(-x), we can equate the two expressions for P(x) and P(-x) to get:

a(x⁴) + b(x⁴) + c(x²) + d(x) + e = a(x⁴) - b(x³) + c(x²) - d(x) + e

Simplifying this equation, we get:

2b(x³) + 2d(x) = 0

Since this equation holds for all values of x, we can set x = 0 to get:

2d(0) = 0

which implies that d = 0. Similarly, setting x = 1, we get:

2b(1³) + 2d(1) = 0

2b = 0

b = 0

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To conclude, the probability of the Acme Drug Company seeing a percent difference of -.13 or less if the true difference is 0 is quite low and is equal to 0.0934.

The probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is quite low. This is because a difference of -.13 is a very small percentage in comparison to a true difference of 0.

Mathematically, the probability of this happening would be equal to the area under the standard normal distribution curve for values between -0.13 and 0. In other words, the probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is equal to the area from the left tail of the standard normal distribution curve up to the mean (0) of the curve.

Using a standard normal distribution calculator, we can see that the probability of the Acme Drug Company seeing a percent difference of -.13 or less is 0.0934. This probability is extremely low and it is not likely that the Acme Drug Company would experience such a small percent difference.

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Answer:

See Below.

Step-by-step explanation:

To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.

In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.

Perimeter = 8 cm + 10 cm + 16 cm + 10 cm

Perimeter = 44 cm

Therefore, the perimeter of the trapezoid is 44 cm.

The smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

To determine the smallest value of n for which S_n has an element of order greater than or equal to 100, we can use the formula

S_n = n!/r!(n - r)!,

where n is the number of elements in the set, and r is the number of elements being chosen at a time.

Given, S_n has an element of order greater than or equal to 100. The smallest value of n should be determined.

The formula for the number of permutations in a set with n elements is given by, `S_n = n!/r!(n - r)!`

where `n` is the number of elements in the set and `r` is the number of elements being chosen at a time.

The element of order `n` in `S_n` is an `n` cycle. For `n = 100`, we have an element of order 100.

This element can be expressed as `(1 2 3 ... 99 100)`. Thus, `r = 100`.

Substituting these values in the formula of S_n we get, S_n = n!/r!(n - r)! => n!/(100!(n - 100)!)

Now, we have to find the smallest value of n for which S_n has an element of order greater than or equal to 100. If we substitute `n = 100`, then we will have an element of order 100. But the question asks for the smallest value of n. So, if we substitute `n = 101`, we will have an element of order `101`. Hence, the smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

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The total resistance of the circuit is  6 + 2i.

Resistance is a unit of measurement for the resistance to current flow in an electrical circuit. The Greek letter omega () represents the unit of measurement for resistance, which is ohms.

Georg Simon Ohm (1784–1854), a German physicist who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance known as an ohm.

The amount of opposition any object applies to the flow of electric current is known as resistance. A resistor is an electrical component utilised in the circuit to provide that particular level of resistance. R = V I is a formula used to calculate an object's resistance.

given :

R1 =  (4 + 6i)

R2 = (2 - 4i)

total resistance of the circuit is

R = R1 + R2

= (4 + 6i) + (2 - 4i)

= 6 + 2i

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The equation RT = + R1 = 4 + 6i ohms and R2 = 2 4i ohms, RT = 6 - 2i ohms, determines the circuit's total resistance.

R1 and R2 are added to determine RT: RT = R1 + R2.

The actual components added together give us 4 + 2 = 6.

When we add the fictitious parts, we obtain 6i - 4i = 2i.

RT is thus equal to 6 - 2i ohms.

To put it another way, the circuit's total resistance is a complex number containing a real component of 6 ohms and an imaginary component of -2 ohms. This shows the combined impact of the circuit's resistances R1 and R2. When a constant voltage differential of one volt (V) is supplied to two conductor points and a current of one ampere (A) results, the resistance between those points is measured in ohms. It is comparable to one volt for every ampere (V/A), to put it simply.

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The probability of randomly drawing a penny is 6/24 or 1/4, since there are 6 pennies out of a total of 24 coins.

How to solve and What is Probability?

The probability of randomly drawing a quarter is 10/24 or 5/12, since there are 10 quarters out of a total of 24 coins. The probability of randomly drawing a coin that is not a penny is 18/24 or 3/4, since there are 18 coins that are not pennies out of a total of 24 coins.

Probability is the branch of mathematics that deals with measuring the likelihood or chance of an event or outcome occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Probability theory is used to make predictions and informed decisions based on available data in various fields, including statistics, finance, engineering, and science.

It involves understanding and analyzing random events, and determining the likelihood of specific outcomes. Probability is an essential tool for decision-making in various applications, such as risk analysis, game theory, and quality control.

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Ryan makes a profit of £240.  the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

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Answer: 4.5

Step-by-step explanation:

A^2 +B^2 =C^2

A^2 + 6^2 =7.5^2

A^2 + 36= 56.25

A^2= 20.25

A= square root of 20.25

A= 4.5

Answer:

the numbers are

[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]

Step-by-step explanation:

then there difference is

square root of 10 + 5 -(- square root of 10 +5)

=

[tex]2 \sqrt{10} [/tex]

and the cube of there sum is 15^3 = 15* 15* 15

= 3375

Answer:

Solve the problems. a) The number a is 4/5 of the number b. What part of number a is number b?

Step-by-step explanation:

a) If a is 4/5 of b, then b is 5/4 of a.

To find what part of a is b, we divide b by a:

b/a = 5/4

This means that b is 5/4 times larger than a, or b is 125% of a.

To find what part of a is b, we subtract 1 from this fraction:

b/a - 1 = 5/4 - 1

b/a - 1 = 1/4

So, b is 1/4 of a, or b is 25% of a.

Answer:

576 books.

Step-by-step explanation:

134+254+188=576 books in total.

Answer:

576

Step-by-step explanation:

This is literally easy!

Checked books are 134 + 254 + 188 = 576

Answer:

the cross is the blue color

Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem

To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.

A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:

Sum of measures of interior angles of triangle = (n-2) × 180 degrees

= (3-2) × 180 degrees [since we are dealing with a triangle]

= 1 × 180 degrees

= 180 degrees

Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.

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Answer: $15.25

Step-by-step explanation:

Let x be the number of apples purchased and y be the number of mangos purchased. Then we have the following constraints:

2.25x + 1.25y ≤ 20 (Jose has $20 to spend)

x + y ≥ 9 (Jose must buy at least 9 apples and mangos altogether)

x ≥ 3 (Jose must buy at least 3 apples)

y ≤ 9 (Jose can buy at most 9 mangos)

To solve this system of inequalities graphically, we can plot the relevant lines and shade the feasible region.

First, we graph the line 2.25x + 1.25y = 20 by finding its intercepts:

When x = 0, we have 1.25y = 20, so y = 16.

When y = 0, we have 2.25x = 20, so x = 8.89 (rounded to two decimal places).

Plotting these intercepts and connecting them with a line, we get:

     |       *

 16  |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    8.89

Next, we graph the line x + y = 9 by finding its intercepts:

When x = 0, we have y = 9.

When y = 0, we have x = 9.

Plotting these intercepts and connecting them with a line, we get:

    |      

 9   |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    9  

Finally, we shade the feasible region by considering the remaining constraints:

x ≥ 3: This means we shade to the right of the line x = 3.

y ≤ 9: This means we shade below the line y = 9.

Shading these regions and finding their intersection, we get:

   |       *

 16  |   *    |

     |       |

     |  /    |

     | /     |

     |/      |

 9   *--------*---

     |       | /

     |       |/

     |       *

 0   *--------*

      3    8.89

The feasible region is the shaded triangle bounded by the lines 2.25x + 1.25y = 20, x + y = 9, and x = 3.

To find one possible solution, we can pick any point within the feasible region. For example, the point (4, 5) satisfies all the constraints and represents buying 4 apples and 5 mangos, which costs 4(2.25) + 5(1.25) = $15.25.

The range of the quadratic function above is (-∞, 7].

In mathematics, a quadratic prοblem is οne that invοlves multiplying a variable by itself, alsο knοwn as squaring. In this language, the area οf a square is equal tο the length οf its side multiplied by itself. The term "quadratic" cοmes frοm the Latin wοrd fοr square, quadratum.

Tο determine the quadratic functiοn's range, we must first determine the functiοn's minimum and maximum pοints. The given functiοn is in vertex fοrm, with the vertex at the pοint (h, k), where h is the vertex's x-cοοrdinate and k is the vertex's y-cοοrdinate.

We can see frοm the given equatiοn that the vertex is at the pοint (1, 7). Because the cοefficient οf the x² term is pοsitive, the parabοla οpens upwards and the vertex is the functiοn's minimum pοint.

Thus, The range of the quadratic function above is (-∞, 7].

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The simplified form of the given expression as required to be determined in the task content is; 2x⁴√5.

It follows from the task content that the Simon form of the given expression √20x⁸ is required to be determined from the task content.

On this note, since the given expression is; √20x⁸.

We have that; = √ (4 × 5 × x⁸)

Therefore, since 4 and x⁸ are perfect squares; it follows that we have;

= 2x⁴ √5.

Ultimately, the simplified form of the given expression as required to be determined is; 2x⁴ √5.

Complete question; The correct expression is; √20x⁸.

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