-10,-17, -24, -31, -38, ...
a) Common Difference:
b) Recursive Formula:
c) Explicit Formula:
d) 843

First, rewrite both numbers as improper fractions.

Next, multiply both numbers. To do so, multiply the numerators and denominators sparatedly:

Since the factor 7 appears both in the numerator and the denominator, we can cancel it out:

Since 24 divided by 4 is 6, then:

There are \(10^{4}\) = 10,000 different possible musical entertainment lineups that can be created from a list of 10 songs.

This is computed by using the formula for combinations without repetition, which is \(n^{r}\), where n is the number of items in the list and r is the number of items to be selected. In this case, n = 10 and r = 4, which results in \(10^{4}\) = 10,000.

It is important to note that this calculation does not take into account any repetitions of songs, so if the same song appears more than once in the list, then the actual number of possibilities could be less. For instance, if there is a list of 10 songs, but 5 of them are the same, then the number of possible lineups would be\(10^{4/5}\)! = 800, taking into account the repetitions.

To illustrate this further, if we were to list all the possible lineups, then we would end up with 10,000 unique combinations of 4 songs. For instance, a possible lineup could be Song 1, Song 5, Song 8, Song 10. Another possible lineup could be Song 4, Song 7, Song 9, Song 10. This process could be repeated with any combination

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There are 201376 ways can a group of 5 lucky students be selected to sit in the front of the classroom.

What are combinations?

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.

Permutations and combinations are often mistaken. The chosen components' order is crucial in permutations, though. For instance, whereas permutations treat the arrangements differently, combinations treat the arrangements ab and ba equally (as one arrangement).

Use the combinations formula:

n = 32, r=5

\(^{n}C_{r}=\frac{n!}{(n-r)! r!}\)

\(^{32}C_{5}=\frac{32!}{(32-5)! 5!}\)

       = (32*31*30*29*28*27!)/(5!*27!)

       = (32*31*30*29*28)/ (5*4*3*2*1)

       = 201376

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The product of 7/8 and 1/8 is 7/64. This can be obtained by multiplying the numerators together to get 7, and multiplying the denominators together to get 64.

To multiply two fractions, we simply multiply their numerators together and then multiply their denominators together. So, 7/8 x 1/8 would be

(7 x 1) / (8 x 8) = 7/64

Therefore, 7/8 x 1/8 equals 7/64.

In words, we can say that 7/8 represents 7 parts out of 8, while 1/8 represents 1 part out of 8.

To find the result of multiplying these fractions, we multiply the parts together: 7 x 1 = 7. Then, we multiply the total number of parts, which is

8 x 8 = 64.

So, the result is 7/64, which means that 7/8 x 1/8 represents 7 parts out of 64.

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Answer: There were 7 children

Step-by-step explanation:

Let's use x to represent the children and y to represent the adults.

We know they combine to make a group of 25 people so x+y=25

We also know that they paid $201 and that there is $3 per child and $10 for adults so 3x+10y=201

I will solve by substitution.

Solve for y in the first equation

\(x+y=25\\x-x+y=25-x\\y=25-x\)

Sub in our value for y into the other equation and solve for x

\(3x+10y=201\\3x+10(25-x)=201\)

Step 1) Simplify

\(3x+250-10x=201\\-7x+250=201\)

Step 2) Subtract 250 from both sides

\(-7x+250-250=201-250\\-7x=-49\)

Step 3) Divide both sides by -7

\(\frac{-7x}{-7} =\frac{-49}{-7}\\x=7\)

Answer:

7 children.

Step-by-step explanation:

Let c = children

Let a = adults

1) We can set up two equations and solve them simultaneously using substitution or elimination method.

c + a = 25

3c + 10a = 201

2) I will use substitution. Make one of the variables the subject; then, substitute it into the other equation.

a = 25 - c

3c + 10(25 - c) = 201

3) Solve for c; then, substitute it into one of the equations.

3c + 250 - 10c = 201

-7c = 201 - 250

-7c = -49

c = -49/-7

c = 7

Let's substitute it into one of the equations.

7 + a = 25

a = 25 - 7

a = 18

Since the question only asked for the number of children, the answer is 7.

Answer:

7 o más

Step-by-step explanation:

lógicamente, si el juego necesitaba 7 taps para jugar y Nico tiene más de 7 taps, entonces Miguel también debería tener 7 o más taps en su bolsa.

Answer:

a) 7:4

b) 6:3

c) 4:2

d) 6:2

e) 4:3

f) 4:4

Answer:

a) 7:4

b) 6:3

c) 4:2

d) 6:2

e) 4:3

f) 4:4

Step-by-step explanation:

Determine the number of consonants and vowels, then turn them into ratios.

The report based on the given question requirements is:

Mathematician: Évariste Galois

(1) Life History:

Évariste Galois was born in Bourg-la-Reine, France on October 25, 1811. Unfortunately, he passed away at the tender age of 20 on May 31, 1832. Amidst the political unrest in France, he engaged in political activism. Despite his premature death, Galois made a lasting impact on the field of mathematics. His non-conformist attitude and intelligence frequently led to conflicts with those in positions of power, earning him a reputation as a rebel. A fascinating piece of information is that Galois dedicated his night prior to his ultimate combat to jotting down his mathematical concepts, eventually emerging as notable enhancements to Algebra.

(2) Mathematical Discoveries:

Galois made remarkable contributions to the field of Algebra. He developed the theory of Galois groups, which revolutionized the study of polynomial equations and their solvability. Galois showed that the solvability of an algebraic equation by radicals is determined by the properties of its Galois group. This insight led to Galois theory, a cornerstone of modern Algebra. Additionally, he developed the concept of field theory, introducing the notion of field extensions, which provided a powerful framework for studying algebraic structures.

(3) Bibliography:

Artin, E. (1998). Galois Theory: Lectures Delivered at the University of Notre Dame. Springer.

Stillwell, J. (2005). Mathematics and Its History (2nd ed.). Springer.

Edwards, H. M. (1983). Galois Theory. Springer-Verlag.

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Answer:

Break even 126 units

105x - (90x + 1890)  Profits will be revenue minutes expenses.

The second answer.

Step-by-step explanation:

105x = 90x +1890  Subtract 90x from both sides

15x = 1890  Divide both sides by 15

x 126

They need to sell 126 units to break even.

105(91) -[90(91) + 1890]

9555-8190-1890

9555 - 16380

-6825

Selling 91 units will produce a loss of 6825

The solution to the equation 9 × (3 ÷ x) = 26 is x = 1.038.

To solve the equation 9 × (3 ÷ x) = 26 for x, we can follow these steps:

Simplify the expression on the left side of the equation:

9 × (3 ÷ x) = 26

27 ÷ x = 26

Multiply both sides of the equation by x to eliminate the division:

(27 ÷ x) × x = 26 × x

27 = 26x

Divide both sides of the equation by 26 to solve for x:

27 ÷ 26 = (26x) ÷ 26

1.038 = x

As a result, x = 1.038 is the answer to the equation 9 (3 x) = 26.

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Therefore, Deanna will need 60 panels of artificial grass to cover the area.

To find out how many panels of artificial grass Deanna will need to cover the area, we can follow these steps:

Step 1: Calculate the total area of the space she wants to cover.

Area = Length × Width

Given that the length is 20 ft and the width is 12 ft:

Area = 20 ft × 12 ft = 240 square feet

Step 2: Convert the area to square inches since the grass panels are measured in square inches.

1 square foot = 12 inches × 12 inches = 144 square inches

240 square feet × 144 square inches/square foot = 34,560 square inches

Step 3: Calculate the number of panels needed by dividing the total area in square inches by the area of each panel.

Each panel has an area of 24 inches × 24 inches = 576 square inches.

Number of panels = Total area / Area of each panel

Number of panels = 34,560 square inches / 576 square inches = 60 panels

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The volume of Uranus having a diameter of 50724000 m is 6.829 x 1022 m3.

Volume is defined as the quantity of the three-dimensional space occupied by a closed three-dimensional figure. In the case of any object, volume is measured in cubic units. In cases of solid objects, their volume is measured in cubic units of length, such as meters, centimeters, etc.

To calculate the volume of spherical objects, viz. for a planet (assuming it is an ideal sphere in shape), the following formula is applied:

Volume (V) = 4/3  π\(R^{3}\) cubic units

where R = radius and π  = 3.14, a mathematical constant.

It is given that the diameter ( D ) of Uranus = 50724000 m.

Therefore radius ( R ) = D/ 2 = 50724000 m/ 2 = 25362000 m.

Therefore volume of planet Uranus = 4/3 π\(R^{3}\).

Substituting  π by 3.14 and R by 25362000m, we get

Volume = 6.829 x 1022 \(m^{3}\)

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Answer: 4x(x - 4)

Step-by-step explanation:

4x² - 16x = 4x(x - 4)

Now we can see that the expression inside the parentheses can also be factored:

x - 4 = (x - 4)

So the fully factorized expression is:

4x² - 16x = 4x(x - 4) = 4x(x - 4)

Answer:

ㅤ

- 4x( x + 4 )

ㅤ

Step-by-step explanation:

ㅤ

\(\large{\pmb{\sf{ - 4x^{2} - 16x}}}\)

ㅤ

\(\large{\underline{\underline{\sf{Taking \: Out \: {\green{4}} \: As \: Common:-}}}}\)

ㅤ

\(\large{\pmb{\sf{\leadsto{- 4(x^{2} + 4x)}}}}\)

ㅤ

\(\large{\underline{\underline{\sf{Taking \: Out \: {\green{x}} \: As \: Common:-}}}}\)

ㅤ

\(\large{\purple{\boxed{\pmb{\sf{\leadsto{- 4x(x + 4)}}}}}}\)

━━━━━━━━━━━━━━━━━━━━━━

\(\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star\)

ㅤ

\(\large{\dashrightarrow}\) Two positive always makes positive sign when multiplied.

ㅤ

\(\large{\dashrightarrow}\) Two negatives always makes positive sign when multiplied.

ㅤ

\(\large{\dashrightarrow}\) A positive and a negative always makes negative sign when multiplied.

ㅤ

\(\large{\dashrightarrow}\) The sum of two positives is always positive with a positive sign.

ㅤ

\(\large{\dashrightarrow}\) The sum of two negatives is always positive with a negative sign.

ㅤ

\(\large{\dashrightarrow}\) The sum of a positive and a negative is always negative with the sign of whose number is greater.

Answer:

YOU MIGHT FALL OFF

Step-by-step explanation:

 that's the answer

-kenma #3

The area values of the circles given in the attachment are :

Area of a circle =

\( {\pi} {r}^{2} \)

Where, r = Radius

\( \frac{\pi {d}^{2} }{4} \)

d = diameter

\(\pi = 3.14\)

1.)

r = 3cm

Area = 3.14 × 3² = 28.26 cm²

2.)

r = 4 in

Area = 3.14 × 4² = 50.24 in²

3.)

r = 10 m

Area = 3.14 × 10² = 314 m²

4.)

r = 2cm

Area = 3.14 × 2² = 12.56 cm²

5.)

r = 9 ft

Area = 3.14 × 9² = 254.34 ft²

6.)

r = 1.2 km

Area = 3.14 × 1.2² = 4.52 km²

7.)

r = 50 in

Area = 3.14 × 50² = 7850 in²

8.)

r = 11 m

Area = 3.14 × 11² = 379.94 m²

9.)

r = 2.5 cm

Area = 3.14 × 2.5² = 19.63 cm²

10.)

d = 16 ft

Area = (3.14 × 16²) ÷ 4 = 200. 96ft²

11.)

d = 40 m

Area = (3.14 × 40²) ÷ 4 = 1256 m²

12.)

d = 10 cm

Area = (3.14 × 10²) ÷ 4 = 78.5 cm²

13.)

d = 3 m

Area = (3.14 × 3²) ÷ 4 = 7.07 m²

14.)

d = 12 in

Area = (3.14 × 12²) ÷ 4 = 113.04 in²

15.)

d = 16 ft

Area = (3.14 × 16²) ÷ 4 = 200. 96ft²

16.)

d = 7cm

Area = (3.14 × 7²) ÷ 4 = 38.47 cm²

17.)

d = 0.6 km

Area = (3.14 × 0.6²) ÷ 4 = 0.28 km²

18.)

d = 2 cm

Area = (3.14 × 2²) ÷ 4 = 3.14 cm²

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Answer:

a. Pop

b. 30 CDs

c. 230 CDs

Step-by-step explanation:

Given that "O" represents 20 CDs

a. The CD that was the mode is the CD that has as much "O", which is Pop.

Mode = Pop

b. Number of Rock CDs = 3 × 20 = 60 CDs

Number of Classical CDs = 1½ × 20 = 30 CDs

Therefore, 30 more CDs of Rock were sold than Classical CDs were sold

c. Pop = 5*20 = 100 CDs

Jazz = 2*20 = 40 CDs

Classical = 1½*20 = 30 CDs

Rock = 3*20 = 60 CDs

Total sold altogether = 100 + 40 + 30 + 60

= 230 CDs

The probability that a minimum of seven adults enjoy superhero movies is P(X ≥ 7) = P(X = 7) + P(X = 8)

You can calculate the specific values using the formulas and then sum them up to find the probability that a minimum of seven adults enjoy superhero movies out of the random sample of eight adults.

To find the probability that a minimum of seven adults enjoy superhero movies out of a random sample of eight adults, we need to calculate the probability of different scenarios: exactly 7 adults, exactly 8 adults, and add them together.

First, let's calculate the probability that exactly 7 adults enjoy superhero movies. We can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the combination formula (n choose k),

p is the probability of success (58% or 0.58 in decimal form),

n is the number of trials (8 in this case), and

k is the number of successes (7).

Using the formula, we can calculate:

P(X = 7) = C(8, 7) * 0.58^7 * (1 - 0.58)^(8 - 7)

Similarly, the probability that exactly 8 adults enjoy superhero movies is:

P(X = 8) = C(8, 8) * 0.58^8 * (1 - 0.58)^(8 - 8)

To find the probability of a minimum of seven adults enjoying superhero movies, we add these two probabilities together:

P(X ≥ 7) = P(X = 7) + P(X = 8)

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Answer:

Bus 18 is more consistent than Bus 47 based on the IQR, which is smaller for Bus 18 (16) compared to Bus 47 (24), indicating less spread of data between the 25th and 75th percentiles.

Step-by-step explanation:

Answer: The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

How to obtain the measures of spread?

First, we consider the dot plot, which shows the number of times that each observation appears in the data set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data set.

The interquartile range is a better measure of spread compared to the range of a data set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Step-by-step explanation:

Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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The answer to the various exercises would be explained and given below.

Parallel lines are those lines that do not meet or intercept at any point.

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The probability that 3 separate flights will all take place is 0.531441

let A = event of scheduled flight actually take place

According to the question, P(A)=0.81

Given that 3 separate flights will all take place is an independent event.

Hence, we can use the multiplicative rule which says If the probability that one given flight takes place is 0.81 then the probability of 3 flights taking place is:

P(A∩B∩C) = P(A)*P(B)*P(C)

= 0.81*0.81*0.81

= 0.531441

so, the Probability that 3 separate flights will take place is 0.531441

The formula used for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

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Answer:

Both true

Step-by-step explanation: 80%*90=72. 72/90=8/9.

20%*90=18. 18/90=1/5

80% of 90 is the same as 8/9 of 90 is false.

20% of 90 is the same as 1/5 of 90 is true.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, 80% of 90 is the same as 8/9 of 90.

80% of 90 is,

= (80/100)×90.

= 8×9.

= 72.

And,

(8/9)×90.

= 8×10.

= 80.

So, 80% of 90 and 8/9 of 90 is not the same.

20% of 90 is the same as 1/5 of 90.

(20/100)×90.

= 2×9.

= 18.

And,

(1/5)×90.

= 18.

So, 20% of 90 is the same as 1/5 of 90.

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Even function:

A function is said to be even if its graph is symmetric with respect to the , that is:

Odd function:

A function is said to be odd if its graph is symmetric with respect to the origin, that is:

So let's analyze each question for each type of functions using examples of polynomial functions. Thus:

FOR EVEN FUNCTIONS:

1. When  becomes  

1.1 Effects on the y-intercept

We need to find out the effects on the y-intercept when shifting the function  into:

We know that the graph  intersects the y-axis when , therefore:

So:

So the y-intercept of  is one unit less than the y-intercept of

1.2. Effects on the regions where the graph is increasing and decreasing

Given that you are shifting the graph downward on the y-axis, there is no any effect on the intervals of the domain. The function  increases and decreases in the same intervals of

1.3 The end behavior when the following changes are made.

The function is shifted one unit downward, so each point of  has the same x-coordinate but the output is one unit less than the output of . Thus, each point will be sketched as:

FOR ODD FUNCTIONS:

2. When  becomes  

2.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is one unit less. So the graph is shifted one unit downward again.

An example is shown in Figure 1. The graph in blue is the function:

and the function in red is:

So you can see that:

2.2. Effects on the regions where the graph is increasing and decreasing

The effects are the same just as in the previous case. So the new function increases and decreases in the same intervals of

In Figure 1 you can see that both functions increase at:

and decrease at:

2.3 The end behavior when the following changes are made.

It happens the same, the output is one unit less than the output of . So, you can write the points just as they were written before.

So you can realize this concept by taking a point with the same x-coordinate of both graphs in Figure 1.

FOR EVEN FUNCTIONS:

3. When  becomes  

3.1 Effects on the y-intercept

We need to find out the effects on the y-intercept when shifting the function  into:

As we know, the graph  intersects the y-axis when , therefore:

And:

So the new y-intercept is the negative of the previous intercept shifted one unit upward.

3.2. Effects on the regions where the graph is increasing and decreasing

In the intervals when the function  increases, the function  decreases. On the other hand, in the intervals when the function  decreases, the function  increases.

3.3 The end behavior when the following changes are made.

Each point of the function  has the same x-coordinate just as the function  and the y-coordinate is the negative of the previous coordinate shifted one unit upward, that is:

FOR ODD FUNCTIONS:

4. When  becomes  

4.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is the negative of the previous intercept shifted one unit upward.

4.2. Effects on the regions where the graph is increasing and decreasing

In this case it happens the same. So in the intervals when the function  increases, the function  decreases. On the other hand, in the intervals when the function  decreases, the function  increases.

4.3 The end behavior when the following changes are made.

Similarly, each point of the function  has the same x-coordinate just as the function  and the y-coordinate is the negative of the previous coordinate shifted one unit upward.

Answer:

answer D is correct maybe that help

Answer:

Not that I'm a chemistry expert but mathematically,The total weight of the bar is directly proportional to the known weight of the bar and the given percentage. I worked it out and found that the the total weight of the bar is 30 ounces. This is how I did it

Step-by-step explanation:

80:24

100:n

80(n)=100×24

A little equation and after it's solve the variable (n) will be equal to 30

The unit is added after calculations so that's how the answer is 30 ounces

Answer

Sam is 13 years old

Step-by-step explanation:

He is 13 years old.

13+7=20

13-3=10

10x2=20

Answer: 13

Step-by-step explanation:

We can represent this in an algebra equation

(x+7)=2(x-3)

(x+7)=2x-6

(x+7)=2x-6

-2x    -2x

-x+7=-6

-7       -7

-x= -13

/-1    /-1

x=13

Answer:

Hình tròn lớn và hình tròn nhỏ có cùng tâm O. Tính diện tích hình tròn lớn, biết rằng diện tích hình tròn nhỏ là 12,56m2.

Step-by-step explanation:

Hình tròn lớn và hình tròn nhỏ có cùng tâm O. Tính diện tích hình tròn lớn, biết rằng diện tích hình tròn nhỏ là 12,56m2.