A cyclist rides her bike at a rate of 12 meters per second. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 3 hours? Do not round your answers.

Answer:

The second term is -6 , the fourth term is 0 , the eleventh term is 21

Step-by-step explanation:

* Lets revise the explicit formula

- An explicit formula will create a sequence using n, the number

 position of each term.

- If you can find an explicit formula for a sequence, you will be able

 to quickly and easily find any term in the sequence by replacing

 n with the number of the term you want

- It defines the sequence as a formula in terms of n.

* Now lets solve the problem

- The formula of the sequence is A(n) = -9 + (n - 1)(3)

- A(n) is any term in the sequence

- n is the position of the number

- To find the second term put n = 2

∵ n = 2

∴ A(2) = -9 + (2 - 1)(3) = -9 + (1)(3) = -9 + 3 = -6

* The second term is -6

- To find the fourth term put n = 4

∵ n = 4

∴ A(4) = -9 + (4 - 1)(3) = -9 + (3)(3) = -9 + 9 = 0

* The fourth term is 0

- To find the eleventh term put n = 11

∵ n = 11

∴ A(11) = -9 + (11 - 1)(3) = -9 + (10)(3) = -9 + 30 = 21

* The eleventh term is 21

Answer:

Second term = -6

Fourth term = 0

Eleventh term = 21

Step-by-step explanation:

We are given the following explicit formula of an arithmetic sequence and we are to find the second, fourth and the eleventh terms of this sequence:

[tex]a_n=-9+(n-1)(3)[/tex]

where [tex]a_n[/tex] = nth term, [tex]a_1=-9[/tex] and [tex]n[/tex] = number of term.

Second term [tex](a_2) = -9+(2-1)(3)[/tex] = -6

Fourth term [tex](a_4) = -9+(4-1)(3)[/tex] = 0

Eleventh term [tex](a_{11}) = -9+(11-1)(3)[/tex] = 21

Answer:

2

Step-by-step explanation:

To find how many real solution a quadratic equation has, we just need to find the value of its discriminant. If the discriminant is zero, the quadratic only has one real solution; if the discriminant is positive, the quadratic has two real solution; if the discriminate is negative, the quadratic doesn't has any real solutions.

The discriminant of a quadratic equation of the form [tex]ax^2+bx+c[/tex] is given by: [tex]b^2-4ac[/tex]

We know from our quadratic that [tex]a=3[/tex], [tex]b=-5[/tex], and [tex]c=-5[/tex].

Replacing values:

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

[tex]25+60[/tex]

[tex]85[/tex]

Since the discriminant is positive, we can conclude that our quadratic equation has two real solutions.

Answer:

8 tons < 20,000

Step-by-step explanation:

1 ton = 2000 pounds

so 8 tons would be 16,000 which makes it less than 20,000

Final answer:

An adult African elephant that weighs approximately 8 tons is not equal to 20,000 pounds; instead, 8 tons equals 16,000 pounds. The provided comparison in the question is incorrect.

Explanation:

To determine if an adult African elephant that weighs approximately 8 tons is equal to 20,000 pounds, we need to convert tons to pounds using the unit equivalence 1 ton = 2,000 pounds. Multiplying 8 tons by the unit equivalence gives us:

8 × 2,000 = 16,000 pounds.

Knowing that the range of weight of a male African elephant is between 12,000 and 16,000 pounds, we can see that 8 tons does not equal 20,000 pounds. Therefore, the comparison 8 tons = 20,000 pounds is incorrect.

A correct comparison would be 8 tons = 16,000 pounds, which is not one of the options provided in the question.

As for the water bottle containing 2,000 milliliters, this is simply stating the volume capacity of the bottle but does not relate to the conversion between tons and pounds.

Answer: 2.29 x 10^4

Step-by-step explanation:

22.9 x 10^4 is the answer oof I’m sorry

When you ask all your classmates for their favorite colors, you are gathering data that can be grouped into categories based on color names, such as "red," "blue," "green," and so on. This type of data is known as categorical data.
Categorical data, also sometimes referred to as qualitative data, consists of information that is not numerical in nature and can be separated into different categories according to some quality or attribute. In the case of favorite colors, you're dealing with categories as you cannot perform arithmetic operations on them (you can't add 'red' to 'blue' and get a sum, for instance).
Let's review the other options:
A) Bivariate data involves two variables and the relationship between them. Since the question only refers to one variable—favorite color—this is not bivariate data.
C) Numerical data involves numbers, and operations such as addition, subtraction, multiplication, and division can be performed on it. Since favorite colors are not numbers, this is not numerical data.
D) Quantitative data is another term for numerical data; it involves quantities that can be measured and expressed using numbers. Since we're not measuring anything in numbers when asking about favorite colors, this is not quantitative data.
Thus, the correct answer is:
B) Categorical

Answer:

s = 4

Step-by-step explanation:

4s * 4 = 64

Simplify: 16s = 64

Divide: s = 64/16

Simplify: s = 4

“ s “ equals 4 therefore 4 is the answer

19

418 divided by 22 is equal to 19

And that’s the answer

Answer:

Break even occurs at 2800 juice boxes.

Step-by-step explanation:

Fixed cost form the factor = $1400

Variable cost per unit juice box = 15 cents = $0.15

Let number of juice boxed produced to get brek even point = x

Then total cost = c(x)= 1400+0.15x

Selling price per unit juice box = 65 cents = $0.65

Then total sales = R(x)= 0.65x

At break even both sales and cost will be equal so we get:

[tex]0.65x=1400+0.15x[/tex]

[tex]0.65x-0.15x=1400[/tex]

[tex]0.50x=1400[/tex]

[tex]x=\frac{1400}{0.50}[/tex]

[tex]x=2800[/tex]

Hence break even occurs at 2800 juice boxes.

It takes 45 seconds. the easiest way to do these is to use a graphic calculator and replace the variables with x and y, for example, this equation would become -5x^2+30x, and if you don't have access to a graphing calculator, you can always use desmos online.

Answer:

It takes 6 seconds to the rocket to reach the ground after it has been launched

Step-by-step explanation:

The height of a fireworks rocket in meters can be approximated by :

h = -5t² + 30t, where h is the height in meters and t is the time in seconds

Now, we need to find the time it takes the rocket to reach the ground after it has been launched

So, When it touches the ground height will be 0

⇒ h = 0

⇒ 0 = -5t² + 30t

⇒ t² - 6t = 0

⇒ t(t - 6) = 0

Now, since the rocket is launched from above the ground ⇒ t ≠ 0

⇒ t - 6 = 0

⇒ t = 6

Hence, It takes 6 seconds to the rocket to reach the ground after it has been launched

Answer:

1/1

Step-by-step explanation:

We can use the points (0, -1) and (1, 0) to solve.

Slope formula: y2-y1/x2-x1

= 0-(-1)/1-0

= 1/1

= 1 (Answer)

Hope This Helped! Good Luck!

Answer:

The second option is the correct answer

Step-by-step explanation: Hope this helps

The group of numbers is listed from greatest to least will be 8, |-6|, 5, |-4|, |1|

The descending order is one in which the numbers are in decreasing pattern or numbers vary from the greatest to the lowest.

In the question there are four options:-

|-3|, |-4|, |-7|, |-8|, |-9|

8, |-6|, 5, |-4|, |1|

-3, |-1|, 0, 2, 7

9, 7, |6|, -5, |-4|

We can clearly see that option second has a series of descending numbers. The series is descending from the number 8 to 1 in the decreasing pattern of the numbers.

Hence a group of numbers are listed from greatest to least will be 8, |-6|, 5, |-4|, |1|

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[tex]t - 6( - 2t + 1) \\ t + 12t - 6 \\ 13t - 6 \\ 13t = 6 \\ t = \frac{13}{6} [/tex]

The correct expression which is equivalent to this expression t - 6(-2t + 1) is,

⇒ 13t - 6

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ t - 6 (- 2t + 1)

Now, We can simplify as;

⇒ t - 6 (- 2t + 1)

⇒ t + 12t - 6

⇒ 13t - 6

Thus, The correct expression which is equivalent to this expression

t - 6(-2t + 1) is,

⇒ 13t - 6

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Answer:

The minimum value of this function is -40.

Step-by-step explanation:

Recall that the minimum of a quadratic whose graph is a parabola that opens up, as this one does, is the vertex of the graph.  The x-coordinate of the vertex is given by x = -b / (2a), where a is the coefficient of the x^2 term and b is that of the x term.

Here, x = -12 / (2*2), or x = -12/4, or x = -3.

Find the y-value at this x-value:  f(-3) = 2(-3)^2 + 12(-3) - 22, or

                                                      f(-3) = 2(9) - 36 - 22, or -40.

The vertex is at (-3, -40).  The minimum value of this function is -40.

The provided quadratic function y=2x²+12x-22 has no local minimum or maximum, as indicated by the application of the second derivative test, which results in a point of inflection rather than an extrema.

The minimum or maximum of the quadratic function y=2x²+12x-22. To locate the extrema of a quadratic function, we often use the first derivative test. However, the information provided indicates the derivative vanishes at x = 2 (y' = 0), but the second derivative test (y" = 6x - 12) reveals that this point is a point of inflection rather than a minimum or maximum. The second derivative being zero at x = 2 implies that there is no concavity change and hence, no local extrema. Therefore, for this particular quadratic function, there is no local minimum or maximum. The function can be rewritten as y = (x - 2)³ + 8, which shifts the function y = x³ two units to the right and eight units upwards, further emphasizing that it indeed has no local extrema.

Answer:

482.8

Step-by-step explanation:

Answer:

The perimeter of the plot of land is approximately 482.8 feets.

Step-by-step explanation:

By the given diagram,

The perimeter of the plot of land = The perimeter of the quadrilateral having the vertices (0,0), (0,120), (140,100) and (140,20),

Since, the perimeter of the quadrilateral having the vertices (0,0), (0,120), (140,100) and (140,20) = The distance between (0,0) and (0,120) + The distance between (0,120) and (140,100) + The distance between (140,100) and (140,20) + The distance between (140,20) and (0,0)

By the distance formula,

[tex]=\sqrt{(0-0)^2+(120-0)^2}+\sqrt{(140-0)^2+(100-120)^2}+\sqrt{(140-140)^2+(20-100)^2}+\sqrt{(0-140)^2+(20-0)^2}[/tex]

[tex]=\sqrt{120^2}+\sqrt{19600+400}+\sqrt{0+80^2}+\sqrt{19600+400}[/tex]

[tex]=120+100\sqrt{2}+80+100\sqrt{2}[/tex]

[tex]=200+200\sqrt{2}[/tex]

[tex]=482.842712475[/tex]

[tex]\approx 482.8\text{ feet}[/tex]

Hence, the perimeter of the plot land is approximately 482.8 feets.

Answer:

Step-by-step explanation:

14^2+20^2=c^2

196+400=c^2

square root of 596=c^2

c^2=24.4

The diagonal length of the suitcase is 24.41 inches if the suitcase measures 14 inches long and 20 inches high.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We have a suitcase measures 14 inches long and 20 inches high.

The diagonal, length, and height will make a right angle triangle.

Let's suppose the length of the diagonal is x inches

From the Pythagoras theorem:

x² = 14² + 20²

x² = 596

x = 24.41 inches

Thus, the diagonal length of the suitcase is 24.41 inches if the suitcase measures 14 inches long and 20 inches high.

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The function m(x) = x + 5/(x-1) has the same domain as the composition of functions (m.n)(x) because they both have the domain of all real numbers except 1.

The domain of a function is the set of all possible input values (often called 'x-values') which will give valid output values. In other words, it's all the values x can take on. The function m(x) = x +5/(x-1) will be undefined when the denominator equals zero, so x cannot equal 1. Therefore, the domain of m(x) is all real numbers except 1.

On the other hand, the function n(x) = x - 3 doesn't have any restrictions and can take on all real numbers. However, (m.n)(x) refers to a composition of functions, specifically m(n(x)). This will inherit the domain restrictions from m(x). Therefore, the function that has the same domain as (m.n)(x) is m(x) because the composition will allow inputs for all real numbers except 1, as dictated by m(x).

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Substitute y = x + 1 into 2x - 5y = 4

-3x - 5 = 4

Solve for x in -3x - 5 = 4

x = -3

Substitute x = -3 into y = x + 1

y = -2

Therefore,

x = -3

y = -2

Answer:

Step-by-step explanation:

The zeros of this cubing function are easily read from the graph:  {-20, -5, 15}.

The factors of this polynomial are therefore (x + 20), (x + 5) and (x - 15).

The y-intercept is (0, 1).

The function is thus f(x) = a(x + 20)(x + 5)(x - 15).

According to the y-intercept, if x = 0, y = 1.

Thus, y = 1 = f(0) = a(20)(5)(-15), or 1 = a(100)(-15), or 1 = -1500a.

Then a = -1/1500, and the function is:

f(x) = (-1/1500)(x^3 + .. +  .. + ... ).  We must multiply out (x + 20)(x + 5)(x - 15) to obtain f(x) in finished form.

Answer:

zeros: (-20, 0), (-5, 0) and (15, 0)

factors: (x + 20), (x + 5) and (x - 15)

f(x) = a*(x + 20)*(x + 5)*(x - 15)

a = -1/1500

f(x) = -1/1500*(x + 20)*(x + 5)*(x - 15)

f(x) = -1/1500*x^3 - 1/100*x^2 + 11/60x + 1

Step-by-step explanation:

The zeros of the function are those points where the function intercepts the x-axis. They are: (-20, 0), (-5, 0) and (15, 0)

The zeros of a polynomial are expressed as factors as follows: (x - a) where a is a zero. Then, for this case, the factors are (x + 20), (x + 5) and (x - 15)

The equation of f(x) use the factors and the leading coefficient as follows: f(x) = a*(x + 20)*(x + 5)*(x - 15)

Applying the distributive property of multiplication, we get the expanded form:

f(x) = a*(x + 20)*(x + 5)*(x - 15)

(x + 20)*(x + 5) = x^2 + 5x + 20x + 20*5 = x^2 + 25x  + 100

f(x) = a*(x^2 + 25x  + 100)*(x - 15)

(x^2 + 25x  + 100)*(x - 15) = x^3 - 15x^2 + 25x^2 - 15*25x + 100x - 100*15 = x^3  + 15x^2 - 275x - 1500

f(x) = a*(x^3 + 15x^2 - 275x - 1500)

The y-intercept of the graph is (0, 1). Replacing this point into the function equation:

1 = a*(0 + 20)*(0 + 5)*(0 - 15)

1 = a*20*5*(-15)

1 = a*(-1500)

a = -1/1500

Replacing this value  into the function equation:

f(x) = (-1/1500)*(x^3 + 15x^2 - 275x - 1500)

f(x) = -1/1500*x^3 - 1/100*x^2 + 11/60x + 1

Answer:

Step-by-step explanation:

The answers would be 2, 3, and 5.

The first situation represents a quadratic equation and the fourth situation represents a linear equation.

Multiply the two numbers first

6*3= 18

Divide the total volume by 18

144/18=6

Answer: Missing length is 6 ft .

Answer:

63.5

Step-by-step explanation:

they all form a triangle, and the formula for that is a²+b²=c²

a=96       b=wire        c=72

96²+b²=72²

9216+b²=5184

-9216        -9216

b²= -4032

square root of -4032 = 63.5

Answer is..

5.88%

(96.25/1636.25)%

= 5.88%

Final answer:

To calculate the gain percentage, subtract the gain from the selling price to get the cost price, and then divide the gain by the cost price and multiply by 100. The dealer's gain percentage is approximately 6.25%.

Explanation:

The subject of the question is to calculate the gain percentage of a dealer who sells an article for ₹1636.25 and gains ₹96.25. To find the gain percentage, we need to identify the cost price first. The cost price (CP) can be calculated by subtracting the gain from the selling price (SP), which gives us CP = SP - Gain = ₹1636.25 - ₹96.25 = ₹1540.

Next, we calculate the gain percentage using the formula:

Gain Percentage = (Gain / Cost Price) * 100

Substituting the values, we get:

Gain Percentage = (₹96.25 / ₹1540) * 100

Therefore, the gain percentage of the dealer is approximately 6.25%.

Answer: 1/4

Step-by-step explanation: Since there are 24 hours in a day, 1/4 would be equal to 6 hours out of the day.

Answer: (25%)

Correct Answer 100%! Pls, give me brainliest. Thank You

it's the third choice because of your radius like how it's 2πR^2

Answer:  [tex]\bold{D)\quad y = 2sin(3x)}[/tex]

Step-by-step explanation:

[tex]\text{The standard form of a sine equation is: y=A sin(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]

In the given graph,

[tex]\implies \large\boxed{y = 2sin(3x)}[/tex]

see graph below for verification

Answer:

To solve this problem, we can use Pythagorean theorem, it tells us that the square of the hypotenuse is equal to the sum of the square of the other two sides.

When we look at these side lengths, we can see that only the second answer is suitable because from the lengths, we can predict that 13 is the length of the hypotenuse, 5 is the length of the shorter leg and 12 is the length of the other leg, and when you actually calculate it, the result is correct as well:

5² + 12² = 25 + 144 = 169

13² = 169

So the answer is B

I’m thinking that the answer is B! Sorry if I’m wrong!:)

The area of a rectangle can be found by using this formula: Area = Length • Width

The question gives us the area and the width, so all we need to look for is the length. To do this, we manipulate the formula so we are solving for length, like so: Length = Area / Width

Area = x^2 -9

Width = x-3

Length = unknown

Now, we plug in what we know (Area and Width) into the formula for Length:

Length = (x^2 - 9) / (x - 3)

x^2 - 9 simplifies to (x - 3)(x+3) so we are left with: Length = (x - 3)(x + 3) / (x - 3) and we see that (x - 3) cancels out

The final answer is that *Length = x + 3*

To check your work, you can plug in each part into the formula for area and see if the answers match

The question is asking for the length of a rectangle given the area and width. This can be found by using the formula for the area of a rectangle which is width * length = area. Dividing the given area by the width results in the length.

To solve the problem, we need to use the formula for the area of a rectangle which is width*length=area. Given the area is x^2-9 and the width is x-3, we can find the length by dividing the area by the width. Therefore, the length of the rectangle is (x^2 - 9) / (x - 3).

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Answer:

A

Step-by-step explanation:

3/5 of the letters are roses and 3/5 = 6/10 = 60%

Final answer:

The correct option that shows 60% roses is b. 50% of the flowers are blue and 50% of the flowers are red.

Explanation:

The question asks which option shows 60% roses. The correct option would be b. 50% of the flowers are blue and 50% of the flowers are red. This is because 60% of the flowers in Karen's garden are roses, and the remaining 40% would consist of other flowers, such as blue and red flowers.

Answer:

Option D. [tex]y-3=5(x+1)[/tex]

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

In this problem we have

[tex]m=5[/tex]

[tex](x1,y1)=(-1,3)[/tex]

substitute the values

[tex]y-3=5(x+1)[/tex]

[tex]

3\times4+2=12+2=\boxed{14}

[/tex]

Answer: 14

Step-by-step explanation: if you substitute B in for 4, You then multiply 3 by 4 and get a product of 12. Then the question says to add 2. Add 2 to what you already have and you get the sum of 14.

Have a great Day!

Answer:

A. 34; B. 40. D. 88

Step-by-step explanation:

The rule is, "multiply by six and subtract two."

So, if we add two to the number, it should be evenly divisible by 6.

We can check each number.

A. 34 + 2 = 36; 36/6 = 6. TRUE.

B. 40 + 2 = 42; 42/6 = 7. TRUE.

C. 55 + 2 = 57; 57/6 = 9½. False.

D. 88 + 2 = 90; 90/6 = 15. TRUE.

E. 119 + 2 = 121; 121/6 = 20⅙. False.

The numbers that satisfy the rule are 34, 40, and 88.