The sum of four consecutive odd numbers is 72 find the numbers​

Answer:

The third side is 2√14

Step-by-step explanation:

The third side is found using Pythagorean theorem

=√(√92)²-(6)²

=√92-36

=√56

=2√14

Answer:

b and g

Step-by-step explanation:

a. is y = 0³ = 0

b. is y = ln(0), which is undefined because ln(x) is only defined for x > 0

c. is y = 1 / (1 + e^-0) = 1 / (1 + 1) = 1/2

d. is y = 0

e. is y = 0² = 0

f. is y = sin(0) = 0

g. is y = 1/0, which is undefined because division by 0 is undefined

h. is y = e^0 = 1

i. is y = |0| = 0

j. is y = √0 = 0

Without specific information about the data set, it is not possible to determine which equation is the best fit.

To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.

However, I can provide a general explanation of the four options:

y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.

y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.

y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.

y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.

Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.

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In Bimodal Distribution two nonadjacent values occur more frequently than any other values in a set of data.

According to the statement

we have to tell about the that type of distribution in which two nonadjacent values occur more frequently than any other values in a set of data

A bimodal distribution has two peaks. In the context of a continuous probability distribution, modes are peaks in the distribution.

and from this definition we have clear that the in this distribution the values are repeated.

it shows the probability distribution with two peaks in the graphical mode.

Bimodal distribution show repeated value.

it is used in many types of data representation because of two peaks graphical representation than the simple graph.

it is the easiest method than the others distributions.

So, In Bimodal Distribution two nonadjacent values occur more frequently than any other values in a set of data.

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The human heart beats approximately 4.1975 x 10⁸ times in one year and it expressed in scientific notation.

According to the question, the average human heart beats 1.15 x 10⁵ times a day. We need to find out how many times the heart beats in one year, which is 3.65 x 10² days.

To calculate the total number of heartbeats in one year, we can multiply the number of heartbeats in a day by the number of days in a year. Therefore, we have:

Total number of heartbeats in one year = 1.15 x 10⁵ beats/day x 3.65 x 10² days/year

= (1.15 x 3.65) x (10⁵ x 10²) beats/year

= 4.1975 x 10⁸ beats/year

This number may seem large, but it is necessary for the heart to pump blood throughout the body to keep us alive and healthy.

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Answer:

see explanation

Step-by-step explanation:

moving the decimal point 4 places left , means the number is smaller by a factor of 10000

this is the operation divide by 10000 or multiply by \(10^{-4}\)

Answer:

The formula is simply this: C = πd. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi.

Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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If the angle G is moved to a different spot in the circle the angle FGH and angle FEH in the cyclic quadrilateral will change to make it supplementary.

A cyclic quadrilateral is quadrilateral inscribed in a circle. It has all its vertices on the circumference of the circle.

Opposite angles in a cyclic quadrilateral are supplementary angles. That means they add up to 180 degrees.

Therefore, if he adjust point G to a different spot on the circle, angle FGH and FEH will adjust to become supplementary.

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The coordinates of point U’ are (0, 30).

Explain the term coordinates

Coordinates refer to a system used to locate a point in space or on a plane. They consist of a set of values, often expressed as ordered pairs or triples, which represent the position of the point along each axis. Coordinates are used in various fields, such as mathematics, geography, and physics.

According to the given information

The coordinates of point U’ are (0 , 30). Here’s how to find it:

The scale factor for Q’U’A’D’ is 6.

The coordinates of point U are (0 , 5).

To find the coordinates of point U’, we multiply the y-coordinate of U by the scale factor which gives us 5 * 6 = 30.

Therefore, the coordinates of point U’ are (0 , 30)

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The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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you didnt put a number line tho :/

Answer:

25

Step-by-step explanation:

that one spongebob meme

haha

:(

theres no number line

See solution below

Explanation:

a) 5x - 7 ≤ -2

collect like terms:

5x ≤ -2 + 7

5x ≤ 5

Divide through by 5:

x ≤ 1

From the graph above, the inequality has a solution.

b) 2/3b > -8

Cross multiply:

2 > -8(3b)

2 > -24b

Divide through by -24:

Note: when we divide an inequality by a negative number, the inequality sign changes.

2/-24 < b

-1/ 12 < b

Hence, b > -1/12

Note: To make it easier to graph, I represented b with x

From the graph above, the inequality has a solution.

c) 3w - 7 - w < 2w + 4

2w - 7 < 2w + 4

collect like terms:

2w - 2w < 4 + 7

0 < 11

Note: To make it easier to graph, I represented b with x

From the graph, the solution is for all real numbers.



the answer is 118 degrees

Answer:

Angle D = 118°

Step-by-step explanation:

Check out the attached photo.

Answer: -75

Step-by-step explanation:

Step-by-step explanation:

well, we pick two points with hopefully integer coordinates on the line.

I selected

(2, 24) and (10, 8)

the slope of the line is the factor of x (or if J in our case here).

and it is the ratio of "y coordinate change / x coordinate change" (or here K change / J change) when going from one point to another on the line.

so,

x (or J) changes by +8 (from 2 to 10).

y (or K) change by -16 (from 24 to 8).

so, the slope (factor or x or J) is -16/+8 = -2.

the second box is the y-(or K)intercept. that is the value of y (or K) when x (or J) = 0, so where the line intercepts the y-(or K-)axis.

we use the J, K coordinates of one point in the equation to calculate that. I chose (2, 24).

24 = -2×2 + intercept = -4 + intercept.

intercept = 28

so, the line equation is

K = -2J + 28

Answer:

angle A and C are both Equal and sides BC and BA of the triangle are congruent

Step-by-step explanation:

1) Rewrite the given differential equation: The given differential equation is y dx - 6(x + y^8) dy = 0. We can rewrite it as: y dx = 6(x + y^8) dy

2. Separate variables:
Now, separate the variables x and y:
(y/6) dx = (x + y^8) dy

3. Integrate both sides:
Integrate both sides of the equation with respect to their corresponding variables:

∫(y/6) dx = ∫(x + y^8) dy

(1/12)xy = (1/2)xy + (1/9)y^9 + C

4. Solve for x(y):
To find the general solution in form x(y), rearrange the equation: x(y) = 3y^8 + Cy^6

5. Find the largest interval:
To find the largest interval over which the general solution is defined, consider the domain of y.

The general solution is defined for all y except y = 0 (since this would result in a division by zero). Therefore, the largest interval is: (-∞, 0) ∪ (0, ∞)

6. Determine transient terms:
Since the general solution does not contain any terms that tend to zero as y approaches infinity, there are no transient terms. So the answer is: NONE

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The price of Brand X rice increased by 15.79% from January to May.

To find the per cent increase in price, we first need to calculate the difference in price between January and May, and then divide that difference by the original price in January and multiply by 100 to express the answer as a percentage.

The difference in price between January and May is $8.80 - $7.60 = $1.20.

The per cent increase in price is calculated as follows:

$1.20 ÷ $7.60 x 100 = 15.79%

So the price of Brand X rice increased by 15.79% from January to May.

We round the answer to 2 decimal places, so the final answer is a 15.79% increase in price.

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Answer:

(-3,2)

Step-by-step explanation:

Answer:

The first 2 are the answers.

The balloon's radius is increasing at a rate of 24 cm/min when the radius is 2 cm.

Given, the rate of change of the volume of the balloon, dV/dt = 48 cubic cm/min. We need to find the rate of change of the radius, dr/dt when the radius, r = 2 cm.

The volume of a sphere is given by V = (4/3)πr^3. Differentiating both sides with respect to time, we get

dV/dt = 4πr^2 (dr/dt)

Substituting the given values, we get

48 = 4π(2)^2 (dr/dt)

dr/dt = 48/(16π)

dr/dt = 3/(π) cm/min

Hence, the balloon's radius is increasing at a rate of 3/(π) cm/min when the radius is 2 cm.

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The balloon's radius is increasing at a rate of 3x / π units per minute.

To find how fast the balloon's radius is increasing at the instant the radius is 2 units, we can use the relationship between the rate of change of the volume of a sphere and the rate of change of its radius.

The volume V of a sphere is given by the formula:

V = (4/3)πr^3

where r is the radius of the sphere.

To find how the radius is changing with respect to time, we can differentiate both sides of the equation with respect to time t:

dV/dt = (dV/dr) * (dr/dt)

where dV/dt represents the rate of change of the volume with respect to time, dr/dt represents the rate of change of the radius with respect to time, and dV/dr represents the derivative of the volume with respect to the radius.

Given that the rate of change of the volume is 48x min (48 times the value of x), we have:

dV/dt = 48x

We need to find dr/dt when r = 2. Let's substitute these values into the equation:

48x = (dV/dr) * (dr/dt)

To solve for dr/dt, we need to determine the value of (dV/dr). Differentiating the volume equation with respect to r, we get:

(dV/dr) = 4πr^2

Substituting this value back into the equation:

48x = (4πr^2) * (dr/dt)

Since we are interested in finding dr/dt when r = 2, let's substitute r = 2 into the equation:

48x = (4π(2)^2) * (dr/dt)

48x = 16π * (dr/dt)

Now, we can solve for dr/dt:

(dr/dt) = (48x) / (16π)

Simplifying the expression:

(dr/dt) = 3x / π

So, at the instant when the radius is 2 units, the balloon's radius is increasing at a rate of 3x / π units per minute.

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Answer:

36

Step-by-step explanation:

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

a) Yes it does, because the graph of their relationship is a Straight line

b) Independent variables are variables whose variation does not depend on another. Number of works does not depend on followers. Therefore, it is independent

C)number of followers depend on the number of locks passing. It is dependent.

D) Slope = (Y₂- Y₁)/(x₂-x₁) = (100-82)/ (3-0) =  18/3 = 6

It represents the increase in number of followers per week,

E) y-intercept is value of y when x=0

y-intercept = 82. It means his initial number of followers

F) Slope-intercept form → y = mx + c m = slope горе C = y-intercept y = no of followers x= weeks.

Y=6x+82

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The net profit for the year ending December 31, 2021, is £1,000. Therefore, the correct answer is d) £1,000.

To determine the net profit for the year ending December 31, 2021, we need to calculate the total revenue and subtract the total expenses. Let's analyze the transactions provided:

The owners invested £550,000 of their own funds into the business bank account. This does not affect the net profit as it represents an owner's contribution of capital.

The business used £16,000 from the bank account to purchase short features and fashion. This expense reduces the net profit.

The business used £10,000 from the bank account to buy new inventory. This expense also reduces the net profit.

The business bought additional inventory worth £9,000 on credit. This is not an expense for the current year as it represents an increase in assets.

The shop sold £28,000 worth of inventory to customers for cash. This revenue increases the net profit.

The business sold goods costing £6,000 to another business on credit for £8,000. This revenue also increases the net profit.

The business paid £9,000 in rent from the bank account. This expense reduces the net profit.

Depreciation and estimated electricity expenses are not mentioned in the given transactions and cannot be calculated.

The owners withdrew £10,000 in cash for personal use. This is not an expense for the business and does not affect the net profit.

Based on the provided information, we can calculate the net profit as follows:

Total Revenue = £28,000 (from sales to customers) + £8,000 (from sales to another business) = £36,000

Total Expenses = £16,000 (short features and fashion) + £10,000 (new inventory) + £9,000 (rent) = £35,000

Net Profit = Total Revenue - Total Expenses = £36,000 - £35,000 = £1,000

Therefore, the net profit obtained is £1,000.

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Answer:

The numerator

Step-by-step explanation:

numerator is the top

denominator is the bottom

Answer:

Step-by-step explanation:

w (width) = 32/8

w = 4

p (perimeter) = 2w + 2l

p = (2 x 4) + (2 x 8)

p = 8 + 16

p = 24

The Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Here, we have,

The Taylor series at x=0 for cos(x) is given by:

cos(x) = ∑(n=0 to infinity) (-1)ⁿ * (x²ⁿ)) / (2n)!

Now, let's find the Taylor series at x=0 for the given function x * cos²((3πx)/2):

To find the Taylor series for the given function, we'll use power series operations.

We'll substitute the Taylor series expansion for cos(x) into the given function and then perform the necessary operations.

Let's start with cos²((3πx)/2):

cos²((3πx)/2) = (cos((3πx)/2))²

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!)²

Expanding the square of the series, we get:

cos²((3πx)/2)

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Now, we'll multiply the x term to obtain the Taylor series for the given function:

x * cos²((3πx)/2) = x * (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Expanding the multiplication and rearranging the terms, we have:

x * cos²((3πx)/2) = ∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Therefore, the Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

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Answer:

To solve for d, we have to isolate it from the other terms.

28 = d/4 + 24

Subtract 24 from both sides.

28 - 24 = d/4 + 24 - 24

Simplify terms in both sides.

4 = d/4

Multiply both sides by 4.

4x4 = d/4 x 4

Simplify terms on both sides.

d = 16

Hope this helps! :)

Answer:

\(d=16\)

Step-by-step explanation:

\(28=\frac{d}{4}+24\\\\28-24=\frac{d}{4}+24-24\\\\4=\frac{d}{4}\\\\4(4)=4(\frac{d}{4})\\\\16=d\)