Question 4 (1 point)
A sixth-grade class collected data on the number of siblings in the class. Here is the dot plot of the data they collected.

What amount of siblings occurred most often? (What is the mode)

The general solution to the differential equation is y = -1/(3x³ + C)

Where C is an arbitrary constant.

The concept used to solve this differential equation is the separation of variables. Separated the variables on either side of the equation and then integrated both sides to get the general solution with a constant of integration.

Note that, the solution is valid only for y ≠ 0 as the differential equation is undefined for y = 0.

Here we have  

dy/dx = 9x²y²

Solve the differential equation using the separation of variables.

=> dy/dx = 9x² y²

Let's separate the variables by dividing both sides by y² and dx:

=> 1/(y²) dy = 9x² dx

Now we can integrate both sides:

=> ∫1/(y²) dy = ∫9x² dx

Using the power rule of integration, we get:

=> -1/y = 3x³ + C

Where C is the constant of integration.

To solve for y, we can multiply both sides by -1:

=> y = -1/(3x³ + C)

Therefore,

The general solution to the differential equation is y = -1/(3x³ + C)

Where C is an arbitrary constant.

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The area covered by grass in the nursery school playground is 5760 square meters.

To find the area covered by grass in the nursery school playground, we first need to calculate the total area of the playground, and then subtract the areas of the swings and the paths.

Given:

Length of playground = 160 m

Width of playground = 80 m

Width of swings = 80 m

Width of paths = 1.5 m

Total area of the playground = Length × Width = 160 m × 80 m = 12800 m²

Area of the swings = Width of swings × Width of swings = 80 m × 80 m = 6400 m²

Since there are two sides of the swings that are parallel to the length of the playground, we need to subtract the area of the paths along those two sides. The total width of the paths is 1.5 m + 1.5 m = 3 m.

Area of the paths along the length = Length of playground × Width of paths = 160 m × 3 m = 480 m²

Similarly, since there are two sides of the swings that are parallel to the width of the playground, we need to subtract the area of the paths along those two sides.

Area of the paths along the width = Width of playground × Width of paths = 80 m × 3 m = 240 m²

Now, we can calculate the remaining area covered by grass by subtracting the area of the swings and the areas of the paths from the total area of the playground:

Area covered by grass = Total area of playground - Area of swings - Area of paths along length - Area of paths along width

Area covered by grass = 12800 m² - 6400 m² - 480 m² - 240 m²

Area covered by grass = 5760 m²

So, the area covered by grass in the nursery school playground is 5760 square meters.

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Answer:

The mean is 8.6 minutes.

Step-by-step explanation:

"mean" is the average, the way people might talk about it in common language (not necessarily math class language.)

To calculate the mean, you ADD and DIVIDE. You add up all the numbers in your list and divide by however many numbers there are.

ADD:

5+5+15+12+14+6+3

= 60

Then DIVIDE by 7 (bc there are 7 items in the list)

60/7

= 8.5714285714

They said to round to the nearest tenth.

8.5714285714 rounds to 8.6

The mean is 8.6 minutes.

Answer:

To find the value of Clare's home in 2006 after an 18% increase, we can use the following formula:

Value in 2006 = Value in 2001 x (1 + Percent Increase)

Plugging in the values given in the problem, we get:

Value in 2006 = $135,000 x (1 + 0.18)

Simplifying this expression, we get:

Value in 2006 = $135,000 x 1.18

Value in 2006 = $159,300

Therefore, Clare's home was worth $159,300 in 2006 after an 18% increase in value from its original price of $135,000 in 2001.

Roehr Corporation Additional Paid-in Capital--Common account will increase by $110,000 by issuing 20,000 shares of $0.50 par common stock for $6 per share.

When a corporation issues common stock, the par value of the stock is recorded in the Common Stock account, and any amount received above the par value is recorded in the Additional Paid-in Capital--Common account. In this case, Roehr Corporation The par value of the common stock is

Total par value = Par value per share x Number of shares

= $0.50 x 20,000

= $10,000

The total amount received from issuing the stock is $6 per share x 20,000 shares = $120,000.

The additional paid-in capital is calculated as the difference between the total amount received and the total par value:

Additional paid-in capital = Total amount received - Total par value

= $120,000 - $10,000

= $110,000

Therefore, the answer is (B) $110,000.

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Answer:

44 <= x

Step-by-step explanation:

Answer:

Answers down below!

Step-by-step explanation:

Mean: 58.75

Median: 63

Range: 70

Mode: 63

Hope this helps!

The ratio of the lengths of the corresponding sides of the similar right triangles indicates that the length of the segment [tex]\overline{BD}[/tex] = 8 units

Similar triangles are triangles that have the same shape, and therefore, the interior angles of each triangle are congruent to the three angles in the similar triangle, however, the sizes of the triangles may be different.

The similar triangles are; ΔABD, ΔBCD, ΔACB

∠ABD ≅ ∠BCD ≅ ∠ACB (Corresponding angles in similar triangles are congruent)

[tex]\overline{AD}[/tex]/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/[tex]\overline{DC}[/tex]

4/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/16

4 × 16 = 64 = [tex]\overline{BD}[/tex]²

[tex]\overline{BD}[/tex] = √(64) = 8

The length of the segment [tex]\overline{BD}[/tex] = 8 units

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The costs of each treat are

To solve this, we use the followign representations

x = cookies

y = ice cream 1

z = ice cream 2

Treat 1

Using the columns to generate the system of equations, we have

x + y + z = 25.71

z + 2x = 23.21

3y = 26.94

So, we have

y = 8.98

The other equations become:

x + 8.98 + z = 25.71

z + 2x = 23.21

When solved, we have

x = 6.48

z = 10.25

Treat 2

Using the rows to generate the system of equations, we have

x + 2y = 7.17

y + 2x = 5.37

3z = 14.97

So, we have

z = 4.99

The other equations when solved, we have

x = 1.19

y = 2.99

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Mass of water vapor (g) / volume of air (m^3) is the humidity measure of absolute humidity

The humidity measure of "mass of water vapor (g) / volume of air (m^3)" is called absolute humidity. Absolute humidity is a measure of the total amount of moisture in the air, expressed as the mass of water vapor per unit volume of air. It is different from relative humidity, which is a measure of the amount of moisture in the air relative to the maximum amount of moisture that the air can hold at a particular temperature.

Mixing ratio is also a measure of the amount of moisture in the air, but it is expressed as the mass of water vapor per mass of dry air, not per unit volume of air. Vapor pressure is a measure of the pressure exerted by water vapor in the air, expressed in units of pressure (such as millibars or pascals), not as a ratio.

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The linear function going through the points (0,2) and (6,0) is given as follows:

y = -x/3 + 2.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

When x = 0, y = 2, hence the intercept b is given as follows:

b = 2.

When x increases by 6, y decays by 2, hence the slope m is given as follows:

m = -2/6

m = -1/3.

Thus the equation of the line is given as follows:

y = -x/3 + 2.

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The one less likely to be picked is the one with less & (Vice Versa).

To find the probability: (#of paper clips/total amount of items)

The width of the rectangle is x + 4

Since the area of the rectangle is x^2 + 15x + 44, the product that give the value can be solved by factorization

To factorize the expression x^2 + 15x + 44, we need to find two numbers whose product is 44 and whose sum is 15. These numbers are 11 and 4, because 11 times 4 is 44 and 11 plus 4 is 15.

Now we can write the expression as:

x^2 + 11x + 4x + 44

Grouping the terms in pairs:

(x^2 + 11x) + (4x + 44)

Factoring out the greatest common factor from each pair:

x(x + 11) + 4(x + 11)

Now we can see that we have a common factor of (x + 11):

(x + 11)(x + 4)

Therefore, the factored form of x^2 + 15x + 44 is:

(x + 11)(x + 4)

the width of the rectangle is x + 4

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The square of binomial have in common is x² - 14x + 49

The first two products you have given, (x + 9)(x + 9) and (x - 7)(x - 7), are examples of the square of a binomial. To find the product of two binomials, we use what's called the FOIL method. FOIL stands for First, Outer, Inner, Last, and it's a way to remember the steps involved in multiplying two binomials.

When we multiply (x + 9)(x + 9), we first multiply the first terms in each binomial: x * x = x². Then we multiply the outer terms: x * 9 = 9x. Next, we multiply the inner terms: 9 * x = 9x. Finally, we multiply the last terms in each binomial: 9 * 9 = 81. So, putting it all together, we get:

(x + 9)(x + 9) = x² + 9x + 9x + 81

= x² + 18x + 81

Similarly, when we multiply (x - 7)(x - 7), we get:

(x - 7)(x - 7) = x² - 7x - 7x + 49

= x² - 14x + 49

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Complete Question:

Find each product. (x + 9) (x + 9) , (x - 7)(x - 7) (2x - 1 )²

a. What do all products of the square of a binomial have in common?

The total area of the four offices in the building is 1296 square feet.

When we talk about the area of a shape, we are referring to the amount of space that it occupies. In this case, since the offices are squares, we can find the area of each office by multiplying the length of one side by itself. This is represented by the formula A = s², where A is the area and s is the length of one side.

So, if each office has a side length of 18 feet, we can find the area of one office by plugging that value into the formula: A = 18² = 324 square feet.

Since there are four offices, we can find the total area of all four offices by multiplying the area of one office by 4: 324 square feet x 4 = 1296 square feet.

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Answer:

When the red lines in a geometric figure are not parallel, the congruency of angles may vary. Vertical angles formed by the intersection of non-parallel lines are always congruent, while corresponding angles and alternate interior angles may or may not be congruent. The congruency of angles depends on the specific relationship between the angles and the lines in the figure, and further analysis of the figure would be necessary to determine which angles are congruent.

a) His monthly salary is, 555.6

b) Total amount spent on his parent​ is, 111.1

Given that;

Mr. Ade plans to spend his monthly salary as follows

food-20%

children-25%

parents-20%

car-10%

entertainment-10%

saving-2½

miscellenceous-2½

And, the amount of saving kept for saving is Ghc 250.00.

Hence, We get;

Monthly salary is,

Since, We have;

Percent of savings = 100% - 20% - 10% - 10% - 12.5% - 2.5%

                             = 45%

Hence, We get;

45% of salary = 250

45/100 x salary = 250

Monthly salary = 25000 / 45

Monthly salary = 555.6

And, Money spent on parents;

20% of 555.6

20/100 x 555.6

111.1

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Answer:

230°

Step-by-step explanation:

Because Arc RSP had three letters that means its a major arc or greater than 180°

Arc RP is the portion of the circle not intercepted by the angle so 360 minus the measure of RP is RSP

360 - 130 = 230

Answer:

A

Step-by-step explanation:

it cant be 9 per hour cuz it is a smaller amount and A is the only one that makes sens

Answer:

true

Step-by-step explanation:

Answer:

10 inches

Step-by-step explanation:

The rule for a 45-45-90 triangle is if the two legs equal x then the hypotenuse is x√2.

So if the hypotenuse is 10√2 then the length of the leg d is 10

Answer: We can use the formula for exponential decay to find the mass of substance A in the dish after 12 hours:

A = A0 * e^(-kt)

where:

A0 = initial mass of substance A (500 grams)

A = mass of substance A after time t

k = decay constant

t = time (in hours)

Since the mass of substance A decreases at the rate of 20% every 6 hours, we can find the decay constant as follows:

20% = 0.2 = e^(-k*6)

Taking the natural logarithm of both sides, we get:

ln(0.2) = -k*6

k = -ln(0.2)/6

k ≈ 0.1155

Substituting the values of A0, k, and t into the formula for exponential decay, we get:

A = 500 * e^(-0.1155*12)

A ≈ 169.2 grams

Therefore, the mass of substance A in the dish at the end of 12 hours is approximately 169.2 grams.

Step-by-step explanation:

The mass of substance A in the dish at the end of 12 hours would be 320 grams.

The mass of substance A decreases at a rate of 20% every 6 hours. After 6 hours, the mass of substance A remaining in the dish would be:

500 - (20/100) * 500

500 - 100

400 grams

After another 6 hours (i.e. at 12 hours), the remaining mass of substance A would be:

400 - (20/100) * 400

400 - 80

320 grams

Therefore, the mass of substance A in the dish at the end of 12 hours would be 320 grams.

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The amount of space that the flower pot will take up is: 38.47 cm²

We are given that the bottom of the given flower pot has a diameter of 7 cm.

Now, the space that the flower pot will cover is simply the area the the circle base.

Formula for the area of a circle is:

A = πr²

where:

A is area

r is radius

We have d = 7 cm

Thus: r = 7/2 = 3.5 cm

A =  π * 3.5²

A = 3.14 * 3.5²

A = 38.47 cm²

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Around 21.13% of the batteries will final(last) between 90.6 and 109.8 hours. 

To unravel this issue, ready to utilize the standard typical conveyance by standardizing the values utilizing the equation:

z = (x - μ) / σ

where

x is the esteem we need to discover the likelihood

μ is cruel(mean), and σ is the standard deviation.

So, for the lower conclusion of the extent, we have:

z1 = (90.6 - 105) / 12 ≈ -1.20

z1 = -1.20

And for the upper conclusion of the extension, we have the:

z2 = (109.8 - 105) / 12 ≈ 0.45

z2 =  0.45

We need to discover the rate of batteries that will final(last) between these two values, which compares to the area under the typical bend between z1 and z2.

Able to utilize a standard ordinary conveyance table or calculator to discover this zone, or we will utilize the properties of the typical conveyance to inexact it.

Since the typical conveyance is symmetric around the cruel, we know that the zone between z1 and z2 is the same as the range between -z2 and -z1 (i.e., the comparing values on the other side of the mean).

So, ready to discover the range between -z2 and -z1, which compares to the rate of batteries that will final between 90.6 and 109.8 hours:

P(-z2 < z < -z1) ≈ P(z < -z1) - P(z < -z2)

Employing a standard typical dissemination table or calculator, we discover:

P(z < -1.20) ≈ 0.1151

P(z < -0.45) ≈ 0.3264

So, the rate of batteries that will final between 90.6 and 109.8 hours is rough:

P(-z2 < z < -z1) ≈ 0.3264 - 0.1151 ≈ 0.2113

Increasing by 100%, we get:

0.2113 * 100% ≈ 21.13D

44 Subsequently, roughly 21.13% of the batteries will final between 90.6 and 109.8 hours. 

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The thickness of the concrete pad is 58 and 2/81 yd³. So correct option B.

Volume is the measure of the amount of space occupied by a three-dimensional object or substance. It is typically measured in units such as cubic meters, cubic feet, liters, or gallons. The formula for calculating the volume of a simple shape like a cube, rectangular prism, or cylinder involves multiplying its length, width, and height or its base area and height. More complex shapes may require more advanced formulas or techniques for determining their volume. Volume is an important concept in many fields, including physics, engineering, architecture, and chemistry, and is often used to measure quantities such as liquids, gases, and solids.

To find the volume of the concrete pad, we need to multiply the length, width, and thickness of the pad.

First, we need to convert the dimensions to yards by dividing by 3 since there are 3 feet in a yard:

Length: 31 and 1/3 yards = 94/3 yards

Width: 16 and 2/3 yards = 50/3 yards

Thickness: 1/9 yard

Now we can calculate the volume:

V = (94/3) * (50/3) * (1/9)

V = 4700/81 cubic yards

V ≈ 58.02 cubic yards

Therefore, the answer is B. 58 and 2/81 yd³.

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The complete question is:

Answer: 50 * 1,967 = 98,350

50 * 1,000 = 50,000

Step-by-step explanation: 50 * 1,967 = 50 * 1,000 + 50 * 967 = 50,000 + 48,350 = 98,350.

Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:

Salary paid in cash = Salary expense in 2014 - Reduction in salary payable

The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:

Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.

The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:

Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.

Hence, (A) $55,100 is the correct response.

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The incorrect measurements of the right triangle is 36² + 60² = 48²

Given data ,

Let the triangle be represented as ABC

Now , let the height of the triangle be AB = 36 miles north

Let the base of the triangle be BC = 48 miles east

Now , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , 36² + 48² = 60²

So , the incorrect option from the data is 36² + 60² = 48²

Hence , the triangle is formed

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The annual interest rate of the account is 3.5%

The formula for simple interest is:

I = Prt

where I is the interest earned, P is the principal (initial amount deposited), r is the annual interest rate (as a decimal), and t is the time in years.

We know that P = £13,000, t = 15 years, and I = £19,825 - £13,000 = £6,825.

Plugging in these values, we get:

£6,825 = £13,000 * r * 15

Simplifying this equation, we get:

r = £6,825 / (£13,000 * 15) = 0.035 = 3.5%

Therefore, the annual interest rate of the account is 3.5% to 1 decimal place.

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The best description of the area under the normal curve that would be used to approximate binomial probability is 'Area to the left of 46.5'.

To approximate the binomial probability, we can use the normal distribution as an approximation for the binomial distribution when the sample size is large enough, and the probability of success is not too close to 0 or 1. The mean of the normal distribution is equal to the mean of the binomial distribution, which is np, and the standard deviation of the normal distribution is equal to the square root of npq, where q is the probability of failure.

In this case, the number of DVDs that may malfunction follows a binomial distribution with parameters n = 319 and p = 1/100, where 1/100 is the probability of a DVD malfunctioning. Therefore, the mean of the binomial distribution is np = 3.19, and the standard deviation is [tex]\sqrt{npq}[/tex] = [tex]\sqrt{3.19*0.99}[/tex] ≈ 1.77.

To find the probability that at most 46 out of 319 DVDs will malfunction, we need to find the area under the normal curve to the left of 46.5 (since we are interested in the probability of at most 46 malfunctions, which includes 46.5 as well). Therefore, the answer is 'Area to the left of 46.5'.

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