Jack wants to know how much water a sphere can hold with a radius of 8 cm. Find the volume. Use 3.14
for pi.
a
2144.7 cm
b
254 cm
С
83.6 cm
d
2220 cm

Answer:

The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1 / m. For example, we found that the slope of the line y = (1/2)x + 3 is 1/2.

The slopes of perpendicular lines when multiplied together gives the product as -1.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.

The negative slope indicates the rate of decrease while the positive shows the rate of increase.

Suppose the two perpendicular lines have equations as follows,

y = m₁x + c₁  and y = m₂x + c₂.

Suppose m₁ = tan θ

Then, m₂ = tan (90° + θ)

Apply the trigonometric identity to obtain,

m₂ = tan (90° + θ)  = -cot θ

Now, m₁ × m₂ = tan θ × -cot θ = -1

Thus, the products of slopes is -1.

Hence, the product of slopes of two perpendicular lines is -1.

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Answer:

Hope this helps :)

you will find every answer in the photo I sent

Answer:

20

Step-by-step explanation:

\(10x - 30\)

\(10 \times 5 - 30\)

\(50 - 30\)

\( = 20\)

Solution

Part A

First school

Loris State Community College

Cost for two year tuition $9,500

15 years to months

Amount to pay monthly

You will have to pay $92.36 monthly

Par B

Marlo State Community College/ Cost for two-year tuition $10,500

Now the monthly pay

15years =180months

The monthly pay is $102.08

Answer:

The numbers are: 8 , 12

Step-by-step explanation:

Ratio of two numbers = 2:3

Two numbers are : 2x , 3x

\(\frac{2x +12}{3x +12}=\frac{5}{6}\\\\\)

Cross multiply,

6*(2x + 12) = 5*(3x+12)

6*2x +6*12 = 5*3x + 5*12

12x + 72 = 15x + 60

72 - 60 = 15x - 12x

12 = 3x

3x = 12

x = 12/3

x = 4

2x = 2*4 = 8

3x = 3*4 = 12

The numbers are: 8 , 12

Answer:

x = 10.

y = 11

Step-by-step explanation:

2x+3y=53

3x-y=19

x = 10; y = 11

The method to convert milimeter to meters will be through multiplication of \( {10}^{-3} \) with the quantity in milimeter.

The abbreviation mm is representative of milimeters. Now, we know that milimeters is 1/1000 meters and hence is smaller unit in comparison to meters.

Based on the above mentioned fact, we can multiply the same number (smaller unit) with negative exponent. It will be carried out like this -

Quantity in meters = quantity in milimeter ×

\( {10}^{-3} \), where \( {10}^{-3} \) has negative exponent. Let us say we have 10⁹ milimeters and need to convert in into meters.

So, quantity in meter = 10⁹ × \( {10}^{-3} \),

Performing multiplication which will be done through subtraction of powers

Quantity in meters = 10⁶ meters

Hence, mm to meters will be multiplication with \( {10}^{-3} \).

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Answer:

m = − 1/2

Step-by-step explanation:

Use the formula to calculate the slope of the line passing through the points.

slope = (y₂ - y₁) / (x₂ - x₁)

Input the values into the formula.

Subtract the values in parentheses.

Simplify the fraction to get the slope.

Answer: y = -1/2x +2

Answer:

Practice!

Step-by-step explanation:

Seriously, ask friends or family for complete random questions. Ask your teacher for tips.

Answer:

equation:

225 + 80x = y

total cost of 9000 stickers:

$865

if two triangles have three pairs of congruent angles, then they must be congruent to each other by the Angle-Angle-Angle (AAA) congruence theorem, and thus cannot be non-congruent.

No, it is not possible to make two triangles that are not congruent and have three pairs of congruent angles. This is because if two angles of a triangle are congruent, then the third angle must also be congruent by the Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees. If two triangles have three pairs of congruent angles, then all three angles in each triangle are congruent, meaning they have the same measure. However, this does not guarantee that the sides of the triangles are congruent. In order for two triangles to be congruent, they must have the same angle measures as well as the same side lengths. Therefore, if two triangles have three pairs of congruent angles, then they must be congruent to each other by the Angle-Angle-Angle (AAA) congruence theorem, and thus cannot be non-congruent.

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According to the translation rule (x, y) → (x + 2, y - 8), B (4,-5) will be transformed to B'

O (6,-13)

A transformation known as a translation involves moving each point in a figure uniformly and in the same direction.

information from the question

Transformation rule (x, y) → (x + 2, y - 8)

B is at 4, negative 5 = B (4, -5)

The transformation rule gives

point B (4, -5)

applying the rule

x' = 4 + 2 = 6

y' = -5 - 8 = -13

The coordinates of point B' (x', y') after translation is = B'(6, -13)

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Answer:

not sure

Step-by-step explanation:

not sure sqauredxfree bagdes

=answer

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Answer:

Option A

Step-by-step explanation:

to be perpendicular, the product of two slopes should be -1

the slope of the first equation is 1/5, so the slope should be -5

(1/5) (-5)= -1

y= -5x +b

Substitute (1,1) to solve for b,

b= 6

Thus, the equation is y= -5x +6

When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is   \(\\26 \frac{2}{5}\).

What is improper fractions?

An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

12 times 120% + 12

12*120%+12

\($$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$\)

Follow the PEMDAS order of operations

Multiply and divide (left to right) \($12 \times \frac{6}{5}: \frac{72}{5}$\)

\(=\frac{72}{5}+12$$\)

Add and subtract (left to right) \($\frac{72}{5}+12: \frac{132}{5}$\)

\(=\frac{132}{5}$$\)

Convert improper fractions to mixed numbers: \($\frac{132}{5}=26 \frac{2}{5}$\)

\(=26 \frac{2}{5}$$\)

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There is an 86.06% chance that the sample mean fill volume for a random sample of 45 bottles will fall between 1.98 and 2.02 liters.

The sampling distribution of the sample mean fill volume for a random sample of 45 bottles is approximately normal by the Central Limit Theorem, provided that the sample size is sufficiently large. The mean of the sample mean fill volume is equal to the target mean fill volume, μ=2.0 liters.

The standard deviation of the sample mean fill volume is equal to the standard error of the mean, which is σ/√n = 0.05/√45 ≈ 0.0075 liters.

To find the probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters, we need to standardize the values using the formula z = (x - μ) / (σ / √n), where x is the sample mean, μ is the target mean, σ is the standard deviation of the population, and n is the sample size.

Thus, we have z1 = (1.98 - 2.0) / (0.05 / √45) ≈ -1.79 and z2 = (2.02 - 2.0) / (0.05 / √45) ≈ 1.79.

Using a standard normal distribution table or calculator, we find that the probability is approximately 0.8606. Therefore, there is an 86.06% chance that the sample mean fill volume for a random sample of 45 bottles will fall between 1.98 and 2.02 liters.

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The probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters is approximately 0.9934 or 99.34%.

(a) The sampling distribution of the sample mean fill volume for a random sample of 45 bottles is approximately normal due to the Central Limit Theorem. The mean of the sampling distribution is equal to the target mean fill volume, which is μ = 2.0 liters. The standard deviation of the sampling distribution, also known as the standard error of the mean, is σ/√n, where σ is the standard deviation of the population and n is the sample size. Therefore, the standard error of the mean is:

SE = σ/√n = 0.05/√45 = 0.00746

So the mean and standard deviation of the sampling distribution are:

Mean = μ = 2.0 liters

Standard deviation = SE = 0.00746 liters

(b) We want to find the probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters. We can standardize the values using the formula:

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean. Thus:

z1 = (1.98 - 2.0) / 0.00746 = -2.68

z2 = (2.02 - 2.0) / 0.00746 = 2.68

Using a standard normal distribution table or calculator, we can find the probability that z is between -2.68 and 2.68:

P(-2.68 < z < 2.68) = 0.9967 - 0.0033 = 0.9934

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Answer:

9.16

Step-by-step explanation:

4.58/.5

Answer:

9.16

Step-by-step explanation:

4.58

--------

0.5

45.8

--------

5

5 into 45 is 9

9 x 5 = 45

45-45= 0

5 into 8 is 1

1 x 5 = 8

8 - 5 = 3

Bring down the zero: 30

5 into 30 is 6

5 x 6 = 30

30 - 30 = 0

the solution for long division of 4.58

                                                    -------- = 9.16

                                                       5

Hope this helps

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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The length of the shadow casted by the high rise building is approximately 37.7 feet

The image in the question forms a right triangle:

Angle θ = 57 degrees

Opposite to angle θ = 58 feet

Adjacent to angle θ = x

To solve for x ( length of the shadow casted by the building ), we use the trigonometric ratio.

Note: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the values:

tan( 57° ) = 58ft / x

Cross multiply and solve for x:

x × tan( 57° ) = 58ft

x = 58ft / tan( 57° )

x = 37.7 ft

Therefore, the value of x is 37.7 feet.

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The simplified expression of the expression given as √72x³z³ is 6xz√(2xz)

From the question, we have the following parameters that can be used in our computation:

√72x³z³

Express 72 as the product of 36 and 2

So, we have the following representation

√72x³z³ = √(36 * 2)x³z³

Take the square root of 36

This gives

√72x³z³ = 6√(2x³z³)

Take the square root of x³z³

So, we have the following representation

√72x³z³ = 6xz√(2xz)

Hence, the solution is 6xz√(2xz)

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Abbie and Ben would not be able to buy locally-grown corn in Rhode Island until late October.

Amount is an indefinite quantity of something, typically money, that is to be paid or received. It is often used in the context of a purchase, loan, or other financial transaction. Amounts can be expressed as a numerical value, such as a dollar amount, or as a percentage of the total transaction. In accounting, the term "amount" is used to refer to the total amount of money that is owed or received.

Abbie and Ben could not buy locally-grown corn in May or June in Rhode Island because the growing season for corn in Rhode Island runs from late June through late October. This is the typical growing season for corn in the Northeastern United States and is largely dependent on the region's climate. Corn is a warm-season crop, meaning it requires temperatures of at least 50 degrees Fahrenheit for germination and growth. In early spring, most of Rhode Island is still too cold for corn to be planted. This means that the earliest corn grown in Rhode Island is planted in late June, and it is not harvested until late October. Thus, Abbie and Ben would not be able to buy locally-grown corn in Rhode Island until late October.

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The solution of each part of the question is given below:

a. Let C be the event that a person smokes cigars, and let S be the event that a person smokes cigarettes. The percentage of Americans who smoke either cigars, cigarettes, or both can be calculated as P(C U S), where U represents the union of two events. From the given information, P(C) = 15% and P(S) = 35%. The probability that a person smokes both cigars and cigarettes is 7%, so P(C ∩ S) = 7%.

P(C U S) = P(C) + P(S) - P(C ∩ S)

P(C U S) = 15% + 35% - 7% = 43%

So, 43% of Americans smoke either cigars, cigarettes, or both.

b. The percentage of Americans who smoke neither cigars nor cigarettes can be calculated as P(C' ∩ S'), where C' represents the complement of event C (not smoking cigars) and S' represents the complement of event S (not smoking cigarettes).

P(C' ∩ S') = 100% - P(C U S)

P(C' ∩ S') = 100% - 43% = 57%

So, 57% of Americans smoke neither cigars nor cigarettes.

c. The percentage of Americans who smoke cigars but not cigarettes can be calculated as P(C ∩ S').

P(C ∩ S') = P(C) - P(C ∩ S)

P(C ∩ S') = 15% - 7% = 8%

So, 8% of Americans smoke cigars but not cigarettes.

d. The conditional probability that a person smokes cigarettes given that he smokes cigars can be calculated as P(S | C), where S represents the event that a person smokes cigarettes and C represents the event that a person smokes cigars.

P(S | C) = P(S ∩ C) / P(C)

P(S | C) = 7% / 15% = 0.47

So, the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars is 0.47, or 47%.

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Answer: I think it’s 13

Step-by-step explanation:

The remaining amount of salt as a function of time is given by 0.01 kg/(1 + B/100) liters. The exact amount of salt in the tank after C minutes would require specific values for B and C.

A) The remaining amount of salt in the tank as a function of time can be found by considering the rate at which salt enters and leaves the tank. Initially, there is 1 kg of salt in 100 liters of brine, so the concentration of salt is 1 kg/100 liters = 0.01 kg/liter.

Each minute, B liters of water are added to the tank, diluting the concentration of salt. The new concentration of salt in the tank is given by (1 kg)/(100 + B) liters = 0.01 kg/(1 + B/100) liters.

B) The graph of the function would show the time on the x-axis and the remaining amount of salt on the y-axis. As time progresses, the amount of salt decreases since water is continuously added and an equal amount of mixture leaves the tank. The graph would show a decreasing trend.

C) To calculate the amount of salt in the tank after C minutes, we need to consider the cumulative effect of dilution over time. The remaining amount of salt after C minutes can be found by substituting C into the function from part A: 0.01 kg/(1 + B/100) liters.

Note that the specific value of B and C would be needed to obtain a numerical result.

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The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

\(b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2\)

Roots of quadrant equation have Samsame sign if product of roots >0.

\(\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0\)

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

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Answer:

10.43

Step-by-step explanation:

3x+4=10x-69

-3x      -3x

4=7x-69

+69  +69

73=7x

/7   /7

10.43=x

-hope it helps