express jenny’s age in terms of a if jenny is three years less than half of Anne’s age.

Answer:

2

Step-by-step explanation:

I know this because they both can go into 2 easily

The total weight of the liquid in the tank is 126295 pounds.

To calculate the total weight of the liquid in the tank, we need to first calculate the volume of the tank and then multiply it by the density of the liquid.

Given; Radius of the hemisphere (r) = 4 feet

Density of the liquid = 95 pounds per cubic foot

The formula for volume of a hemisphere is:

Volume = (2/3) × π × r³

Plugging in the given value of the radius (r):

Volume = (2/3) × π × (4 feet)³

Volume = (2/3) × π × 64 cubic feet

Next, we can multiply the volume by the density of the liquid to get the total weight of the liquid in the tank;

Total weight = Volume × Density

Plugging in the given value of the density:

Total weight = [(2/3) × π × 64 cubic feet] × 95 pounds per cubic foot

Total weight = 120160/3 × π pounds

Using the value of π as approximately 3.14 and rounding to the nearest full pound;

Total weight = 120160/3 × 3.14 pounds

Total weight = 126295.45 pounds

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Answer:

"To graph y = x² - 4, you would shift the graph of y = x² _down_ a distance of __4__ units.

Step-by-step explanation:

Start with the parent function

y = x²

When you substitute y - k for y, you are shifting the graph vertically k units.

The translated function is

y = x² - 4

Add 4 to both sides.

y + 4 = x²

y was substituted by y + 4.

We must write the substitution as y - k, so rewrite y + 4 as

y - (-4). Now compare y - (-4) with y - k.

k = -4

The vertical shift is -4, so the graph was translated 4 units down.

"To graph y = x² - 4, you would shift the graph of y = x² _down_ a distance of __4__ units.

To draw graph y = x² - 4, we shift the graph y = x² down a distance of 4 units.

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

Draw the graph y = x² - 4 with the help of graph y = x².

Now,

Since, The translated graph is,

y = x² - 4

Add 4 both side, we get;

y + 4 = x²

Clearly, y is substituted by y + 4.

Since, when we substitute y - k for y , then we shift k units down.

So, By comparing we get;

y + 4 = y - (-4)

The graph y = x² - 4 is shift down to 4 units.

Thus, To draw graph y = x² - 4, we shift the graph y = x² down a distance of 4 units.

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Answer: Choice C.

How many 1/4-meter long pieces of ribbon are needed to have a total of 3 1/2 meters of ribbon.

==========================================================

Explanation:

Let's consider a similar problem without the fractions.

Let's say you want to know how many 2 meter lengths of ribbon you can cut from an overall length of 24 meters. That would be 24 ÷ 2 = 12 pieces total.

So we divide the two values (large ÷ small)

The same idea applies to this problem as well. The larger amount (3 & 1/2 meters) is what we cut up, and each slice is 1/4 of a meter. To find the number of pieces, we would compute 3 1/2÷1/4

Note: it might help to convert the mixed number 3 & 1/2 to the improper fraction 7/2

Answer:

znvipahgvahgv

Step-by-step explanation:

Answer:

5\(\sqrt{3}\)

Step-by-step explanation:

in a 30-60-90 triangle the ratio of sides, respectively, is 1 : \(\sqrt{3}\) : 2

you can set up a proportion like this to solve for 'x':

\(\sqrt{3}\) / 1 = 15 / x

cross-multiply:

\(\sqrt{3}\)x = 15

x = 15/\(\sqrt{3}\)

rationalize the denominator by multiply top and bottom by \(\sqrt{3}\)

you get 15\(\sqrt{3}\) ÷ 3 which is 5\(\sqrt{3}\)

A graph which represent the solution to the inequality 0.75 is less than the product of a number and −1.5 is: B. number line with open circle on point on negative 0.5 with arrow shaded left.

In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Let the variable n represent the unknown number. Therefore, translating the word problem into an inequality, we have the following:

0.75 < -1.5 × n

Next, we would find the solution to this given inequality in order to determine its graph:

0.75 < -1.5n

0.75 + 1.5n < 0

1.5n < -0.75

Dividing both sides of the inequality by 1.5, we have:

n < -0.75/1.5

n < -0.5

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Answer:

The same amount

Step-by-step explanation:

Because its Borrowed money you cant just go around spending unlimited money with out paying the bank back it would not be fair.

Answer:

(x+3)² + (y-2)² = 16

Step-by-step explanation:

the equation of a circle is

(x-a)² + (y-b)² = r²

with (a,b) being the center, and r the radius.

Answer:

Step-by-step explanation:

8 I think

Answer:

Defination:

.the collection of distinct elements or members.

Step-by-step explanation:

A statistic is a a) sample characteristic, so the correct option is a) a sample characteristic.

A statistic is a numerical value calculated from a sample of data that is used to describe or make inferences about a larger population from which the sample was drawn. It is different from a parameter, which is a numerical value that describes a characteristic of a population.

Statistics are used in various fields, including science, business, economics, social sciences, and government. They can help researchers to summarize and analyze data, test hypotheses, and make predictions about future events or outcomes.

It is important to note that statistics are subject to variability due to sampling error, which can be reduced by increasing the sample size. Additionally, the distribution of statistics depends on the underlying distribution of the population from which the sample was drawn, and it may not always be normally distributed.

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Answer:

16 ties be be made from it

The  country's motivation for creating a single-party government is to promote unity.

A single party state can be defined as the state in which only one single political party  win an election after contesting  for an election and this party is the only party that will rule or dominate the state which is this type of party system is called dominant state compare to multi-party system in which two or more political parties are allow to contest for an election.

A country's motivation for creating a single-party government is that the countries may want to promote peace and unity among people.

The reason a country would  want to limit the number of parties in its system is that the country may want a unified set of goals and procedures for the country's future.

Therefore The  country's motivation for creating a single-party government is to promote unity.

The complete question is:

North Korea, China, and Cuba are modern examples of governments that legally or practically permit only one political party. In single-party states, other parties and their points of view are prohibited or discouraged.

Write a short paragraph discussing a country's motivation for creating a single-party government. Why would a country want to limit the number of parties in its system?

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The corrected exact values are cosine (5π/6) = -1/2, cosine (π/12) cannot be simplified further, sine (5π/6) = 1/2, sine (π/12) cannot be simplified further.

Let's correct the calculation of the exact values of the given trigonometric expressions:

1. Cosine (5π/6):

  The angle 5π/6 is in the second quadrant. The reference angle for 5π/6 is π/6. Since the cosine function is negative in the second quadrant, the exact value is -cos(π/6) = -1/2.

2. Cosine (π/12):

  The angle π/12 is not a special angle, so we cannot simplify it further using known exact values.

3. Sine (5π/6):

  The angle 5π/6 is in the second quadrant. The reference angle for 5π/6 is π/6. The sine function is positive in the second quadrant, so the exact value is sin(π/6) = 1/2.

4. Sine (π/12):

  The angle π/12 is not a special angle, so we cannot simplify it further using known exact values.

Therefore, the corrected exact values are:

cosine (5π/6) = -1/2,

cosine (π/12) cannot be simplified further,

sine (5π/6) = 1/2,

sine (π/12) cannot be simplified further.

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By using permutation it can be inferred that

Total number of ways she can arrange the 4 pieces in the program = 24

What is permutation?

The mathematical technique that is used to determine the number of arrangements in a set when the order of arrangement is taken into account is called permutation

This is a concept of  permutation

A pianist plans to play 4 pieces at a recital.

The first position can be filled in 4 ways,

The second position can be filled in 3 ways

The third position can be filled in 2 ways

The fourth position can be filled in 1 day

Total number of ways she can arrange the 4 pieces in the program =

                                                                                          \(4 \times 3 \times 2 \times 1\)

                                                                                         = 24

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Answer:

Amy has 12 5¢ coins

Step-by-step explanation:

Let x represent 20¢ coins and y represent 5¢ coins.

Amy has four more 20¢ coins than 5¢ coins. Hence:

\(x=y+4\)

And the total value of all her coins is $3.80. Thus:

\(0.2x+0.05y=3.8\)

This yields a system of equations:

\(\displaystyle \begin{cases} x=y+4 \\ 0.2x+0.05y=3.8\end{cases}\)

We can solve by substitution. Substitute the first equation into the first:

\(\displaystyle 0.2(y+4)+0.05y=3.8\)

Distribute:

\(\displaystyle 0.2y+0.8+0.05y=3.8\)

Combine like terms:

\(\displaystyle 0.25y = 3\)

And divide both sides by 0.25. Hence:

\(y=12\)

Thus, Amy has 12 5¢ coins.

Using the first equation:

\(x=y+4\)

Substitute:

\(x=(12)+4=16\)

Thus, Amy has 16 20¢ coins.

In conclusion, Amy has 12 5¢ coins and 16 20¢ coins.

Answer:

Answer

a Geometry :- shapes Are composed of regular lines and curves

b Organic shapes:- Unpredictable, irregular lines that suggest the natural world. Chaotic and unrestrained.

c Texture :-The surface quality of a work of art , for example coarse/fine detailed/lacking details

right answer organic..

i hope this helps you (⁠ ⁠◜⁠‿⁠◝⁠ ⁠)⁠♡

Therefore, An unpredictable and irregular shape is called an organic shape.

These shapes often mimic the forms found in nature, such as the shape of a leaf or a tree branch. Organic shapes lack the symmetry and geometric precision of their counterpart, the geometric shape. In art, organic shapes are commonly used to create a sense of movement, flow, and naturalism in a composition. In design, organic shapes can add visual interest and break up the monotony of straight lines and sharp angles. To sum up, the type of shape composed of unpredictable, irregular lines is an organic shape.

Therefore, An unpredictable and irregular shape is called an organic shape.

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N(A) is an ideal of R and N(N(A)) = N(A).

a) To prove that N(A) is an ideal of R, we need to show that it is closed under addition and multiplication by elements of R.

Let x, y ∈ N(A) and r ∈ R. Then there exist integers m and n such that xm ∈ A and yn ∈ A. By the commutative property of R, we have:

(x + y)n = xn + xny + yxn + yn ∈ A

(rx)n = rnxn ∈ A

Therefore, x + y ∈ N(A) and rx ∈ N(A), so N(A) is an ideal of R.


b) To prove that N(N(A)) = N(A), we need to show that N(N(A)) ⊆ N(A) and N(A) ⊆ N(N(A)).

Let x ∈ N(N(A)). Then there exists an integer n such that xn ∈ N(A). This means that there exists an integer m such that (xn)m ∈ A. By the associative property of R, we have:

(xn)m = xnm ∈ A

Therefore, x ∈ N(A), so N(N(A)) ⊆ N(A).

Let x ∈ N(A). Then there exists an integer n such that xn ∈ A. Since A ⊆ N(A), we have xn ∈ N(A). Therefore, x ∈ N(N(A)), so N(A) ⊆ N(N(A)).

Hence, N(N(A)) = N(A).
Conclusion: N(A) is an ideal of R and N(N(A)) = N(A).

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Answer:

25 students

Step-by-step explanation:

85 minus 10 = 75. this tells you how many he gave away.

75 pieces of gun divided by 3 is 25.

He gave out 3 pieces of candy, 25 times

Answer:57 degrees

Step-by-step explanation:

It is just below the 60-degree line. And it is less than 90 degrees.

Answer:

X=10

Step-by-step explanation:

Those two are the same angles.

4x=3x+10

x=10

The total distance d2 traveled by the particle during the time interval 0 ≤ t ≤ 5 is 25 as distance cannot be negative and the displacement d1 = 5 - (-10) = 15.

(a) The displacement d1 traveled by the particle during the time interval 0 ≤ t ≤ 5 can be found by evaluating the change in position. We can calculate this by finding the difference between the position at the end of the interval and the position at the beginning.

At t = 0, the position is \(v(0) = 3(0) - 10 = -10\).

At t = 5, the position is \(v(5) = 3(5) - 10 = 5\).

Therefore, the displacement d1 = 5 - (-10) = 15.

(b) The total distance d2 traveled by the particle during the time interval 0 ≤ t ≤ 5 can be found by considering the absolute value of the particle's velocity function. This gives us the magnitude of the particle's velocity regardless of its direction.

The velocity function \(v(t) = 3t - 10\) is positive for t > 10/3 and negative for t < 10/3. In the given time interval, the velocity function is always positive.

To find the total distance, we integrate the velocity function over the time interval:

\(d2 = \int_0 ^5 |3t - 10|\, dt\)

Splitting the interval into two parts where the velocity changes sign:

\(d2 = \int_0 ^ {10/3} (10 - 3t)\, dt + \int_{10/3}^ 5(3t - 10)\, dt\)

Evaluating the integrals:

\(d2 = [10t - (3t^2)/2] from 0 to 10/3 + [(3t^2)/2 - 10t] _{10/3} ^ 5\)

Simplifying further:

\(d2 = [10(10/3) - (3(10/3)^2)/2] - [10(0) - (3(0)^2)/2] + [(3(5)^2)/2 - 10(5)] - [(3(10/3)^2)/2 - 10(10/3)]\)

Calculating the values:

\(d2 = [100/3 - 100/6] - [0 - 0] + [75/2 - 50] - [100/2 - 100/3]\\d2 = 200/3 - 50/3 + 75/2 - 50 - 100 + 200/3\)

Simplifying the expression:

\(d2 = 400/3 - 250/3 + 150/2 - 50 - 100\\d2 = 150/3 + 150/2 - 150\\d2 = 50 + 75 - 150\\d2 = -25\)

Since, distance cannot be negative, so we take the absolute value:

d2 = | -25 | = 25.

Therefore, the total distance d2 traveled by the particle during the time interval 0 ≤ t ≤ 5 is 25 as distance cannot be negative.

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(a) T(n) has an upper bound of O(n log n) and a lower bound of Ω(n log n).

(b) T(n) has an upper bound of O(n) and a lower bound of Ω(n).

(f) T(n) has an upper bound of O(n) and a lower bound of Ω(n).

(g) T(n) has an upper bound of O(n^2) and a lower bound of Ω(n^2).

(a) For recurrence (a) T(n) = 2T(n/2) + n, we can apply the Master Theorem. Here, the value of a is 2, b is 2, and f(n) = n. Since log base b of a (log base 2 of 2) is equal to 1, and f(n) = n, it falls under Case 2 of the Master Theorem.

Hence, the upper bound is O(n log n). For the lower bound, we can use the Ω notation, which also gives a lower bound of Ω(n log n).

(b) For recurrence (b) T(n) = T(7n/10) + n, we notice that the size of the problem decreases by a factor of 10/7 in each recursion. Therefore, the number of recursive calls is logarithmic with base 10/7, resulting in an upper bound of O(n).

The lower bound can also be determined as Ω(n) since we have no information suggesting a smaller lower bound.

(f) For recurrence (f) T(n) = 2T(n/4) + n, we can again apply the Master Theorem. Here, the value of a is 2, b is 4, and f(n) = n. The log base b of a (log base 4 of 2) is equal to 0.5, which is less than 1.

Hence, it falls under Case 1 of the Master Theorem, and the upper bound is O(n). For the lower bound, we can again use the Ω notation, which also gives a lower bound of Ω(n).

(g) For recurrence (g) T(n) = T(n-2) + n^2, each recursive call decreases the problem size by 2. Since the number of recursive calls is n/2, the overall complexity is O(n^2). The lower bound can also be determined as Ω(n^2) since we have no information suggesting a smaller lower bound.

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Answer:

see explanation

Step-by-step explanation:

using the identity

cos²x = 1 - sin²x

consider the left side

\(\frac{1-cosx}{sinx}\)

multiply numerator/ denominator by (1 + cosx)

= \(\frac{(1-cosx)(1+cosx)}{sinx(1+cosx)}\) ← expand numerator

= \(\frac{1-cos^2x}{sinx(1+cosx)}\)

= \(\frac{sin^2x}{sinx(1+cosx)}\) ← cancel sinx on numerator/ denominator

= \(\frac{sinx}{1+cosx}\)

= right side , thus proven

Answer:6 is 127 degrees

7 is 53 degrees

Step-by-step explanation:

Hey there! :)

Answer:

(2, 3) and (-2, 11).

Step-by-step explanation:

To solve this system of equations, we can set both equations equal to each other:

x² -2x + 3 = -2x + 7

Combine like terms:

x² -4 = 0

Factor using difference of squares:

(x - 2)(x + 2) = 0

Therefore, x = 2 and -2. Plug both of these into an equation to solve for the 'y' value:

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

f(x) = -4 + 7

f(x) = 3

------------------

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

f(x) = 4 + 7

f(x) = 11

Therefore, the two ordered pairs are (2, 3) and (-2, 11).

Answer:

20,612.0 m³

Step-by-step explanation:

Formula for area of cone: 1/3h\(\pi\)r²

Since there is a 45 - 45 - 90 triangle and 27 meters is one of the congruent sides, the other side must also be 27 meters.

Then, just plug it in.

1/3 x 27m x 3.1415... x (27m)²

= (27m)³ x 3.1415 x 1/3

= 20,611.3815m³

≈ 20,612.0 m³

answer: mary - 13 apples

John - 8 apples

Richard - 16 apples

13 + 8 + 16 = 37