The price of an item was reduced by 10% and then by 20%. Is that the same as reducing the price by 30%? If not, then what percentage reduction is equivalent to the two reductions?

To ensure that you have at least two cards with the same denomination, you would need to draw five cards.

This problem is a variation of the pigeonhole principle, also known as the birthday paradox. There are 13 denominations in a standard deck of cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King), and drawing five cards creates five pigeonholes. Since there are more pigeonholes than there are denominations, it is guaranteed that at least two of the cards will have the same denomination. To see this, note that drawing six cards will also guarantee two cards with the same denomination, since there would be six pigeonholes and only 13 denominations.

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Answer:

A

Step-by-step explanation:

Change in population (in thousands) in 10 year period:

1970-1980: 175-158 = 17

1980-1990: 195-175 = 20

1990-2000: 227 - 195 = 32

32,000 is the largest growth in a 10 year period, so the answer is 1990-2000.

Answer: A

Answer:

1/5

Step-by-step explanation:

solution [ calculation of probability ]

P= (3/3+6) × (6/3+6-1)

=3/9×6/10

=1/5

Answer:

-75.7224

Step-by-step explanation:

Multiplication in base five can be challenging. However, I will try my best to break the information down into into steps to make it easy to understand and master.

It is similar to multiplying numbers in base 10. However, because we are not used to do this in base 5, it may appear tough.

Plan to spend some time reading this lesson about multiplication in base five more than once.

First, know the difference between base 5 place value and base 10 place value.

I show the difference with two numbers: 48573 and 134125

For 48573, 5 is in the hundreds place and it means there are 5 hundreds

For 134125

, 4 is in the twenty-fives place and it means there are 4 twenty-fives

Difference between base 10 and base 5

The most difficult concept with multiplication in base five is to master how to carry numbers.

Study the following two multiplications carefully. The one on the right is the multiplication in base five.

Example showing how to do multiplication in base five

8 6 4

× 3 6

_____________

3 4 35

× 2 45

______________

5 3 2

8 6 4

× 3 6

__________

5 1 8 4 3 3 2

3 4 35

× 2 45

___________

3 0 3 25

Step 1:

6 × 4 = 24.

24 = 10 + 10 + 4

You have 2 tens to carry.

Write 4 down in the ones place.

Carry 2 tens by putting 2 in the tens place (Shown in red) Step 1:

4 × 3 = 12.

12 = 5 + 5 + 2

You have 2 fives to carry.

Write 2 down in the ones place.

Carry 2 fives by putting 2 in the fives place (Shown in red)

Step 2:

6 × 6 = 36.

36 + 2 = 38 tens

38 tens = 10 tens + 10 tens + 10 tens + 8 tens

= 100 + 100 + 100 + 80

= 100 + 100 + 100 + 8 tens

You have 3 hundreds to carry. Write 8 down in the tens place and carry 3 hundreds by putting 3 in the hundreds place (Shown in green) Step 2:

4 × 4 = 16.

16 + 2 = 18 fives

18 fives = 5 fives + 5 fives + 5 fives + 3 fives

= 25 + 25 + 25 + 15

= 25 + 25 + 25 + 3 fives

You have 3 twenty-fives to carry. Write 3 down in the fives place and carry 3 twenty-fives by putting 3 in the twenty-fives place (Shown in green)

Step 3:

6 × 8 = 48.

48 + 3 = 51 hundreds

51 hundreds = 10 hundreds + 10 hundreds + 10 hundreds + 10 hundreds + 10 hundreds + 1 hundred

= 1000 + 1000 + 1000 + 1000 + 1000 + 100

= 1000 + 1000 + 1000 + 1000 + 1000 + 1 hundred

You have 5 thousands to carry. Write 1 down in the hundreds place and carry 5 thousands by putting 5 in the thousands place (Shown in black)

Bring down the 5 in the thousands place Step 3:

4 × 3 = 12.

12 + 3 = 15 twenty-fives

15 twenty-fives = 5 twenty-fives + 5 twenty-fives + 5 twenty-fives + 0 twenty-five

= 125 + 125 + 125 + 0

= 125 + 125 + 125 + 0 twenty-five

You have 3 one hundred twenty-fives to carry. Write 0 down in the twenty fives place and carry 3 one hundred twenty-fives by putting 3 in the one hundred twenty-five place (Shown in black)

Bring down the 3 in the one hundred twenty-fives place.

Notice again the 0 in the twenty-fives place.

2 1 1

8 6 4

× 3 0

________________

2 5 9 2 0 1 1 1

3 4 35

× 2 05

_______________

1 2 4 1 05

Step 4:

3 × 4 = 12 tens.

12 tens = 10 tens + 2 tens = 100 + 2 tens

Carry 1 hundred by putting 1 in the hundreds place (Shown in red)

Write 2 down in the tens place.

Since there is nothing in the ones place, just put a 0. Step 4:

2 × 3 = 6 fives.

6 fives = 5 fives + 1 five = 25 + 1 five

Carry 1 twenty five by putting 1 in the twenty-fives place (Shown in red)

Write 1 down in the fives place.

Since there is nothing in the ones place, just put a 0.

Step 5:

3 × 6 = 18 hundreds.

18 hundreds + 1 hundred = 19 hundreds

19 hundreds = 10 hundreds + 9 hundreds

= 1000 + 9 hundreds

Write 9 down in the hundreds place and carry 1 thousand by putting 1 in the thousand place (Shown in green)

Step 5:

2 × 4 = 8 twenty-fives.

8 twenty-fives + 1 twenty-five = 9 twenty-fives

9 twenty-fives = 5 twenty-fives + 4 twenty-fives

= 125 + 4 twenty-fives

Write 4 down in the twenty-fives place and carry 1 one hundred twenty-five by putting 1 in the one hundred twenty-five place (Shown in green)

Step 6:

3 × 8 = 24 thousands.

24 thousands + 1 thousand = 25 thousands

25 thousands = 10 thousands + 10 thousands + 5 thousands

= 10000 + 10000 + 5 thousands

Write 5 down in the thousands place and carry 2 ten thousands by putting 2 in the ten thousands place (Shown in black)

Bring the 2 down in the ten thousands place Step 6:

2 × 3 = 6 one hundred twenty-fives.

6 one hundred twenty-fives + 1 one hundred twenty five = 7 one hundred twenty-fives

7 one hundred twenty-fives = 5 one hundred twenty-fives + 2 one hundred twenty-five = 625 + 2 one hundred twenty-five

Write 2 down in the one hundred twenty-fives place and carry 1 six hundred twenty-five by putting 1 in the six hundred twenty-five place (Shown in black)

Just add now. You may need to review addition in base five before even starting this lesson about multiplication in base five.

Adding the results in base ten.

1 1 1

5 1 8 4

2 5 9 2 0

____________

3 1 1 0 4

Adding the results in base five.

1

3 0 3 2

1 2 4 1 0

______________

2 0 4 4 2

Again, it is quite challenging to do multiplication in base five. I recommend you take your time when reading this lesson. Don't give up

The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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Answer:

-6

Step-by-step explanation:

you would use the slope formula y2-y1/x2-x1. the equation should be like 8-2/-2-(-1). Then simplify: 6/-1 or -6

Answer:

66.6% (see below)

Step-by-step explanation:

Each sphere 4/3\(\pi\)r²=4/3\(\pi\)(4²)=268.08cm³

Assuming the tube is the same width and height as the three spheres,

V=\(\pi\)r²h=\(\pi\)(4²)24=1206.37

The three spheres are 268.08*3=804.24cm³

The tube is 1206.37cm³

I’m not sure if your question is asking the percentage of the tube that’s filled, or the percentage that’s unfilled.

Filled: 804.24÷1206.37=0.66666=66.6%

Unfilled: 1206.37-804.24=402.13

402.13÷106.37=0.33333=33.3%

Answer:

Percentage of Tube Unfilled : 33 and 1/3%

Step-by-step explanation:

It's most likely that we want to calculate the percentage of the tube unfilled, as the tube itself wouldn't be provided otherwise. We can start by calculating the volume of the tube --- (1)

The volume of a cylinder is represented by πr²h. Substituting we would receive π(4)²h. h is represented by 3 times the diameter of each sphere, as it is aligned such. Diameter = 2 * r = 2 * 4 = 8, so h = 3 * 8 = 24. Therefore Tube Volume = π(4)²(24) = π(16)(24) = 384π.

Now let's solve for the volume of a sphere, multiplying by three to receive the total volume of all 3 spheres --- (2)

Volume of 1 Sphere : 4 / 3πr³ = 4 / 3π(4)³ = 4 / 3π * 64 = 256 / 3π

Volume of all 3 Spheres : 256 / 3π * 3 = 256π

And now the volume of the tube that is unfilled, will be 384π - 256π = 128π. The total volume of the tube is 384π, so the percentage of the unfilled tube will be 128π / 384π or 128 / 384 = 0.333333333 * 100 = 33.33333...%. Therefore the percentage of the tube that is not filled will be 33.33% approximately, or 33 and 1/3% in exact terms.

Answer:

The correct answer is - C.  11.45 ounces to 11.75 ounces.

Step-by-step explanation:

According to the empirical rule of the distribution for 68% falls under the normal curve falls within 1 standard deviation of the mean.

That is:

μ±δ

From the given information, the mean is

μ = 11.60

and the standard deviation is

δ = 0.15

We substitute the given parameters to obtain;

11.60±0.15

11.75 and 11.45

This means the lower limit is

11.45

and the upper limit is

11.75

Answer:

see below

Step-by-step explanation:

You need to know the base a and height h.

then use formula

Area = a²+2a+√(a²/4+h²)

Answer: y=-9x+5

Step-by-step explanation:

slope intercept form is y=mx+b

simply plug in the values.

m= the slope

the slope you gave was -9, so plug that in to m.

b= the y intercept aka when the number touches the y axis. in this case, it would be 5.

y=-9x+5

The measure of the angle with variable x is 70 degrees.

The two tangents forms an angle x. The angle x is opposite the arc angle 250 degrees.

∠x =  250 - (360 - 250)/ 2

∠x = 250 - 110 / 2

∠x = 140 / 2

∠x = 70°

Therefore, ∠x = 70 degrees.

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The additive inverse of –2+ 8i will be 2 – 8i. The additive inverse of a digit is the digit that delivers zero when added to it.

The additive inverse of a number is the number that produces zero when added to it. A negative number's additive inverse is positive. The additive inverse of itself is zero.

From the definition;

\(\rm x= 2+ 8i \\\\ \rm x= 2+ 8i + 2-8i \\\\ \rm x= 0\)

Option C gives zero on addition. That's why it is correct.

Hence the additive inverse of –2+ 8i will be 2 – 8i.

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Answer:

The answer is C:

2-8i

Step-by-step explanation:

Edge 2022 :-)

Answer:

dunny but 4950

Step-by-step explanation:

4960-

Given:

a = 2 and b = -2.

To find:

The value of \(a^3+3b^2\).

Solution:

We need to find the value of expression \(a^3+3b^2\) at a = 2 and b = -2.

Substituting a = 2 and b=-2 in \(a^3+3b^2\), we get

\((2)^3+3(-2)^2\)

\(=8+3(4)\)

\(=8+12\)

\(=20\)

Therefore, the value of expression \(a^3+3b^2\) at a = 2 and b = -2 is 20.

The value of the given expression is 1/16

Given the exponential function below as shown;

(1/2)^4

This means the product of 1/2 in 4 places. This can be expressed as;

(1/2)^4 = 1/2 * 1/2 * 1/2 *1/2

(1/2)^4 = 1/4 * 1/4

(1/2)^4 =1/16

Hence the value of the given expression is 1/16

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\(5x + 3y = 25 \\ 5x = 25 - 3y \\ x = \frac{25 - 3y}{5} \\ x = \frac{25}{5} - \frac{3y}{5} \\ x = 5 - \frac{3y}{5} \\ 3x + 4y = 26 \\ 3 (5 - \frac{3y}{5} ) + 4y = 26 \\ 15 + \frac{11y}{5} = 26 \\ \frac{11y}{5} = 26 - 15 \\ \frac{11y}{5} = 11 \\ \frac{5}{11} \times \frac{11y}{5} = 11 \times \frac{5}{11} \\ y = 5 \\ x = 5 - \frac{3y}{5} \\ x = 5 - \frac{3(5)}{5} \\ x = 2\)

(x,y)—> (2,5)

In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

A normally distributed phenomenon using standard nomenclature can be described as follows:

A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).

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Answer: x+y+1=0

Step-by-step explanation:

m=y2-y1/x2-x1

 = 4-(-2) /-5-1

 =6/-6

 =-1

equation of line

y-y1=m(x-x1)

y-(-2) =-1(x-1)

y+2=-x+1

x-1+y+2=0

x+y+11=0

The correct statement is: The length of the remaining side (the side opposite to the base) is 7.86 inches approximately.

To find the length of the remaining side, we can use the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side of a right triangle.

In this case, we have a non-right triangle, but we can use the Law of Cosines to find the length of the remaining side.

The Law of Cosines states that the square of the length of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.

Applying this formula, we get: c^2 = a^2 + b^2 - 2ab cos(C)

c^2 = 6^2 + 8^2 - 2(6)(8)cos(30°)

c^2 = 36 + 64 - 96(√3)/2

c^2 = 100 - 48√3

c ≈ 7.86

Therefore, the length of the remaining side is approximately 7.86 inches.

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                                    "Complete questions"

A triangular brace has an angle measure of 30 degrees, with a side opposite this angle measuring 8 inches. The base of the triangular brace, which is adjacent to the given angle measure, is 6 inches in length. Which of the following statements is correct?

A. The angle opposite the side measuring 6 inches has one solution of approximately 28 degrees. B. The angle opposite the side measuring 6 inches has two solutions of approximately 28 degrees and 36 degrees. O C. The angle opposite the side measuring 6 inches has one solution of approximately 22 degrees. D. There is not a solution for the angle opposite the side measuring 6 inches.

I think the answer is c in which graph shown in the above

Answer:

see attached, x>=1

Step-by-step explanation:

Answer:

(8, -15)

Step-by-step explanation:

Midpoint formula: \((\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2})\)

where \((x_1,y_1)\) is the first point (T) and \((x_2,y_2)\) is the second point (S)

Step 1. plug in what we have so far into the midpoint formula

\((\frac{0+x_2}{2} ,\frac{5+y_2}{2} )\)

but remember, the midpoint is (4, -5)

Step 2. solve for point (S)

The first coordinate of point (S) is the x-coordinate. And to solve for the x-coordinate, (since they're being divided by 2) multiply 2 by 4 (the x-coordinate of the midpoint)

\((\frac{0+8}{2},\frac{5+y_2}{2})\)

... (hard to explain for the y-coordinate of point (S))

Point S = \((8,-15)\)

I believe the answer is -12x, so sorry if that is incorrect.

Answer:

12x

Step-by-step explanation:

17x+(-5x)=17x-5x=12x

True. The cost feasibility of a systems development project is indeed dependent on the project's scope.

The cost feasibility of a systems development project refers to the evaluation of whether the project can be completed within the allocated budget. One of the key factors influencing cost feasibility is the scope of the project. The scope defines the boundaries and objectives of the project, including the features, functionalities, and deliverables that are expected to be developed.

When the scope of a project is well-defined and limited, it tends to be more cost-feasible. A smaller scope usually requires fewer resources, less development time, and ultimately, lower costs. On the other hand, projects with a broader or more complex scope often involve a larger number of requirements, greater integration challenges, and increased development efforts, which can drive up the costs.

Therefore, the scope of a systems development project plays a crucial role in determining its cost feasibility. Project managers and stakeholders need to carefully analyze and define the project's scope to ensure that it aligns with the available resources and budget, thereby increasing the chances of successful and cost-effective project completion.

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Answer:

Noa hiked 2 mi up a mountain trail and then hiked 2 mi down a trail

A hot air balloon ascended 2000 ft from the ground and then descends 2,000 ft

Step-by-step explanation:

The  additive inverses should be that

if a number i.e. a so it would be inverse like -a

And the sum of both would be zero i.e.

a + (-a) = 0

Now going through the options given

1st option should be

2 + (-2) = 0

This shows the additive inverses

The second option be

= + 3+ (-2)

= 3 - 2

= 1

The third option is

= 2000 + (-2000)

= 0 ft

This shows the additive inverses

The fourth option is

= -$70 + $100

= $30

Therefore the first and third option is additive inverses

Answer:

Step-by-step explanation:

a=20

b=70

c=20

d=70

e=110

Answer:

A. 20

B. 70

C.20

D.70

E. 110

Step-by-step explanation:

Hope this helps  

pls tell me if im wrong

Answer:

i tried and i got pie something

Step-by-step explanation:

Answer:28

Step-by-step explanation:

28/2=14

14+4=18

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

Explanation:

Perfect square trinomials are in the form (a+b)^2 = a^2+2ab+b^2

So the first and last terms must be perfect squares. The middle term is twice that of the square roots of each first and last term.

Choice D fits the description because 4x^2 = (2x)^2 is the first term, so a = 2x and 25 = 5^2 is the last term meaning b = 5. Note how 2ab = 2*2x*5 = 20x is the middle term.

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

(a+b)^2 = a^2+2ab+b^2

(2x+5)^2 = (2x)^2+2*2x*5+5^2

(2x+5)^2 = 4x^2 + 20x + 25

Answer:

(2x+5)² or (2x+5)(2x+5)

Step-by-step explanation:

4x²+ 20x + 25

(2x       ) (2x      )     first step 2x*2x=4x²

(2x  +  5   )(2x  +   5  )  the constant sign is plus so it can be ( minus × minus=plus OR plus×plus=plus) look at the middle value it is positive so the two signs are positive or plus sign.

(2x+5)²