A basket contains 5 purple pencils and 9 brown pencils. If two pencils are picked at random
one after the other without replacement, then what is the probability that both the pencils
are purple?
5/182
10/91
2/91
9/182

please state reasoning as to why it is what ever answer you provide..

The Vales of x in the equations are : 1) 3 (2) 1  (3) 5  (4) 14  (5) 10 respectively

A linear equation in one variable is that in which the highest power of its variable is 1

The given equations and their solutions are

2x +1 = 7

By collecting like terms we have

2x = 3

x = 3

2) The given equation is 4x +7 = 11

By collecting like terms we have

4x = 4

Making x the subject we have

x = 1

3) 2x -3 = 7

By collecting like terms we have

2x = 10

Making x the subject we have

x = 5

4) 1/2 x - 3 = 7

By collecting like terms we have

1/2x = 7

x= 14

5) The given equation is 3x - 11 = 19

By collecting like terms we have

3x= 30

Therefore x= 10

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Depreciation implies the rate at which an asset is written off per year. So that the required formula is: value = $1150 - $127.78x.

Depreciation of an asset is a simple way of writing off the asset with respect to its life span. Using straight line method, the formula for determining depreciation is:

Depreciation = \(\frac{Cost of asset - Residual value}{Time(years)}\)

The residual value is the cost of the asset after its useful life.

Thus, in the given question, residual value of the asset = 0

So that,

Depreciation = \(\frac{Cost of asset}{Time}\)

                      = \(\frac{1150}{9}\)

Depreciation = 127.78

Thus, the depreciation of the asset is $127.78 per year.

Therefore since the asset depreciates by 127.78 every year, then the formula for its value as a function of time in years is:

Value = $1150 - $127.78x

where x is in years.

The required formula for the value is $1150 - $127.78x

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Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

given that m is parallel to n,

the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.

using the corresponding angle rule we know that:

2x + 16 = 96

2x = 80

so x = 40

Answer:

2:1

Step-by-step explanation:

12:6 reduced to the simplest form is 2:1

Answer:

12:6 in the simplest form is 2:1.

Step-by-step explanation:

Answer:

18 1/2

Step-by-step explanation:

add 13 1/3 and 4 3/4

Answer:

by using middle term break method

Step-by-step explanation:

9x^2 + 12x + 4

9x^2+ (6 + 6)x + 4

9x^2 + 6x + 6x + 4

3x(3x + 2) + 2(3x + 2)

(3x + 2)(3x + 2)

(3x + 2)^2

To line up the decimals on their decimal points is shown below.

A group of numbers between integers on a number line are known as decimals. They are merely an additional mathematical representation of fractions. Decimals allow us to express measurable quantities like length, weight, distance, money, etc. with greater accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are represented to the right of the decimal point. The next place, which is (1/10)th or tenth place value, is (1/10) times smaller if we move immediately from the first place. For illustration, look at the decimal place value chart for 12.45 that is shown below.

Given:

25.393

-24.138

_______

1.255

To calculate decimal subtraction. first align the decimal

Points of each number, then calculate according to the law of integer

subtraction, and finally align the decimal points on the horizontal line in

the obtained number.

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Answer:

Step-by-step explanation:

Given D,E, and F are collinear points and E is between D and F, then the expression DE + EF = DF.... 1 is true

If DE is six times the length of EF, then;

DE = 6DF

DF = DE/6 .....2

Substitute equation 2 into 1;

DE + EF = DF

DE + DE/6 = DF

find the LCM

(6DE+DE)/6 = DF

cross multiply

6DE+DE = 6DF

7DE = 6DF

Given DF = 84units

7DE = 6(84)

7DE = 504

Divide both sides by 7

7DE/7 = 504/7

DE = 72

Hence  the length of segment DE is 72units

The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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The vertex of the graph is a maximum at (-2, 4)

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

The graph

The graph is a quadratic function

From the graph, we can see that the graph has a maximum value

This maximum value represents the vertex of the graph

And it is located at (-2, 4)

So, we have

Maximum = (-2, 4)

Hence, the maximum value of the function is (-2, 4)

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The slope of the line is 7/9

It is important to note that the equation of a line is represented as;

y = mx + c

Where;

The formula for calculating the slope of a line is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

Now, let's substitute the values into the formula from the points given we have;

Slope, m =1 -(-6)/ -3 - (-6)

expand the bracket

Slope, m = 1 + 6/ 3 + 6

add the values

Slope, m = 7/9

Hence, the value is 7/9

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Answer:

With what? there is nothing here

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

10 - (-18)

=> 10 + 18

=> 28

Hoped this helped.

Answer:

10 - (-18)

= 10 + 18

= 28

Step-by-step explanation:

Answer:

3lbs

Step-by-step explanation:

he has 10. subtract 4 for the basket, that leaves $6

blueberries are 2/pound

6/2= 3lbs

of course, that is blueberries- not vegetables.

Dunno if it's a typo or a trick question.

Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.

Part 1 of 2:

The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.

To calculate the new cost after 11 years, we can use the formula:

New Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

New Cost = $0.60 * (1 + 3%)^11

        ≈ $0.60 * (1 + 0.03)^11

        ≈ $0.60 * (1.03)^11

        ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.

Part 2 of 2:

If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.

Using the formula:

Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

Final Cost = $0.60 * (1 + 3%)^11

          ≈ $0.60 * (1 + 0.03)^11

          ≈ $0.60 * (1.03)^11

          ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the final cost would also be $0.86.

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Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?

Given a discount of 20% and a manufacturer's coupon of $200, the price after the discount and coupon, (C ∘ D)(x), is 0.8x - 200.

A discount is an amount that reduces the price of a retail item.

Discounts are offered as rates and the discounted price is computed by multiplying the discount factor and the price.

Discount rate on offer = 20%

Discounting factor = 80% or 0.8 (100 - 20%)

Manufacturer's coupon off the price = $200

Let the price of the bureau = x

The price after the discount (discounted price) is given by D(x)

D(x) = 0.8x

The price after the coupon = C(x) = x - 200

The price after applying the discount and the coupon, (C ∘ D)(x) = 0.8x - 200

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Wilson's Warehouse sells a certain brand's bureau. They are offering a 20% discount in addition to accepting a manufacturer's coupon for $200 off. Let the price of the bureau be x. If the price after the discount is given by D(x) and the price after the coupon is C(x), find (C ∘ D)(x).

Answer:

Step-by-step explanation:

Given equation for sum of the first n terms

Using the equation solve the following

The first term \(t_1\), is same as the sum of the first 1 term, so n = 1

Sum of the first 2 terms, when n = 2

Common difference is the difference between two consequitive terms.

First, find the second term:

Now find the difference between the first two terms:

We need to find such n that \(S_n\) = - 30

So the answer is 6

Simplifying in steps as below

The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.

We have,

Cylinder and prism.

Here we have to find the equivalent ratio to 8/2.

First simplifying the given ratio as

8/2

= (4 x 2)/2

= 4 /1

Now, some more ratios equivalent to 8/2.

1. 8/2 x 3/3 = 24/ 6

2. 8/2 x 4/4 = 32/8

3. 8/2 x 6/6= 48/12

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Answer:

A

Step-by-step explanation:

y -2 = -5/6(x -3)

y-2 = -5/6x + 15/6

y = -5/6x + 27/6

y = -5/6x + 9/2

Answer:

42 units

Step-by-step explanation:

Area of a trapezoid is always 1/2(b1+b2)*h

so here base 1 is 4 units, and base 2 is 10 units. When we add these we get 14, divided by 2 which is 7, and multiplied by height of 6, which is 42

Step-by-step explanation:

\(y = \sqrt{4x + 6} \)

\( {y}^{2} = 4x + 6\)

\( {y}^{2} - 6 = 4x\)

\( \frac{1}{4} ( {y}^{2} - 6) = x\)

Swap x and y

\( \frac{ {x}^{2} - 6 }{4} = y\)

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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The probability that the first marble drawn is blue and the second marble drawn is red is 1/4 or 0.25, which can also be expressed as 25%.

To determine the probability of drawing a blue marble on the first draw and a red marble on the second draw, we need to consider the total number of marbles and the number of blue and red marbles in the bag

In this case, we have a bag with 12 blue marbles and 12 red marbles, making a total of 24 marbles.

When drawing the first marble, there is a 12/24 probability of selecting a blue marble since there are 12 blue marbles out of the total 24 marbles in the bag.

After replacing the first marble back into the bag and mixing up the marbles, the probability of drawing a red marble on the second draw is also 12/24, as there are still 12 red marbles remaining out of the total 24 marbles.

To find the overall probability, we multiply the probabilities of each event since they are independent events:

P(first marble is blue and second marble is red) = P(first marble is blue)\(\times\)P(second marble is red)

\(= (12/24) \times (12/24)\)

\(= (1/2) \times (1/2)\)

= 1/4.

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Answer:

$1300

Step-by-step explanation:

so, he would get the $400 basic salary plus 6% of the $15000.

15000 = 100%

1% = 100%/100 = $150

6% = 1%×6 = 150×6 = $900

so, in total, he would make

$400 + $900 = $1300 in that week.

The value of y is 48

y= kx

let's solve for k which is the constant

y= 8 , x= 4

k= 8/4

k= 2

Next is to calculate the value of y when x is 24

y = 2 × 24

y= 48

Hence the value of y is 48

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Answer:

A. 3x+12

Step-by-step explanation:

8x+3-5x+9

8x-5x=3x

3+9=12

then put them together

3x+12

answer= A