Solve the following using the fritz-john conditions. the given answers are correct.
Maximize 2x1 + 5x2 S.T. 2x12 + 5x22 = 13

It is already in the simplest form.

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2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

the one you selected is correct.

Step-by-step explanation:

i did the math-

Answer:

the correct answer is the third option:y=-2/5x+5

Step-by-step explanation:

let's change this to y=mx+b format

2x+5y=25

subtract both sides by 2x

5y=-2x+25

divide both sides by 5

y=-2/5x+5

if your equation is in mx+b form, the coefficient of x is your slope.

Now that we know the slope, a line parallel to a given line will have the same slope.

The only option with the slope -2/5 is the third option

Answer:

9636.66666665,or, 9637

Step-by-step explanation:

Answer:

36 cups of water

Step-by-step explanation:

Make a proportion, where x is the number of cups of water needed:

\(\frac{2}{3}\) = \(\frac{24}{x}\)

Cross multiply and solve for x:

2x = 72

x = 36

So, 36 cups of water will be needed

Answer:

36

Step-by-step explanation:

Answer:

The answer would be y=3 x=1  

Answer:

Step-by-step explanation:

The awnser to this The 1x4)16 plus 18 and divided by the 3x2 u should be able to get your factor by negative 2, and negative 1 by 2 qnd 3.

Answer:

I'd have to say C

Step-by-step explanation:

The correct option is option B i.e., the total amount George would make if he sells all his cards will be equal to $400 approx.

George estimates that he can make $4.75 per card if he sells baseball cards online. He has total 83 cards.

We have to find out the closest amount George would make if he sells all his cards.

What is the unitary method?

The unitary method is a method in which we find the value of a unit and then the value of the required number of units.

As per the question ;

George estimates that he can make $4.75 per card.

The total no. of cards George have = 83 cards

So ,

The total amount , George would make if he sells all his cards can be calculated by multiplying the total no. of cards to price of each card.

i.e.,

Total amount George will made ;

= 83 × $ 4.75

= $ 394.25

≈ $ 400

Thus , the correct option is option B i.e., the total amount George would make if he sells all his cards will be equal to $400 approx.

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When Gracie distributes her carrots equally among the 5 bunnies, each bunny gets 7,878 whole carrots, and 3,939 whole carrots remain without being given to a bunny. These figures are whole numbers.According to the statement, Gracie has 5 pet bunnies that love to eat whole carrots. Gracie has 3,939 carrots to feed the bunnies, and she will use as many carrots as she can and give each bunny the same number.

To calculate the number of carrots each bunny will get:Total number of whole carrots ÷ Total number of bunnies = Number of whole carrots each bunny gets Gracie distributes the 3,939 carrots equally among the 5 bunnies, with each bunny getting 7,878 carrots. This is illustrated in the calculation below:3,939 ÷ 5 = 7,878Hence, the number of whole carrots each bunny gets is 7,878.

When it comes to the number of carrots that remain without being given to a bunny, we need to calculate it using the following formula:Total number of whole carrots − (Number of whole carrots each bunny gets × Total number of bunnies) = Number of whole carrots that remain without being given to a bunnyUsing the figures from the above calculations, the computation will be as follows:3,939 − (7,878 × 5) = 3,939 − 39,390 = -35,451. Therefore, the number of whole carrots that remain without being given to a bunny is -35,451. However, since the answer must be a whole number, we can round this up to 0 carrots. This implies that all of the carrots were given to the bunnies.

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If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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Answer:

3. Yes because it is the same thing. (short answer just elaborate more)

4. No, a trapezoid cannot be a parallelogram. Trapezoid has only one pair of parallel sides while in a parallelogram there are two pairs of parallel sides.

5. see last sentence in 4

6. group 1: the diamond and the square tilted, and the square.

   group 2: the second one, the cup like shape, the cup shape but taller(the last one)

7. hard to see

8. hard to see

Step-by-step explanation:

Answer:

I think the correct answer to this, (if I'm not wrong), would be D.

Step-by-step explanation:

I hope this helped!! Have a wonderful day and never forget to smile!!

Answer:

A: 12 B: 80

Step-by-step explanation:

92 - 80 = 12

80 students

12 Chaperones

Answer:

12 chaperones and 80 students

Step-by-step explanation:

Start by multiplying the numbers seperatly and then add. Keep doing this till you get to 92.

  20(2)=40. 3(2)=6 46

  20(3)=60. 3(3)=9 69

  20(4)=80. 3(4)=12 92

Now you know there are 12 chaperones and 80 students. There are other ways to answer this problem like using systems of equations but it still gives the correct answer and is less advanced.

       Hope this helps:)

The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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(a) To find the velocity after 2 seconds, we need to take the derivative of s(t) with respect to time t. It takes 9.25 seconds for the velocity to reach 40 m/s.

s(t) = 3t + 2t^2
s'(t) = 3 + 4t
Plugging in t = 2, we get:
s'(2) = 3 + 4(2) = 11
Therefore, the velocity after 2 seconds is 11 m/s.
(b) To find how long it takes for the velocity to reach 40 m/s, we need to set s'(t) = 40 and solve for t.
3 + 4t = 40
4t = 37
t = 9.25 seconds (rounded to two decimal places)

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Answer:

The value of 3^5 is 243.

The mean and standard deviation of the random variable X, representing the Apgar score of a randomly selected newborn baby, can be calculated using the given probability distribution table. The mean is a measure of the average score, while the standard deviation indicates the variability or spread of the scores.

To calculate the mean, multiply each score by its corresponding probability and sum the results. For example, if the Apgar score is 0, the probability is 0.05. If it is 1, the probability is 0.10, and so on. Multiply each score by its respective probability and sum the products. This will give you the mean.

The standard deviation is a bit more complex to calculate. First, subtract the mean from each score, square the differences, multiply them by their respective probabilities, and sum the products. Then, take the square root of this sum. The result is the standard deviation.

Interpreting the mean, it represents the expected average Apgar score of the randomly selected newborns based on the given probability distribution. The standard deviation, on the other hand, provides a measure of the variability or spread of the Apgar scores around the mean. A higher standard deviation indicates a wider range of scores, suggesting more variability in the newborns' conditions at birth.

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Answer

x=3

Step-by-step explanation:

We have to subtract 4 from 7, while will equal to 3. Therefore, x = 3

hope it's right

Answer:

9 units

Step-by-step explanation:

The dotted line, which is the height, is labeled as 9, so it is 9 units.

Hope that helps!

Answer: 9 units

Step-by-step explanation: If you look at the question on the photo you see a dotted line with a 9 on it. On a triangle when you something like that you know it the actual height of the triangle

Answer:

15

Step-by-step explanation:

from the first then it is 0+7=7

and from the last it is 0+8=8

then the number of cars available in the station is 8+7=15

Answer:

yea what he said..........

XY is less than 14,  MR is less than 10.5, if DE || AB, AC = 15, DC = 10, and EC = 8 then BE is equal to 18.75, the sides are not proportional and DE is not parallel to AB.

To find XY, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Using this theorem, we have:

WZ + ZX > WY

6 + 8 > 9

14 > 9

XY must be less than the sum of WZ and ZX. Therefore, XY is less than 14.

To find MR,

RS + ST > RT

6 + 4 1/2 > 3

10.5 > 3

Since the inequality holds true, we can conclude that MR must be less than the sum of RS and ST. Therefore, MR is less than 10.5.

By the similar triangles property:

EC/DC = AC/BC

Substituting the given values:

8/10 = 15/BC

Cross-multiplying:

8 × BC = 10 × 15

BC = 150/8

BC = 18.75

BC=BE

BE is equal to 18.75.

If DE is parallel to AB, then the ratio of the lengths of the corresponding sides AD and BE should be equal.

Using the given lengths:

AD/BE = 4/3

Ratio does not equal 1, which means the sides are not proportional and DE is not parallel to AB.

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The 2 sides of the equation are not equal; hence, I cannot prove them to be true.

Step-by-step explanation:

2/3  * 150  = 1/2  * ?

   100  =    1/2 * ?       Multiply both sides by 2 to get

    200 = ?

The recursive formula for the altitude of the plane with the given pattern after t minutes is equal to A(t)=30000 - 550(t−1).

As given in the question,

When time t = 1

Altitude of the plane is 30,000feet

t = 2 , altitude of the plane = 29,450 feet

t = 3 , altitude of the plane = 28,900 feet

Let A(t) be the altitude of the plane after time 't' minutes

Here , A(1) = 30,000

A(2) - A(1) = A(3) - A(2)

So, it is arithmetic progression series

Common difference 'd' = A(2) - A(1)

                                  = 29,450 - 30,000

                                  = -550

Recursive formula of the altitude of the plane represented by  't' th term of arithmetic progression series

A(t) = A(1) + ( t - 1 ) d

⇒ A(t) = 30,000 + ( t - 1 )(-550)

⇒A(t) = 30,000 - 550( t - 1 )

Therefore, the recursive formula of the altitude of the given plane after 't' minutes is equal to A(t) = 30,000 - 550( t - 1 ).

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The length of the rectangle is 6 meters longer than the width of the rectangle. Let's suppose the width is x meters. So, the length of the rectangle is (x + 6) meters.Area of rectangle is 28 square meters.Area of rectangle = length × width28 = (x + 6) × x.Solve for xx² + 6x - 28 = 0(x + 7)(x - 4) = 0x = -7 or 4

The negative value of x because it is not possible.So, the width of the rectangle is 4 meters.The length of the rectangle is (x + 6) meters= 4 + 6= 10 meters.The length of a rectangle is 6 meters longer than the width. If the area is 28 square meters, we need to find the dimensions of the rectangle. Let's suppose the width of the rectangle is x meters. We know that the length of the rectangle is 6 meters more than the width, so the length of the rectangle is (x + 6) meters.Area of a rectangle is the product of its length and width. So, the area of the rectangle is (x + 6) × x. We know that the area of the rectangle is 28 square meters. Therefore, we can write the following equation:28 = (x + 6) × x.To find the value of x, we need to solve this quadratic equation.28 = x² + 6x.Rearranging the terms, we get:

x² + 6x - 28 = 0

We can solve this equation by using the quadratic formula, but we will use the factoring method. We need to find two numbers whose product is -28 and whose sum is 6. These numbers are +7 and -4. Therefore, we can write:

x² + 7x - 4x - 28 = 0x(x + 7) - 4(x + 7) = 0(x + 7)(x - 4) = 0

Therefore, x + 7 = 0 or x - 4 = 0.If x + 7 = 0, then x = -7, which is not a valid solution because the width of the rectangle cannot be negative.If x - 4 = 0, then x = 4. Therefore, the width of the rectangle is 4 meters. The length of the rectangle is x + 6 = 4 + 6 = 10 meters. So, the dimensions of the rectangle are 4 meters by 10 meters.

Therefore, the width of the rectangle is 4 meters, and the length of the rectangle is 10 meters. The dimensions of the rectangle are 4 meters by 10 meters.

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Answer:

huh

Step-by-step explanation:

We have the next numbers on the spinner:

1,2,3,4

Now, the prime numbers are:

2,3

Hence, the probability to get a primer number is:

P( prime number) = # of prime numbers/ total # on the spinner.

Then,

P( prime number) = 2/4 = 1/2

Now, the divisor of 14:

1,2

Hence, the probability to get a divisor of 14 is:

P( divisor of 14) = # of divisor / total # on the spinner.

Replacing:

P( divisor of 14) = 2/4 = 1/2

P(prime and divisor of 14) = 1/4

Finally, we need to find the probability of:

P( prime or divisor of 14) = P( prime number)+ P( divisor of 14) - P(prime and divisor of 14) = 1/2 +1/2 -1/4= 3/4 =0.75*100 = 75%

Hence, the P( prime or divisor of 14) is 75%.