What is 375 grams of a 12% solution?

The value of b in x²+ bx + 16/49 is 8/7 and the squared binomial is (x + 4/7)²

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

X^2+bx+16/49

Rewrite properly

So, we have the following representation

x²+ bx + 16/49

When represented as a square, we have

x²+ bx + 16/49 = (x + a)²

Expand the bracket

So, we have the following representation

x²+ bx + 16/49 = x² + 2ax + a²

By comparison, we have

bx = 2ax

a² = 16/49

Take the square root of both sides

a = 4/7

Substitute a = 4/7 in bx = 2ax

bx = 2 * 4/7x

So, we have

b = 2 * 4/7

Evaluate

b = 8/7

In (a), we have

x²+ bx + 16/49 = (x + a)²

Where

a = 4/7

So, we have

x²+ bx + 16/49 = (x + 4/7)²

Hence, the binomial is (x + 4/7)²

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Answer:

[tex]\textsf{1)} \quad b = \dfrac{8}{7}[/tex]

[tex]\textsf{2)} \quad \left(x+\dfrac{4}{7}\right)^2[/tex]

Step-by-step explanation:

Perfect Square Trinomial

A trinomial that can be written as the square of a binomial.

For example the perfect trinomial  x²+2dx+d² can be written  as (x+d)².

Given trinomial:

[tex]x^2+bx+\dfrac{16}{49}[/tex]

To express the given trinomial as a perfect square trinomial, determine the value of b.

As the coefficient of the x² term is one, b equals twice the square root of the constant of the trinomial:

[tex]\implies b = 2 \sqrt{\dfrac{16}{49}}[/tex]

[tex]\implies b = 2 \cdot \dfrac{4}{7}[/tex]

[tex]\implies b = \dfrac{8}{7}[/tex]

Therefore, the perfect square trinomial is:

[tex]x^2+\dfrac{8}{7}x+\dfrac{16}{49}[/tex]

To factor in the form of a squared binomial (x + d)², d is half the value of b:

[tex]\implies d = \dfrac{1}{2}b[/tex]

[tex]\implies d = \dfrac{1}{2} \cdot \dfrac{8}{7}[/tex]

[tex]\implies d=\dfrac{8}{14}[/tex]

[tex]\implies d=\dfrac{4}{7}[/tex]

Therefore, the perfect square trinomial as a squared binomial is:[tex]\implies \left(x+\dfrac{4}{7}\right)^2[/tex]

The minimum volume of the box =  11220 cubic centimeters

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

One notebook:

length, l= 29 cm

width = 21.5 cm

height = 1.5 cm

Volume of 1 notebook =  l*w*h

                                     =  29*21.5*1.5

                                     =  935.25

                                     ≈  935 cubic centimeters ( nearest whole number )

Volume of 12 notebooks = 935 * 12 = 11220 cubic centimeters

So, the minimum volume of the box =  11220 cubic centimeters

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Answer:

11,223

Step-by-step explanation:

Answer:

The man's monthly rental rate is $1600.

Step-by-step explanation:

To figure out the answer to your question, it says to find how much is monthly rental is. So, we can do this by simply dividing the two numbers:

4800 ÷ 3 = $1600

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(a) Let P be the amount deposited at the end of each quarter. Then, the future value F after n quarters is given by

F = P(1 + 0.09)^n

Given that there must be enough money in the fund, we can set F = A, the amount required. Therefore,

A = P(1 + 0.09)^n

Solving for P,

P = A(1 + 0.09)^-n

(b) Let P be the amount deposited at the end of each quarter. Then, the future value F after n quarters is given by

F = P(1 + 0.045)^n

Given that there must be enough money in the fund, we can set F = A, the amount required. Therefore,

A = P(1 + 0.045)^n

Solving for P,

P = A(1 + 0.045)^-n

Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

(6/9) × (3/8)

Cross simplify:

(3/3) × (1/4)

3/12

1/4

Answer:

17: 0.65

18: 0.05

19: 0.27

20: 1840

Step-by-step explanation:

Answer: 18 ft ^2

Step-by-step explanation:

Answer:

4w>39+w

3w>39

w>13

Step-by-step explanation:

Answer:

0.8385, turned into a percentage is 83.9%

Step-by-step explanation:

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Answer:210

Step-by-step explanation:

Michael will score about 288 points in 12 weeks. This is because he scores 12 points in each game and there are 2 games each week, so he will score 24 points in each week. Multiplying 24 points by 12 weeks, Michael will score 288 points.

Answer: y = -x - 15

Step-by-step explanation:

            Slope intercept form is written as y = mx + b where m is the slope and b is the y-intercept. In other words, we need to isolate the y-variable.

   Given:

x + y = - 15

   Subtract x from both sides of the equation:

y = -x - 15

Answer:

y = 3.8x

Step-by-step explanation:

Let y = the cost of the cherries

Let x = pounds of cherries

We can find the unit rate by either:

[tex]\frac{7.98}{2.1}[/tex] =  $3.80 per pound

or

[tex]\frac{10.64}{2.8}[/tex] = $3.80 per pound

Now we can write the equation

hy = 3.8x

Based on the function, the population of the small town in 5 years is 3898

The complete question is added at the end of this solution

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

Initial population = 23000

Number of years = 5

These parameters can be represented as

Ao = 23000

t = 5

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

A(t) = A0e^(-0.355t)

Substitute Ao = 23000 and t = 5 in the above equation

So, we have the following representation

A(5) = 23000 * e^(-0.355 * 5)

Evaluate the products

A(5) = 3898

Hence, the population in 5 years is 3898

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Complete question

The population of a small town follows A(t) = A0e-0.355t where t is the time in years

What is the population in 5 years if the initial population is 23000

Answer:

(6, -1.5) or (6, -1 1/2)

Answer: the percent decrease is 9%

Step-by-step explanation:

Formula :12500/14000x100% and this formula can use in any of question likes this

Answer:

y = 31

Step-by-step explanation:

2y-5+123=180

123 - 5 = 118

2y+118=180

subtract 118 from both sides

2y+118 - 118 = 180 - 118

180 - 118  = 62

2y = 62

divide 2 by both sides

2y/2 = 62/2

y = 31

Answer:

Step-by-step explanation:

2y+−5+123=180

Step 1: (Combine Like Terms)

(2y)+(−5+123)=180

Step 2:  (Subtract 118 from both sides)

2y+118−118=180−118

2y=62

Step 3: Divide both sides by 2

2y/2= 62/2

y=31

The value of 3¾ft in yards would be = 1 6/25 yard

A mixed number is the type of number that is made up of three parts such as the whole number, a numerator and a denominator.

To convert to yards;

1 ft = 0.33 yard

3¾ = X yards

make x yards the subject of formula;

X yards = 3¾ × 0.33

X yards = 3.75×0.33

X yards = 1.24 yards

X yards in mixed number= 124/100 = 31/25 = 1 6/25 yard.

Note that the final value which is 124/100 is reduce to the lower figure by dividing through with 4 to arrive at the mixed number 1⁶/25

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Answer: x> 38

Step-by-step explanation:

The best way to find the answer is to solve for x. To start you would add 38 and 39, getting 77, then subtract that from 180 to get the last angle in the triangle, 103. Finally, you would subtract 103 from 180, getting 77, to get x. The only thing you need to do now is to look at all of the answers and figure out which one makes sense for the answer you got. You know it can't be x<77 because it doesn't have the or equal to sign. You know it can't be x>103 because 77 is lower than 103. You know it can't be x<39 because 77 is greater than 39, so the answer has to be x > 38. (this was copy'd n pasted from another question that is the exact same.)
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The area of a circle with diameter of 14 yards is  153.86 yards².

The diameter of the circle is 14 yards . The area of the circle can be found as follows;

area of a circle = πr²

where

The radius of a circle is half of its diameter.

Therefore,

r = 14 / 2 = 7 yards

Hence,

area of a circle = πr²

area of a circle = 3.14 × 7²

area of a circle = 3.14 × 49

area of a circle = 153.86 yards²

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Decrease in the price is $1887, the price of the next model car is $35,113.

Percentage is a measurement to find value of the given number out of hundred.

Given that,

Price of current model = $37,000

The price of next model car is 5.1% less than the current model.

The price of the next model car = 94.9% of price of current model car

                                                     = 94.9 x 37,000/100

                                                      = 35,113

The decrease in the price = 37,000 - 35,113 = 1887

The price of the next model car is $35,113 and decrease in the price is $1887.

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Answer: It is B

Step-by-step explanation:

If you put leg a (3) and leg b (4) into a Pythagorean equation it will turn out like this

3^2+4^2=x^2

9+16=x^2

25=x^2

√25=√x

5=x

5 is the missing side length, which corresponds to option b

The percent error of the estimate is -2.14%

In this question, the figures are given as

Estimate = 5.5 cm

Actual = 5.62 cm

The percentage of the error is then calculated using the following equation

Error percentage = (Estimate - Actual)/Actual * 100%

Substitute the known values in the above equation, so, we have the following representation

Error percentage = (5.5 - 5.62)/5.62 * 100%

Evaluate

Error percentage = -2.14%

Hence, the error percentage is -2.14%

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The Cartesian equation will be;

⇒ (x - 3) / 1 = (y - 0)/2

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation is,

⇒ r = 3i + λ (i + 2j)

Where, 'λ' is a parameter.

Now,

Since, The equation is,

⇒ r = 3i + λ (i + 2j)

Where, 'λ' is a parameter.

Hence, The Cartesian equation is find as;

⇒ xi + yj = 3i + λi + 2λj

By compare, we get;

⇒ x = 3 + λ

⇒ y = 2λ

Thus, The Cartesian equation is;

⇒ (x - 3) / 1 = (y - 0)/2 = λ

Therefore, The Cartesian equation will be;

⇒ (x - 3) / 1 = (y - 0)/2

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Answer: x =4

Step-by-step explanation: The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4 thus option (A) will be correct.

What is the equation?

There are many different ways to define an equation.

More than one variable may be present inside a linear equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

24 + 0.44x = 19 + 1.69x

24 - 19 = 1.69x - 0.44x

5 = 1.25x

x = 4

Hence "The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4".

Answer:

20m

Step-by-step explanation:

Volume of Cube:   s³ = 8000m³

                               ∛s³ = ∛8000m³

                               s = 20m

Answer:

20

Step-by-step explanation:

We know that,

volume of cube = l*l*l

8000 = l*l*l

l = 3√8000

l= 20

Answer

The amount you will have $6,500 with 5% in six years using continuous compounding is of:

$8,774.

The amount you will need to have the entire $32000 in the 6 years is of:

$18,890.46.

The balance of an account after t years, using continuous compounding, is given as follows:

[tex]B(t) = Pe^{kt}[/tex]

In which the parameters are given as follows:

Putting the $6,500 into the account, the values of the parameters are given as follows:

P = 6500, k = 0.05, t = 6.

Hence the balance will be of:

B(6) = 6500 x e^(0.05 x 6) = $8,774.

The balance to have the entire $32,000, considering what you already have, will be of:

32000 - 6500 = 25500

Hence the principal is obtained as follows:

Pe^(0.05 x 6) = 25500

P = 25500/e^(0.3)

P = $18,890.46.

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Answer:x=3.5 x 60

the answer is yes because when she's doing 3.5 hour, and she can do 420 square feet