Why is the value of x limited to 0 in. < x < 4.25 in.?

Answer:

78.5

Step-by-step explanation:

I don't really understand what you are asking, but 25 x pi = 78.5

Answer:

B

Step-by-step explanation:

Because there is a problem in that situation

Answer:

A) |x| + 1 B) |x| - 1 C) |x+1| D) |x-1|

Step-by-step explanation:

Just follow what I wrote for other questions and you'll be fine :D

The two binomial factors of the expression x² - 100 are ( x + 10 ) and ( x - 10 ).

Given the expression in the question:

x² - 100

To factor the expression x² - 100 as the product of two binomials, simply apply the difference of squares formula.

The difference of squares formula states that:

a² - b² can be factored as (a + b)(a - b).

x² - 100

Replace 100 with 10²:

x² - 10²

Now, apply the difference of squares:

a² - b² = (a + b)(a - b)

x² - 10²

a = x and b = 10

x² - 10² = ( x + 10 )( x - 10 )

Therefore, the binomial factors are ( x + 10 ) and ( x - 10 ).

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The expression x^2-100 is a difference of squares and can be factored into the product of two binomials as (x + 10)(x - 10).

To factor the expression x^2-100 as the product of two binomials, we can recognize that it is a difference of squares. A difference of squares can be factored into the form (a + b)(a - b), where a and b are the square roots of the terms in the expression. In this case, the square root of x^2 is x, and the square root of 100 is 10. Therefore, the factored form of x^2-100 using two binomials is (x + 10)(x - 10).

Answer:

54 cups of rice are needed to feed 135 people.

Step-by-step explanation:

Given:

Balvina knows that 6 cups of rice will make enough spanish rice to feed 15 people.

Now, to find the cups of rice needed to feed 135 people.

Let the cups of rice needed to feed 135 people be [tex]x.[/tex]

As, 6 cups of rice is needed to feed 15 people.

So, 6 is equivalent to 15.

Thus, [tex]x[/tex] is equivalent to 135.

Now, to get the cups of rice needed to feed 135 people we use cross multiplication method:

[tex]\frac{6}{15} =\frac{x}{135}[/tex]

By cross multiplying we get:

[tex]810=15x[/tex]

Dividing both sides by 15 we get:

[tex]54=x\\\\x=54\ cups.[/tex]

Therefore, 54 cups of rice are needed to feed 135 people.

Balvina would need 54 cups of rice to feed 135 people.

Given:

6 cups of rice will make enough Spanish's rice to feed 15 people.

Total number of people= 135

Let x to represent the number of cups of rice needed to feed 135 people.

The proportion can be set up as follows:

[tex]\(\dfrac{6 \text{ cups}}{15 \text{ people}} = \dfrac{x \text{ cups}}{135 \text{ people}}\)[/tex]

Solving for x as

6 * 135 = 15x

810 = 15x

Now, divide both sides by 15 to solve for x:

810/15 = x

x= 54

Thus, Balvina would need 54 cups of rice.

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Answer:

1636 cm^2

Step-by-step explanation:

cut in itwo two shapes a rectangle and isosceles trapizoid

Area - 1/2 hight(base x length)

1/2 x 14(6x17) = 714 cm^2

Area of rectangle-  2(wl x hl x hw) = 922 cm^2

l = 17

w = 13

h = 8

add the areas - 922 + 714 = 1636 cm^2

Answer:

  4x +5y = -20

Step-by-step explanation:

Starting with an equation in standard form, you can write the equation for the perpendicular line by swapping the x- and y-coefficients and negating one of them. You want the x-coefficient to be positive, so it is convenient to negate that one here. This gives you the equation ...

  4x +5y = (some constant)

You find the value of the constant by evaluating the expression at the given point:

  4x +5y = 4(5) +5(-8) = -20

The desired equation is ...

  4x +5y = -20

Answer:

1. y = 0.6x² - 7.2x + 12

2. y = x² - 8x + 28

3. y = x² + 6x + 24

4. y = -0.5x² + 2x + 16

Step-by-step explanation:

1. The two x-intercepts are 2 and 10. The y-intercept is -12

A(x - 2)(x - 10)

A(x² - 12x + 20)

20A = 12

A = ⅗ = 0.6

y = 0.6x² - 7.2x + 12

2. The Axis of Symmetry is x = 4. The y-intercept is 28

(x - 4)² + C

x² - 8x + 16 + C

16 + C = 28

C = 12

y = (x - 4)² + 12

y = x² - 8x + 28

3. The Axis of Symmetry is x = -3. The y-intercept is 24.

(x + 3)² + c

x² + 6x + 9 + C

9 + C = 24

C = 15

y = x² + 6x + 24

4. The x-intercepts are 8 and -4. The y-intercept is 16.

A(x - 8)(x+ 4)

A(x² - 4x - 32)

-32A = 16

A = -0.5

y = -0.5x² + 2x + 16

Answer:

The volume required to fill the punch bowl till 1 inch from the top is 1385.44 inches³

Step-by-step explanation:

Total Height of the punch bowl = 10 inches

Diameter of the bowl = d = 14 inches

Since, radius is half of the diameter, the radius of the bowl would be = r = 7 inches.

The shape of punch bowl is given to be cylindrical and we have to find the volume of the bowl. The formula to calculate the volume of a cylinder is:

[tex]Volume=\pi r^{2} h[/tex]

Here, h represents the height.

We have to find the volume to fill the bowl till 1 inch from the top. Since, the height of bowl is 10 inches, we have to fill it to 9 inches. Therefore, the value of height(h) which we will substitute in the formula will be 9. Using the values in the formula gives us:

[tex]Volume =\pi (7)^{2} \times 9\\\\ Volume =441\pi \\\\ Volume = 1385.44[/tex]

This means, the volume required to fill the punch bowl till 1 inch from the top is 1385.44 inches³

Final answer:

The volume required to fill the punch bowl till 1 inch from the top is 1385.261 inches³

Explanation:

To find the volume of punch needed to fill the punch bowl 1 inch from the top, we first need to calculate the volume of the punch bowl.

The formula for the volume of a cylinder is

V = πr²h,

where

r is the radius and h is the height.

Given that the diameter is 14 inches, the radius is half of that, which is 7 inches.

Plug in these values and the height of 10 inches into the formula to find the volume of the punch bowl.

V = 3.142 × (7 inches)² × 10 inches = 1539.178 cubic inches

To find the volume of punch needed to fill the bowl 1 inch from the top, we subtract 1 inch from the height of the bowl and use the same formula.

V = 3.142 × (7 inches)² × 9 inches = 1385.261 cubic inches

Answer:

Step-by-step explanation:

Euler's formula comes into play here. That tells you ...

  [tex]e^{ix}=\cos{x}+i\sin{x}[/tex]

Then 1 can be written as ...

  [tex]1 = e^{2ki\pi} \qquad\text{for any integer k}[/tex]

Then the n-th root of 1 will be ...

  [tex]1^{\frac{1}{n}}=e^{2ki\pi /n}=\cos{(2k\pi /n)}+i\sin{(2k\pi /n)}[/tex]

Since the trig functions are periodic with period 2π, useful values of k are from 0 to n-1.

__

1) The cube roots of 1 are ...

  cos(2πk/3) +i·sin(2πk/3) . . . . for k = 0 to 2

  = {1, cos(2π/3) +i·sin(2π/3), cos(4π/3) +i·sin(4π/3)}

__

2) The fourth roots of 1 are ...

  cos(2πk/4) +i·sin(2πk/4) = cos(kπ/2) +i·sin(kπ/2)

  = {1, i, -1, -i}

Answer: the maximum number of toy they can get is 16.

Step-by-step explanation:

If chloe has $30 and her friend has 1/3 of the amount, it means that the amount that her friend has is

1/3 × 30 = $10

The total amount that they have is

30 + 10 = $40

They need a bag of food that cost $7 and they also want toys that are $2 each.

Let x represent the number of toys that they want to get. The total cost of a bag of food and x toys is

7 + 2x

Since they have $40, then the expression would be

7 + 2x ≤ 40

2x ≤ 40 - 7

2x ≤ 33

x ≤ 33/2

x ≤ 16.5

Since the number of toys cannot be a fraction, then the maximum number of toy they can get is 16

We want to see what is the maximum number of toys that Chloe and Charlie can get a maximum of 16 toys.

So we know that they need a bag of dog food that costs $7 and some toys, such that each toy costs $2.

So, if they buy x toys, the cost will be:

C(x) = $7 + $2*x

Now, we know that Chloe has $30 and charlie has 1/3 of that, so Charlie has:

(1/3)*$30 = $10

Then in total they have $30 + $10 = $40, so the maximum cost can be $40, then we must solve:

C(x) = $40 = $7 + $2*x

         $40 - $7 = $2*x

         $33 = $2*x

         $33/$2 = 16.5 = x

Rounding down (because they can't buy a 0.5 of a toy) we see that the maximum number of toys that they can buy is 16.

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Final answer:

To determine the probability, we add the number of students who took AP World History and AP European History and subtract the number of students who took both. Out of 825 incoming seniors, 178 are allowed to enroll in AP U.S. History. The probability is approximately 0.216.

Explanation:

To determine the probability that a randomly selected incoming senior is allowed to enroll in AP U.S. History, we need to find the number of seniors who have taken either AP World History or AP European History. We can do this by adding the number of students who took AP World History (175), and the number of students who took AP European History (36), and then subtracting the number of students who took both (33).

175 + 36 - 33 = 178

Therefore, out of the 825 incoming seniors, 178 are allowed to enroll in AP U.S. History.

The probability can be calculated by dividing the number of students allowed to enroll (178) by the total number of incoming seniors (825):

P(allowed to enroll) = 178/825 ≈ 0.216 (rounded to three decimal places)

Answer:

  False

Step-by-step explanation:

Since no particular geometry is specified, the relationship between the measure of the arc and the measure of the angle is unknown. The statement must be said to be FALSE.

Answer:

The stock Norman purchased increased in its value by 25%.

Step-by-step explanation:

Original Value of the stock = $ 420

New(Current) value of the stock = $ 525

We have to find the percentage change in the value of stock. The formula to calculate the percentage change is:

[tex]\text{Percentage Change}=\frac{\text{New Value - Original Value}}{\text{Original Value}} \times 100\%[/tex]

Substituting the given values into this formula results in:

[tex]\text{Percentage Change}=\frac{525-420}{420} \times 100\% \\\\ \text{Percentage Change}=\frac{105}{420} \times 100\%\\\\ \text{Percentage Change}=0.25 \times 100\% \\\\ \text{Percentage Change}=25 \%[/tex]

A positive value of Percentage Change indicates a growth. This means that the stock Norman purchased increased in its value by 25%.

The value of Norman's stock has increased by 25%.

To determine the percentage increase in the value of Norman's stock, we need to calculate the percent change. Percent change is calculated by subtracting the original value from the new value, then dividing the difference by the original value and multiplying by 100. In this case, the original value of the stock is $420 and the new value is $525.

Percent change = ((New value - Original value) / Original value) * 100

Percent change = (($525 - $420) / $420) * 100
Percent change = ($105 / $420) * 100

Percent change = 0.25 * 100

Percent change = 25%

The value of Norman's stock has increased by 25%.

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Answer:

5 centimeters

Step-by-step explanation:

We know the equation to find volume is V = B x h, where B is the base of the prism. (It is also known as the simple V = l x w x h.)

No matter what equation you use, you will end up with V = l x w x h, since the base of a rectangular prism is length x width. So, we're going to plug in our known information to get 420 = 6 x 14 x h.

Then, we're going to multiply 6 x 14 to get 84. Now we have 420 = 84 x h. To isolate the h (in order to find what it is), we must divide both sides by 84.

420/84  = 5, so whats left of the equation is 5 = h, meaning your height is 5 centimeters.

Answer:

1) [tex]\frac{dy}{dt}=2.5-\frac{3y}{2t+100}[/tex]

2) [tex]y(t)=(50+t)- \frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }}[/tex]

3) 98.23lbs

4) The salt concentration will increase without bound.

Step-by-step explanation:

1) Let [tex]y[/tex] represent the amount of salt in the tank at time t, where t is given in minutes.

Recall that: [tex]\frac{dy}{dt}=rate\:in-rate\:out[/tex]

The amount coming in is [tex]0.5\frac{lb}{gal}\times 5\frac{gal}{min}=2.5\frac{lb}{min}[/tex]

The rate going out depends on the concentration of salt in the tank at time t.

If there is [tex]y(t)[/tex] pounds of  salt and there are [tex]100+2t[/tex] gallons at time t, then the concentration is: [tex]\frac{y(t)}{2t+100}[/tex]

The rate of liquid leaving is is 3gal\min, so rate out is [tex]=\frac{3y(t)}{2t+100}[/tex]

The required differential equation becomes:

[tex]\frac{dy}{dt}=2.5-\frac{3y}{2t+100}[/tex]

2) We rewrite to obtain:

[tex]\frac{dy}{dt}+\frac{3}{2t+100}y=2.5[/tex]

We multiply through by the integrating factor: [tex]e^{\int \frac{3}{2t+100}dt }=e^{\frac{3}{2} \int \frac{1}{t+50}dt }=(50+t)^{\frac{3}{2} }[/tex]

to get:

[tex](50+t)^{\frac{3}{2} }\frac{dy}{dt}+(50+t)^{\frac{3}{2} }\cdot \frac{3}{2t+100}y=2.5(50+t)^{\frac{3}{2} }[/tex]

This gives us:

[tex]((50+t)^{\frac{3}{2} }y)'=2.5(50+t)^{\frac{3}{2} }[/tex]

We integrate both sides with respect to t to get:

[tex](50+t)^{\frac{3}{2} }y=(50+t)^{\frac{5}{2} }+ C[/tex]

Multiply through by: [tex](50+t)^{-\frac{3}{2}}[/tex] to get:

[tex]y=(50+t)^{\frac{5}{2} }(50+t)^{-\frac{3}{2} }+ C(50+t)^{-\frac{3}{2} }[/tex]

[tex]y(t)=(50+t)+ \frac{C}{(50+t)^{\frac{3}{2} }}[/tex]

We apply the initial condition: [tex]y(0)=0[/tex]

[tex]0=(50+0)+ \frac{C}{(50+0)^{\frac{3}{2} }}[/tex]

[tex]C=-12500\sqrt{2}[/tex]

The amount of salt in the tank at time t is:

[tex]y(t)=(50+t)- \frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }}[/tex]

3) The tank will be full after 50 mins.

We put t=50 to find how pounds of salt it will contain:

[tex]y(50)=(50+50)- \frac{12500\sqrt{2} }{(50+50)^{\frac{3}{2} }}[/tex]

[tex]y(50)=98.23[/tex]

There will be 98.23 pounds of salt.

4) The limiting concentration of salt is given by:

[tex]\lim_{t \to \infty}y(t)={ \lim_{t \to \infty} ( (50+t)- \frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }})[/tex]

As [tex]t\to \infty[/tex], [tex]50+t\to \infty[/tex] and [tex]\frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }}\to 0[/tex]

This implies that:

[tex]\lim_{t \to \infty}y(t)=\infty- 0=\infty[/tex]

If the tank had infinity capacity, there will be absolutely high(infinite) concentration of salt.

The salt concentration will increase without bound.

Answer:

26.04 inches

Step-by-step explanation:

A revolution is in the shape of a circle.

We can therefore say that the bike tires that complete 20 revolutions complete the length of 20 circumferences of the tires.

The length of the 20 revolutions (20 circumferences) is 136 ft

Therefore, the length of one revolution and hence, one circumference is:

C = 136 / 20 = 6.8 ft

The circumference of a circle is given as:

C = pi * d

Where d = diameter of the circle.

Hence, the diameter of the tire will be:

6.8 = 3.14 * d

d = 6.8 / 3.14

d = 2.17 ft

1 foot is equal to 12 inches, hence, 2.17 ft in inches will be:

2.17 * 12 = 26.04 inches

The diameter of the tire is 26.04 inches.

Answer:

I hope this helped you!

Then the x-intercept will be at (3, 0) and the vertex will be at (3, 0).

The quadratic equation is given as ax² + bx + c = 0.

The quadratic function is given below.

g(x) = -5(x - 3)²

Then the x-intercept will be

-5(x - 3)² = 0

- (x - 3)² = 0

    x - 3 = 0

         x = 3

Then the x-intercept will be at (3, 0) and the vertex will be at (3, 0).

The graph is given below.

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Answer:

Step-by-step explanation:

rotation

Answer:

rotation

Step-by-step explanation:

i clicked on it

Edge told me it was right

To determine the volume of a cylinder-shaped candle using its radius and height measurements, the formula πr²h is applied. Given a radius of 3 inches and a height of 5 inches, about 141 cubic inches of wax is required.

The problem at hand involves finding the volume of a cylinder, representing the amount of wax needed to create a candle. Given the measurements, the radius is 3 inches and the height is 5 inches. We use the formula for the volume of a cylinder, which is πr²h. Plug the values into the formula, substitute 3.14 for π, and calculate. Here are the calculations: Volume = 3.14 * 3² * 5 = 3.14 * 9 * 5 = 141.3 cubic inches. After rounding to the nearest whole number, you need approximately 141 cubic inches of wax to produce the candle.

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Answer: $96.33

Step-by-step explanation:

$14.82 • 6.5 = $96.33

Answer:

96.33

Step-by-step explanation:

14.82 x 6.5 = 96.33

Answer:

you know that you have the Opposite side and the Adjacent side. therefore you would use Tangent (T= O/A)

because you are finding the angle you would go Tan^-1(12÷20) =31°

it is 12÷20 because O/A and the 12 is the opposite side therefore It would be O and 20 is the adjacent side therefore equaling 20 so O/A = 12/20

Your answer is 31°

The measure of the missing angle x is approximately 59 degrees.

To find the measure of the missing angle \(x\) in the right-angled triangle with a base of 12 and a height of 20, we can use the tangent function from trigonometry. Here are the steps:

1. Identify the sides of the triangle:
  - Opposite side (height) = 20
  - Adjacent side (base) = 12

2. Use the tangent function:
  [tex]\[ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{12} \][/tex]

3. Simplify the fraction:
  [tex]\[ \tan(x) = \frac{20}{12} = \frac{5}{3} \][/tex]

4. Find the angle \(x\):
  Use the arctangent (inverse tangent) function to find the angle:
[tex]\[ x = \arctan\left(\frac{5}{3}\right) \][/tex]

5. Calculate the angle:
  Using a calculator to find the arctangent of \( \frac{5}{3} \):
  [tex]\[ x \approx \arctan\left(1.6667\right) \approx 59.04 \text{ degrees} \][/tex]

6. Round to the nearest whole number:
  [tex]\[ x \approx 59 \text{ degrees} \][/tex]

So, the measure of the missing angle x is approximately 59 degrees.

Answer:

last answer

Step-by-step explanation:

hello : last answer

Answer:

NO

Step-by-step explanation:

The sides do not fit into the Pythagorean theorem

a2 + b2 = c2

Answer:maybe

Step-by-step explanation:it depends on how it is placed

Answer:8

Step-by-step explanation:if im wrong sorry

Answer:

6

Step-by-step explanation:

Answer:

x = 1 in

Step-by-step explanation:

We can use ratios to solve since they are similar triangles

6         6+x

----- = ---------

5          6

Using cross products

6*6 = 5*(6+x)

36 = 30+6x

Subtract 30 from each side

36-30 = 30-30+6x

6 = 6x

Divide each side by 6

6/6 = 6x/6

1 =x

Answer:

their should be 9 people in each group

Step-by-step explanation:

36/4=9

9 x 4 equals 36

therefore their should be 9 people in each group

Answer:

there sjould be 9 students in the four groups

Step-by-step explanation:

36 students divided by 4 group equals nine students per group

Final answer:

To find the value of the expression −x2 − 4x − 4 for x = −3, substitute −3 into the expression and simplify to get −5.

Explanation:

To evaluate the expression −x2 − 4x − 4 for x = −3, we substitute −3 for x in the expression and simplify.

First, substitute x with −3: −(−3)2 − 4(−3) − 4.

Simplify the square of −3: −(9) − 4(−3) − 4.

Multiply 4 by −3: −(9) + 12 − 4.

Finally, add and subtract the numbers: −9 + 12 − 4 = −1 − 4 = −5.

So, evaluating the expression for x = −3 gives us −5.