How many milliliters of a 28% sugar Solution do we need to mix with 75 milliliters of a 10% sugar solution so that the resulting mixture is a 13% sugar solution?

Answer:

The radius of the cylinder is equal to 10 feet.

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

Volume of a cylinder, V = πr²h

Where:

By substituting the given parameters into the formula for the volume of a cylinder, we have the following;

V = πr²h

1,570 = 3.14 × r² × 5

1,570 = 15.7r²

r² = 1,570/15.7

r² = 100

Radius, r = √100

Radius, r = 10 feet.

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Answer:

11. Not enough information

12. You can say DB = DC by SAA congruence rule and CPCTC (Corresponding parts of congruent triangles are congruent)

Step-by-step explanation:

For 12, you can say ΔABD≅ΔACD because they have a side in common (AD) and they have 2 congruent angles. Thus, you can use the SAA congruence criterion. Then, you can use CPCTC (Corresponding parts of congruent triangles are congruent) to say that DB = DC.

Hope this helps :)

the equation of the sphere is: x{power}2 + y{power}2 + z{power}2 = 49 To solve this problem, we need to first visualize the objects involved: a cylinder with radius 5 and a sphere with radius 7.

The cylinder has a height that is infinite (i.e., it extends infinitely in the vertical direction), while the sphere is centered at the origin.

To set up the equation of the cylinder, we can use the cylindrical coordinate system. The equation of a cylinder with radius r and infinite height in cylindrical coordinates is given by:

r{power}2 + z{power}2 = R{power}2

where r is the radial distance from the z-axis, z is the height, and R is the radius of the cylinder. In our case, we have R = 5, so the equation of the cylinder is:

r{power}2 + z{power}2 = 25

To set up the equation of the sphere, we can use the Cartesian coordinate system. The equation of a sphere with radius R centered at the origin in Cartesian coordinates is given by:

x{power}2 + y{power}2 + z{power}2 = R{power}2

In our case, we have R = 7, so the equation of the sphere is:

x{power}2 + y{power}2 + z{power}2 = 49

Now, we want to find the volume of the ring-shaped solid that remains when we bore a hole through the center of the sphere using the cylinder. To do this, we need to find the volume of the intersection of the cylinder and the sphere.

To find the intersection, we can substitute the equation of the cylinder into the equation of the sphere and solve for z. This gives us:

x{power}2 + y{power}2 + (r{power}2 - 25) = 49

r{power}2 = 74 - x{power}2 - y{power}2

So the intersection is defined by the set of points (x, y, z) that satisfy both equations. To find the volume of the intersection, we can integrate over the region where the cylinder and sphere intersect. In cylindrical coordinates, the region of integration is defined by:

r{power}2 + z{power}2 ≤ 49

r{power}2 + z{power}2 ≥ 25

Using the equation we derived earlier for r{power}2, we can rewrite this region as:

25 ≤ r{power}2 ≤ 74 - x{power}2 - y{power}2

-sqrt(74 - x{power}2 - y{power}2) ≤ z ≤ sqrt(74 - x{power}2 - y{power}2)

Finally, we can use a triple integral to find the volume of the intersection:

V = ∫∫∫ (r dz dr dθ)

Over the limits of the region described above.

After computing the integral, the result will be the volume of the ring-shaped solid that remains.

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The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

This is an arithmetic sequence because there is a common difference of 4 between each term

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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Answer:

w = -0.8

sum = 0

Step-by-step explanation:

An additive inverse is when two numbers add up to 0. 0.8+ (-0.8) = 0.

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × \(r1^2\) × h

V1 = π × \((0.4 cm)^2\) × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × \(r2^2\) × h

V2 = π × \((0.1 cm)^2\) × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³

V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

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Answer:

800

Step-by-step explanation:

The Answer Is 8,000,000 Because

8×2 16 so 8,000,000 × 2=16,000,000

Answer:

x^2-5xy+4y^2

Step-by-step explanation:

In the equation we see only 1 example of like terms, 2xy-7xy=-5xy

So the simplified equation is

x^2-5xy+4y^2

This is your answer:

x^2+5xy+4y^2

Answer:

$3240 a month

Step-by-step explanation:

First, find her reduced salary:

3000(0.9)

= 2700

Then, find her salary after the raise:

2700(1.2)

= 3240

So, her salary after the raise is $3240 a month

The amount of water tank  with water after 10 minutes will be 4950 liters.

To solve this problem, we need to keep track of the net flow of water into the tank over the course of 10 minutes. The tap filling water adds water to the tank, while the tap emptying water removes water from the tank.

Let's calculate the net flow rate of water per minute:

Flow rate = (filling tap flow rate) - (emptying tap flow rate)

Flow rate = 40 L/min - 25 L/min

Flow rate = 15 L/min

Now, we can calculate the net flow of water over 10 minutes:

Net flow of water = (flow rate) * (time)

Net flow of water = 15 L/min * 10 min

Net flow of water = 150 L

Therefore, over the course of 10 minutes, the net flow of water into the tank is 150 liters.

Initially, the tank had 4800 liters of water. Adding the net flow of water, we can determine the final amount of water in the tank:

Final amount of water = (initial amount of water) + (net flow of water)

Final amount of water = 4800 L + 150 L

Final amount of water = 4950 L

After 10 minutes, there will be 4950 liters of water in the tank.

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Clara can reach a height of 2.57 meters when she jumps.

Given information:

The ceiling in Clara’s basement is 2.75 meters high.

When Clara jumps she is 18 centimeters short of being able to touch the ceiling.

We can start by converting the height of the ceiling and Clara's jump to the same units, either meters or centimeters. Let's convert Clara's jump to meters:

18 centimeters = 0.18 meters

Now we can subtract Clara's jump from the height of the ceiling to find how high she can reach:

2.75 meters - 0.18 meters = 2.57 meters

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Answer:

5

Step-by-step explanation:

plug everything in:

48+4h=68

-48      -48

4h=20

divide by 4 to isolate h

h=5

Answer:

H=5

Step-by-step explanation:

S=68, L=6, w=2, H=?

68=4x6x2+2x2xH

68=48+4H

68-48=4H (collect like terms)

20=4H (divide both side by the coefficient of H)

H=5

Answer:

3.5

Step-by-step explanation:

First you distribute. 24x-38=46.

Then add 38 to both sides

24x=84

Then divide both sides by 24

x=3.5

Answer:

x= 3.5

Step-by-step explanation:

Answer:

a) Domain: x≥0

b) Range:  y≤-2

c) x-intercepts: None

d) y-intercepts: (0,-2)

e) f(4)= -4

Step-by-step explanation:

If this helps please mark as brainliest

(a) domain is [0,∞)

(b)  Range is [-2,-∞)

(c) X intercept is none

(D) Y intercept is (0,-2)

(E) f(4)=-4

Given :

Use the given graph to determine the domain , range etc.

Explanation :

Domain is the set of x values on the graph

The graph starts at x=0 and goes on .

So domain is [0,∞)

Range is the set of y values on the graph

The graph starts at y=-2 and it goes down

Range is [-2,-∞)

X intercepts are the points where the graph crosses or touches x axis

The graph does not cross the x axis

X intercept is none

Y intercepts are the points where the graph crosses or touches  y axis

The graph touches y axis at -2

Y intercept is (0,-2)

To find out f(4) we look at the y value when x=4

f(4)=-4

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there you go i think

The subsets of real numbers are known as:

Best of Luck!

Answer:

41.4%

Step-by-step explanation:

The formula for determining the frequency:   --A

where h is the number of half-steps from the A above middle C on the keyboard.

A note is six half-steps away from the A above middle C.

Now we are supposed to find How much greater is the frequency of the new note compared with the frequency of the A above middle C?

Now initially there is no half steps .

So, substitute h =0

Now we are given that A note is six half-steps away from the A above middle C

So, substitute h =6Now To find change percentage

Hence  the frequency of the new note is 41.4% greater with the frequency of the A above middle C.

The given formula \(f(x) = 440(2)^x/12\) is used to determine the frequency of any pitch relative to the A above middle C (A440), where x represents the number of half-steps above or below A440.

The correct answer is :  d) 440 * (x square root)\(2^{12\).

The given formula \(f(x) = 440(2)^x/12\) is used to determine the frequency of any pitch relative to the A above middle C (A440), where x represents the number of half-steps above or below A440.

To determine the equivalent expression of f(x), we need to simplify the given formula.

First, we can simplify \(2^x/12\) by using the property of exponents, which states that \((a^m)^n = a^{(mn)\).

So, we can rewrite \(2^x/12\) as \((2^1/12)^x.\)

Substituting this value in the given formula,

we get f(x) = \(440 * (2^1/12)^x.\)

Now, we can rewrite \((2^1/12)\) as a square root of 2 raised to the power of 1/6.

So, the equivalent expression of f(x) is:

f(x) = \(440 * (2^1/6)^x\) = 440 * (x square root)\(2^{12\)

Therefore, the correct answer is d) 440 * (x square root)\(2^{12\).

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complete question:

On a piano, the formula to determine the frequency f of any pitch relative to the A above middle C (A440) is given by the expression f(x)=440(2)^x/12 where x represents the the number of half-steps above or below A440. Which of the

following is equivalent to f(x)?

a) 440•x(square root) 2^12

b) 440•12(square root) 2^x

c) 440• (12 square root) 2^x

d) 440•(x square root) 2^12

Answer:  C) Perimeter = 46.28

Step-by-step explanation:

The lengths of the sides on the bottom half of the shape are given as :

left = 10, bottom = 20, right = 10 = 40.

Need to find the perimeter of the semicircle at the top of the shape.

Perimeter of a circle is the Circumference = 2πr

So the perimeter of a semicircle = πr

                                                             = 3.14(2)

                                                             = 6.28

Add up the lengths of the left, bottom, right, and top: 40 + 6.28 = 46.28

Since there is only one option for Perimeter = 46.28, there is no need to solve for the Area.

The volume of a triangular pyramid is 8 mi².

We have,

The volume of a triangular pyramid.

V = 1/3 x the base area x the height

Now,

From the figure,

Height = 4 mi

And,

Base area.

= 1/2 x 3 x 4

= 6 mi

Now,

The volume of a triangular pyramid.

= (1/3) x base area x height

= 1/3 x 6 x 4

= 8 mi²

Thus,

The volume of a triangular pyramid is 8 mi².

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The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3

For the equation to be true, two scenarios need to be considered:

When the expression 6x-3 is positive and equals 3:

6x-3 = 3

When the expression 6x-3 is negative and equals -3:

6x-3 = -3

By solving these two equations, we can find the equivalent statement:

Solving 6x-3 = 3:

Adding 3 to both sides gives us:

6x = 6

Dividing both sides by 6:

x = 1

Solving 6x-3 = -3:

Adding 3 to both sides gives us:

6x = 0

Dividing both sides by 6:

x = 0

Therefore, the equivalent statement to |6x-3|=3 is:

6x-3=3 or 6x-3=-3, which can be further simplified to:

6x-3=3 or 6x-3=-3

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Answer:

-2 or -5

Step-by-step explanation:

( shown in photo below )

Answer:

2/15

Step-by-step explanation:

first you have to make both numbers have an equal denominator the subtract how much that was left from how much she Initially ate

Answer:

42 in

Step-by-step explanation:

According to the question, 0.9898732331 km is equal to 9.898732331 × 10¹¹ nm (in scientific notation).

The addition of equal groups is known as multiplication in mathematics. The number of things within the group grows as we multiply. There is a multiplication problem that involves the product in addition to the two components. In the multiplication formula 6 9 = 54, 6 and 9 are factors, and 54 is the answer.

given,

To convert from kilometers to nanometers, we need to multiply by a conversion factor that relates the two units. One nanometer is equal to 10⁻¹² kilometers. Therefore, we can write:

1 km = 10¹²  nm

To convert .9898732331 km to nm, we can multiply by this conversion factor as follows:

0.9898732331 km * 10¹² nm/km = 9.898732331 × 10¹¹ nm

Therefore, 0.9898732331 km is equal to 9.898732331 × 10¹¹ nm (in scientific notation).

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