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Make sure to find the missing angle measure AND the 2 missing side lengths.

The radius is 3.50 cm  and height of the cylindrical portion is  6.17 cm

First let's denote the radius of the test tube as "r" and the height of the cylindrical portion as "h". We can use the given information to set up two equations.

First, we know that when 4554/7 cu cm of water is poured, the test tube is exactly full. The volume of a hemisphere with radius r is (2/3)πr³, and the volume of a cylinder with radius r and height h is πr²h. So we can write:

(2/3)πr³ + πr²h = 4554/7

Second, we know that when only 396 cu cm is added, there is 9 cm of empty space left in the tube. We can find the height of the water in the tube using similar triangles:

h_water / (2r) = (4554/7 - 396) / (2/3)πr³

Simplifying this equation, we get:

h_water = (9/7)πr³ - (9/2)r

Now we can substitute this expression for h_water into the first equation:

(2/3)πr³ + πr²[(9/7)πr³ - (9/2)r] = 4554/7

Expanding and simplifying, we get a cubic equation in r:

(16/21)πr⁴ - (81/2)πr³ + (4554/7)πr² - (4554/14)r = 0

Using numerical methods or a graphing calculator, we can solve this equation to find that:

r ≈ 3.5 cm

Substituting this value back into the equation for h_water, we get:

h_water ≈ 8.5 cm

So the height of the cylindrical portion is:

h_cylinder = h - (2/3)r = 8.5 - (2/3)(3.5) = 6.166... cm

Therefore, Rounding to two decimal places the radius is 3.5 0cm  and height of the cylindrical portion is 6.17 cm

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The distance of 7km in miles is 4.349597 miles.

It's important to note that kilometers are the primary unit of distance measurement in most countries, while miles are used primarily in the United States and a few other countries. To convert 7km to miles, we need to know the conversion factor between the two units.

By knowing how to convert between these two units is a useful skill when traveling internationally or when working with different units of measurement. Here, One kilometer is equal to 0.621371 miles.

Therefore, to convert 7km to miles, we simply multiply 7 by the conversion factor:

7km x 0.621371 miles/km = 4.349597 miles

So, 7km is equal to approximately 4.35 miles.

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Answer:

Step-by-step explanation:

To find the next 3 terms in this geometric sequence, we need to first find the common ratio (aka the number you multiply in to get from one term in the sequence to the next). We find that if we multiply 54 by 3, we get to 162. If we multiply 162 by 3, we get to 486. Therefore, our common ratio is 3. Continuing on with this process,

486*3=1458

1458*3=4374

4374*3=13122

The next three terms in each geometric sequence 54, 162, 486 are 1458, 4374, and 13122.

The sequence given is a geometric sequence, which means that each term is obtained by multiplying the previous term by a constant factor. To determine the next three terms in the sequence, we must first determine the common ratio (r) by dividing any term by its preceding term:

r = 162/54 = 3

Similarly, r = 486/162=3

We can use this common ratio to find the next three terms:

To find the fifth term, we multiply the fourth term by the common ratio: 486 x 3 = 1458.

To find the sixth term, we multiply the fifth term by the common ratio: 1458 x 3 = 4374.

To find the seventh term, we multiply the sixth term by the common ratio: 4374 x 3 = 13122.

Therefore, the next three terms in the sequence are 1458, 4374, and 13122.

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51 centimetres equal to 20.08 inches.

In the International System of Units( SI), the current replication of the metric system, a centimetre (symbol cm) is a unit of length.

The symbol of inch is 'in'.

As one inch was exactly equal to 25.4 millimetres.

1 in equal to 2.54 cm

So, 1 cm equals [tex]\frac{1}{2.54}[/tex]  inch

Here we want to convert 51 cm to inches.

For the conversation of cm into the inches multiply the cm value by 0.3937 or  [tex]\frac{1}{2.54}[/tex]

We can write as:

51 cm = 51 × [tex]\frac{1}{2.54}[/tex] inches.

51 cm = 20.08  inches (rounded to two decimal places)

Therefore, 51 cm is equivalent to 20.08 inches.

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Answer: The scale factor is 2/5 and the length of BC is 10

Given: We have to find the factor of dilatation by looking at the pre-image ABCD and the image A'B'C'D' and then we have to find the length of the segment BC.

Explanation: To calculate the dilatation factor we have to look at two given segments, the side D'C' and the side DC since the segment DC belong to the pre-image and the segment D'C' belongs to the image we know that the factor of dilation will be the same for the change relation between those two sides and any other side of the figure so:

Scale factor = 2/5

Now in order to find the measure of the side BC we have to multiply 4 by the inverse scale factor because we are going from the image to the pre-image so:

Length of BC = 4 * 5/2 = 10

The value for the length of CD is equal to 3.9 mm using the intersecting secant theorem

The intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

DY × CY = BY × AY

{AY = 2 mm + 6 mm}

2.5 × CY = 2 mm × 8 mm

2.5 × CY = 16 mm

CY = 16mm/2.5 {divide through by 2.5}

CY = 6.4

{CD = CY - DY}

CD = 6.4 - 2.5

CD = 3.9

Therefore, the value for the length of CD is equal to 3.9 mm using the intersecting secant theorem.

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Answer:

2 feet.

Step-by-step explanation:

Since the volume of cube A is 64, we can divide the edge (4) by two because cube B can only hold half as much liquid.

Thus, the edge of cube b is 2 feet.

Hope it helped!

Answer:

10

Step-by-step explanation:

[tex]7.2\\+\\2.8\\--\\10[/tex]

10 is an integer, there is no way to express it in decimal form.

Answer: 10

Step-by-step explanation:

2.8+7.2=10

yup

Answer:

x > -8

Step-by-step explanation:

5 - (x + 5) > -2(x + 4) (distribute)

5 -x - 5 > -2x -8 (combine like terms)

-x > -2x - 8 (add 2x to both sides)

x > -8

The inequality that represents all possible values of m, the number of miles Lola can travel in the car with the remaining gasoline in the tank is m ≤ 282.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Several types of inequalities are represented by a variety of notations, including:

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

Let the number of miles = m.

Given that, Lola’s car can travel no more than 445 miles on one full tank of gasoline.

m ≤ 445

After filling up the tank, she traveled 163 miles in the car.

Remaining distance is:

m ≤ 445 - 163

m ≤ 282

Hence, the inequality that represents all possible values of m, the number of miles Lola can travel in the car with the remaining gasoline in the tank is m ≤ 282.

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Answer:

The domains are (1,4,9) Ranges are (-1,-2,-3)

Step-by-step explanation:

The domain is on the x-axis and the range is on the y-axis

The area of hemisphere is given by  3πr² and the volume of the hemisphere is given by 2/3πr³.

When we divide the sphere into two equal halves, we get a hemisphere. The curved surface area of the hemisphere plus the base area will add up to the hemisphere's total surface area. Here, the foundation has a circular shape. We may discover many examples of hemispheres in daily life, such as how our planet Earth is divided into the southern and northern hemispheres.

A hemisphere's surface area is the sum of all of its faces. When a sphere is cut along a plane that runs through its centre, a three-dimensional shape known as a hemisphere is created. A hemisphere is, in other terms, one-half of a sphere.

3πr²

 A hemisphere has one flat circular base and a curving surface. The quantity of unit cubes that can fit inside a hemisphere is known as its volume.

2/3πr³.

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Answer:

Below

Step-by-step explanation:

I will assume this question has messed up syntax and is supposed to be :

x^5  *   x^4   * x    =

x^5   * x^4   * x^1

x^(5 + 4+ 1) =  x^10

At 7 a.m., the temperature was 2°.

Temperature is a measure of the average kinetic energy of particles in a system, measured in degrees on a specific scale (such as Celsius or Fahrenheit). The higher the temperature, the faster the particles move. Temperature is also related to heat, which is the transfer of energy between two systems at different temperatures. Heat always flows from a higher temperature system to a lower temperature system. In addition, temperature is related to pressure, which is the force exerted by the particles in a system. When the temperature of a system increases, so does the pressure.

At 7 a.m., the temperature was 2°. This is because temperatures dropped by 2° per hour until 2 o'clock in the morning. In the 6 hours (from 2 a.m. to 8 a.m.) there were 12° of decrease in temperature (2° per hour x 6 hours). This means that the temperature at 7 a.m. was -6° (2° - 12° = -6°).

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To  calculate unit vector online we have to divide the original value of the vector by its magnitude.

A vector with a length of one is known as a unit vector. A direction vector is a unit vector that represents a spatial direction.

It is possible to determine the unit vector along the same direction if you are given an arbitrary vector. To accomplish it, use the following formula:

û = u / |u|,

Our distance calculator can be used to determine a vector's magnitude, or you can use the straightforward equation:

|u| = √(x² + y² + z²)

Finding the midpoint of a segment can be done with the help of the vector magnitude calculation.

When defining linear transformations, the unit vector is a helpful concept to understand. The matrix norm, for instance, represents the amount by which a unit vector is stretched when multiplied by a matrix.

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Answer:

  120°

Step-by-step explanation:

You want to know the measure of the obtuse angle x° at B in the attached diagram.

This problem is quickly solved by using your knowledge of "special" triangles. Referring to the attached figure, triangles ACE and DGC are isosceles right triangles, so their base angles are 45°. Triangle CDE is equilateral, so all of its internal angles are 60°.

Line AB forms a "straight angle" at C. That means the sum of angles on one side of the line is 180°. This can be used to find the measure of angle DCB.

  ∠ACE +∠ECD +∠DCB = 180°

  45° +60° +∠DCB = 180°

  ∠DCB = 180° -105° = 75°

From above, you know that angle CDG is 45°.

The marked angle x° is an exterior angle to triangle BCD. As such, its measure is equal to the sum of the remote interior angles of that triangle:

  x° = ∠BCD +∠BDC = 75° +45°

  x° = 120°

__

Additional comment

As with many math problems there are other ways to work this. If you draw a perpendicular to AB at C, you find it makes a 45° angle with CE and a 15° angle with CD. That same 15° measure is the measure of angle GCB. Of course, angle G is 45°, so it takes x° = 120° to make the internal angle sum of ∆GCB equal to 180°.

The value after conversion Fahrenheit to Celsius is equal to 375 Fahrenheit to 190.556 Celsius.

The unit which represents the measurement of the temperature in Standard form is given by Fahrenheit and Celsius.

Relation between Fahrenheit and Celsius is represented by the formula as written below

(°F − 32) × 5/9 = °C

Here Substitute the value 375 Fahrenheit in the above formula to get into Celsius ,

= ( 375°F − 32) × 5/9

= 343 × 5/9

= 1715 / 9

= 190.55555 Celsius

= 190.556 Celsius

Therefore, the converted value of 375 Fahrenheit into the Celsius is given by 190.556 Celsius .

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The missing side length, C, is approximately 23.53 units.

To find the missing side length in a right triangle, we need to use trigonometry. Given the angle A = 27° and the side length opposite to it, B = 12C, we can follow the following steps to find the missing side length:

1. Locate the angle measured: In this case, we are given angle "A = 27°."

2. Label the sides of the right triangle: Let's label the hypotenuse as H, the side opposite to angle A as O, and the side adjacent to angle A as A. We can choose any side as the hypotenuse, so let's choose H to be the side opposite to angle B.

3. Which side do you know? Which side are you trying to find?: We know the length of side B and are trying to find the length of side C.

4. Decide which trig function (cosine, sine, or tangent) fits the sides chosen in step 3: We are given the length of the opposite side (B) and are trying to find the length of the adjacent side (C), so we will use the tangent function.

5. Write your equation. Fill in the known measurements: The tangent of angle A is defined as the ratio of the length of the opposite side to the length of the adjacent side. So we can write:    tan(A) = B/C

      Substituting the known values, we get:

      tan(27°) = 12/C

6. Create two fractions. Cross-multiply to solve: To solve for C, we can cross-multiply and simplify the equation as follows:

      tan(27°) = 12/C  

      C * tan(27°) = 12          

      C = 12/tan(27°)                                                                                

        Using a calculator, we can evaluate the value of tan(27°) to be approximately 0.5095. Therefore,                                                     

       C = 12/0.5095 ≈ 23.53

Hence, the missing side length, C, is approximately 23.53.

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Answer: Impossible to answer/ 12 chickens 8 rabbits

Step-by-step explanation: The question asks how many hens there are, or female chickens. We do not know if the chickens are female or male, so we cannot answer. If you meant how many chickens there were, then we start with 20 chickens and 0 rabbits. Doing so, we have 40 legs. When we switch a chicken for a rabbit, we have 19 chickens and 1 rabbit, and 42 legs. So, we can subtract 56-40 giving us 16 extra legs we need, so we divide 16/2 giving us 12 chickens and 8 rabbits.

answer : x(2)x(-3--6)

Answer:

12%

Step-by-step explanation:

based on the simulation info, if there is both

1. A "1"

2. An "A" or "B",

then it will rain on both days. This occurs 3 times out of 25, or 3/25 = 0.12 = 12%

1. 2nd row 1st column

2. 3rd row 4th column

3. 5th row 2nd column

Answer:

It will take about 13.5 years for the money to grow to $5,500
That would be about 13 years and 6 months

Step-by-step explanation:

The formula for accrued amount(principal + interest) is given by:
[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}\quad(1)\\[/tex]

where
P = Principal amount
r = R/100 where R is the annual interest rate as a percentage
n= number of times compounded per year
t = number of years

Given

A = $5,600
P = $3,500
R = 3.35% ==> r = 3.35/100 = 0.0335
n = 12 (since there are 12 months in a year)

We have to find out t

Plugging known values into equation (1)

[tex]5500 = 3500\left(1+ \dfrac{0.0335}{12}\right)^{12t}\\\\5500 = 3500 \left(1+ 0.002791\right)^{12t}\\\\5500 = 3500 (1.002791)^{12t}[/tex]

Switch sides so unknown appears on the left side:
[tex]3500 (1.002791)^{12t} = 5500[/tex]

Divide by 3500 both sides:
[tex](1.002791)^{12t} = \dfrac{5500 }{3500}\\\\(1.002791)^{12t} = 1.5714\\\\[/tex]

Take logs on both sides:
[tex]\ln \left(1.002791^{12t}\right)=\ln \left(1.5714\right)\\\\[/tex]

We have
[tex]\ln \left(1.002791^{12t}\right) = 12t\ln \left(1.002791\right)\\\\[/tex]

Therefore we get
[tex]12t\ln \left(1.002791\right)=\ln \left(1.5714\right)\\\\t\ln \left(1.002791\right)=\ln \left(1.5714\right)\\\\\\[/tex]

Dividing both sides by [tex]12\ln \left(1.002791\right)[/tex] this works out to
[tex]t=\dfrac{\ln \left(1.5714\right)}{12\ln \left(1.002791\right)}[/tex]

[tex]t = 13.51359\; years[/tex]

Rounding to one decimal place
[tex]t = 13.51\; years\\[/tex]

This would be roughly 13 years and 6 months

The solution to the system of inequalities is:

x ≥ -3.8 and

x ≤ 3

This can also be expressed as

-3.8 ≤ x ≤ 3

solving the first inequality:

-2x - 3x ≤ 19

Combining like terms, we get:

-5x ≤ 19

Dividing both sides by -5 :

x ≥ -3.8

So we have found that x is greater than or equal to -3.8.

From the second inequality:

-8x ≥ -24

Dividing both sides by -8:

x ≤ 3

So we have found that x is less than or equal to 3.

Therefore, the solution to the system of inequalities is:

-3.8 ≤ x ≤ 3

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The measure of ∠S is 75 degrees

The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:

cos(S) = (q² + r² - s²)/2qr  

where q, r and s are the lengths and Q, R and S are the angles

Using the formula:

cos(S) = (q² + r² - s²)/2qr

cos(S) = (99² + 17² - 96²)/(2*99*17)

cos(S) = 0.2597

S = cos⁻¹(0.2597)

S = 75 degrees

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If a p-series is 1 np, you can determine if it converges or not. It converges when p > 1. This is how you test a P series convergence.

The situation diverges if the terms are not close to zero. If you are able to fully control a well-known divergent series with the series, it diverges. To determine if a p p -series is converging or diverging, one can apply the p p -series test. If the denominator's power satisfies p>1 p > 1, the series converges; otherwise, it diverges.

A sequence's convergence can be checked using a variety of techniques. We only need to know the sequence's limit at n n to infinity in some cases. If a series of absolute values P |an| is convergent, the series P an is said to be absolutely convergent.The Geometric Series test is the opposite of the P-Series test in that it requires us to locate a variable raised to a number. We are trying to find a raised number that is a variable!

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A table used to find the area under the standard normal distribution to determine the probability of a z-score being less than a given value.

A negative z-score table is a tool used in statistics to find the probability of a z-score being less than a certain value. A z-score is a measure of the number of standard deviations an observation or data point is above or below the mean of a dataset.

The standard normal distribution is a bell curve with a mean of zero and a standard deviation of one. The negative z-score table lists the area under the curve to the left of a negative z-score, which can be used to calculate probabilities. The table is used by finding the corresponding row and column for the desired z-score and reading the probability from the table.

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Answer:

13

Step-by-step explanation:

943.50 + 31.50x = 1353

This is in the form y=mx+b.

To isolate for x, move 943.50 to the other side and subtract it from 1353.

31.50x = 409.50

now, divide by 31.50 to get x by itself.

x =13

The team can bring 13 players to the tournament.

Answer:

1 solution, x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We can factor [tex]4x^2 - 4x + 1[/tex] first:

[tex](2x-1)(2x-1)[/tex]

= [tex](2x-1)^2[/tex]

To find the solution, we can do:

[tex]2x-1=0[/tex]

Let's find x now:

2x = 1

x = [tex]\frac{1}{2}[/tex]

Therefore, there is 1 solution and it is x = [tex]\frac{1}{2}[/tex]

Answer: 20.8

Step-by-step explanation: .