A composite figure is formed by placing a half-sphere atop a cylinder. The half-sphere and the cylinder both have a radius of 3 centimeters. The height of the cylinder is 12 centimeters.

What is the exact volume of the composite figure?

Step-by-step explanation:

The 36 cm would be the hypotenuse of a RIGHT triangle with equal leg lengths ( square plate )

 so use Pythagorean Theorem

   Hypotenuse^2 = leg1^2 + leg2^2     ( leg1 = leg2)

       36^2      =   2 leg1^2  

       1296  = 2 leg1^2

         leg1 = 25.5 cm  = square plate side length

It is observed that the ice in Leah's glass of juice will melt first that the ice in Philip's glass of juice which sits on the table.

___________________________________

It is given that Leah and Philip both have a glass of juice with ice cubes. Leah stirs her juice with her spoon. Philip let's his sit on the table.

Now, we need to answer whose ice cubes will melt first and why;

Firstly, let us assume that the ice is at a temperature of 0°C and the surroundings of the ice are at a temperature of 20°C.

Now, for the ice to melt, it should gain some energy from it's surroundings which can be transferred to the ice from it's surroundings by conduction through metal piece or a plastic piece.

We know that, metal is a best conductor as compared to plastic which means that the above-mentioned energy will be transferred more quickly through the metal as compared to plastic.

Furthermore, in the given condition, Leah stirs her juice with her spoon which we assume is of metal, proving the above-mentioned statements true.

Therefore, it is observed that the ice in Leah's glass of juice will melt first that the ice in Philip's glass of juice which sits on the table.

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The negative correlation coefficient of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer suggests that as vitamin A consumption increases, the cancer rate tends to decrease.

A correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, a correlation coefficient of -0.73 indicates a negative correlation between consumption of vitamin A and the cancer rate.

Interpreting this correlation, it can be inferred that there is an inverse relationship between the two variables. As consumption of vitamin A increases, the cancer rate tends to decrease.

However, it is important to note that correlation does not imply causation.

It would be incorrect to conclude that consuming more vitamin A causes this type of cancer. Correlation does not provide information about the direction of causality.

Other factors and confounding variables may be involved in the relationship between vitamin A consumption and cancer rate.

To establish a causal relationship, further research, such as experimental studies or controlled trials, would be necessary. These types of studies can help determine whether there is a causal link between vitamin A consumption and the occurrence of this particular cancer.

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Romans experimental probability is 0.176.

Probability simply means the likelihood that something will happen or take place.

In this case, Roman spun the spinner 34 times and landed on 4 a total of six time.

The probability will be:

= Number of occurence / Total available value

= 6 / 34

= 0.176

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The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer:

The coefficient of x becomes 4. Hope it helps you

Step-by-step explanation:

Answer: 2

Step-by-step explanation: Mark me brainliest

number of eighth-graders who want fruit smoothies: 150

total number of students: 800

relative frequency: 150/800 = 3/16 ≈ 0.19

The present value of an investment that will pay you $15,000 in 9 years, with an appropriate discount rate of 8 percent compounded daily, is $7,638.61.

This is calculated using the following formula:

\(\begin{equation}PV = \frac{FV}{(1 + r)^n}\end{equation}\)

\(\begin{equation}PV = \frac{15000}{(1 + 0.08)^{3285}} = 0.00001059\end{equation}\)

Present Value = $7,638.61

The number of years is 9 years multiplied by 365 days per year, which is 3285 days. The interest rate is 8 percent divided by 365 days per year, which is 0.0002191780822.

In other words, if you invest $7,638.61 today at 8 percent compounded daily, you will have $15,000 in 9 years.

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Answer:

2 1/3

Step-by-step explanation:

if you ate a whole box, (1) and your friend ate 1/3 MORE than you, it would be: 1 + 1 1/3. hope this helped :)

Add 100 pounds of weight to the luggage hold to balance the aircraft.

The CG is out of equilibrium forward with the existing numbers; weight must be increased, preferably to the aft portions, to bring the moment into acceptable bounds. Fuel addition will just increase weight; it won't shift the CG back.

The 100 pounds of luggage will cause the CG to shift back. Add 100 pounds to the maximum weight of everything to get a total weight of 2890 pounds.

The CG is now at the new weight as well as in balance since the aft arm of the luggage compartment increases the total moment arm by 140 pounds, to 2362 pounds, bringing it into balance.

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Answer:

C. No, because the sides aren't congruent

Step-by-step explanation:

Answer:

Step-by-step explanation:

square root of 100 is 10 and the only point that is on 10 is f so f = 10 or square root of 100

square root of 80 equals about 8.9 and the only point on 8.9 d so d is equal to square root of 80

3 * pi is about 9.4 and the only option left is e so e = 3 * pi

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After applying the coupon, the large pizza price came down to $13.00 from $16.25

We need to figure out the percentage change of this.

The formula for percent change is:

The amount of change (decrease) is:

16.25 - 13.00 = 3.25

The original amount is:

16.25

We substitute these information into the formula and figure out our answer:

Thus, the decrease is 20%.

We can say that the coupon was 20% off coupon.

Equation of the line is y = -3x + 7.

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines.

Suppose the line's equation is y=mx + c, where m and c are unknowns.

Since it is parallel to the equation y = -3x + 4 and -3x - y = -4, its slope is now -3. So m = -3.

Additionally, point  (1,4). Therefore, this should be satisfied by our line's equation.

Consequently, 4 = -3(1) + c

therefore c = 7

The line's equation changes to y = -3x + 7.

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Answer:

57

Step-by-step explanation:

they are congruent

Answer:

\(\huge\boxed{57 \textdegree}\)

Step-by-step explanation:

We can use basic angle relationships to find the measure of ∠CDG.

We already know that ∠HGD is 57°. Since Lines CE and FH are parallel, we can tell that ∠HGD and ∠CDG are alternate interior angles. This means that their angle measures will be the exact same.

So, since ∠HGD is 57°, so it ∠CDG.

Hope this helped!

The term you're looking for is "uncertain digits."

Uncertain digits refer to the digits in a measurement that exceed the level of certainty provided by the measuring instrument.

Measurements, it is crucial to recognize the limitations of the instruments being used, as this can impact the precision and accuracy of the results.
Precision is the degree to which an instrument can consistently produce the same measurement, while accuracy is the closeness of a measurement to its true value.

Uncertain digits can affect both of these aspects.
To better understand uncertain digits, consider the following step-by-step explanation:
Identify the measuring instrument:

This could be a ruler, thermometer, or any other device used to take measurements.
Determine the instrument's least count:

The least count is the smallest unit the instrument can measure.

A ruler with millimeter markings has a least count of 1 millimeter.
Record the measurement:

When taking a measurement, include all the certain digits (those within the instrument's least count) and one uncertain digit.

The uncertain digit is an estimate, and it represents the best guess within the least count of the instrument.
Keep in mind the limitations:

Recognize that uncertain digits are an inherent part of the measuring process and that they affect the precision and accuracy of the results.
Uncertain digits are the digits that exceed the certainty of a measuring instrument.

It is important to consider these digits and the limitations of the instruments used when conducting experiments or making measurements.

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The length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

The circumference of a circle is the distance around its outer boundary, also known as its perimeter. It is one of the fundamental properties of a circle, along with its radius and diameter.

Since the garden is circular, its widest point is its diameter, which is twice the radius. Therefore, the widest point of the garden is 12 feet across.

To find the length of the edging material needed to enclose the garden, we need to find the circumference of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius and π (pi) is approximately 3.14. Substituting,  r = 6 into the formula, we get:

C = 2π(6)

C = 12π

To approximate this value using 3.14, we can substitute π = 3.14 and get:

C ≈ 12(3.14)

C ≈ 37.68

Therefore, the length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

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The distance between the two tangent lines is $0$.

Let's first draw a diagram to better understand the problem:

css

Copy code

       A

      / \

     /   \

    /     \

   B-------C

We are given that $AB$ and $BC$ are diameters of circles with radius $1$. Let $O_1$ and $O_2$ be the centers of the circles with diameters $AB$ and $BC$, respectively. Since $AB$ and $BC$ are diameters, $O_1$ and $O_2$ coincide with $B$.

Let $D$ be the point where the tangent to the circle with diameter $BC$ intersects $AB$, and let $E$ be the point where the tangent to the circle with diameter $AB$ intersects $BC$. Since the tangent lines are parallel, we have $\angle CDE = \angle ABC$. Furthermore, we know that $\angle ABC =\(90^\circ$\) since $AB$ is a diameter. Therefore, $\angle CDE = \(90^\circ$.\)

css

Copy code

       A

      / \

     /   \

    /     \

   B-------C

     \   /

      \ /

       D

Since $\angle CDE = \(90^\circ$\), we have $CD \perp DE$. Since $AB$ is a diameter, $AB \perp DE$. Therefore, $CD$ and $AB$ are parallel lines.

Let $F$ be the point where the tangent to the circle with diameter $BC$ intersects $CD$. We know that $AB \parallel CD$, so $\angle CDF = \angle ABC =\(90^\circ$\). This means that $CDF$ is a right triangle.

css

Copy code

       A

      / \

     /   \

    /     \

   B-------C

     \   / |

      \ /  |

       D   |

       |   |

       F   |

Let $x$ be the distance between the tangent lines. We want to find the value of $x$.

We have $DF = 1$ since $DF$ is a radius of the circle with diameter $BC$. We also have $CD = x$ since $CD$ is parallel to $AB$. Using the Pythagorean theorem in triangle $CDF$, we can find $CF$:

\($CF^2 = DF^2 + CD^2 = 1^2 + x^2 = x^2 + 1$\)

Since $CF$ is a radius of the circle with diameter $AB$, we have $CF = 1$. Therefore,\($x^2 + 1 = 1^2\)$, which gives us \($x^2 = 0$\). Since $x$ represents a distance, we can conclude that $x = 0$.

Therefore, the distance between the two tangent lines is $0$.

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Answer:

a) experimental : 4 ÷ 20 = 1/5 or 20%

Theoretical : 1/6

b) experimental: 18÷20= 9/10 or 90%

Theoretical : 5/6 or 83%

c) experimental: 2÷20 = 1/10 or 10%

Theoretical : 1/6

Step-by-step explanation:

d = a  -  - a   = a + a = 2a

The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

Answer:

Exact Form:

-45/14

Decimal Form:  -3.21428571

…

Mixed Number Form:

−

-3  3/14

-

The given statement "As the level of confidence increases the number of item to be included in a sample will decrease when the error and the standard deviation are held constant." is False because error increases.

As the level of confidence increases, the required sample size will increase when the error and standard deviation are held constant.

This is because as the level of confidence increases, the range of the confidence interval also increases, which requires a larger sample size to ensure that the estimate is precise enough to capture the true population parameter with the desired level of confidence.

For example, if we want to estimate the mean height of a population with a 95% confidence interval and a margin of error of 1 inch, we would need a larger sample size than if we were estimating the same mean height with a 90% confidence interval and the same margin of error.

The larger sample size ensures that the estimate is more precise and that we have a higher level of confidence that it captures the true population parameter.

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In this equation, y represents the unknown number. We are taking the difference of y and 9 by subtracting 9 from y, then multiplying it by 2 to get twice the difference.

The sentence "Twice the difference of a number and 9 equals 3" can be translated into an equation using the variable y for the unknown number as follows:

2(y - 9) = 3

The result of this expression is equal to 3, which is given in the sentence.

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Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △RST;

The vertices are, R(4, 1), S(7, 3), and T(6, 4)

Here, Translation: (x, y) → (x, y−1)

And, Reflection in the y-axis.

Hence, New coordinate of the image of △RST are,

⇒ R' = (- 4, 1 - 1) = (- 4, 0)

⇒ S' = (- 7, 3- 1) = (- 7, 2)

⇒ T' = (- 6, 4 - 1) = (- 6, 3)

Thus, Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

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