The figure shows a grapefruit half. The radius to the outsideof the rind is 5 cm. The radius to the inside of the rind is 4 cm.The edible part ofthe grapefruit is divided into 12 equal sections.Find the volume of the half grapefruit and the volume of one ediblesection. Give your answers in terms of .

Given:

System of linear equations.

Explanation:

System 1:

The above system of equations can be simplified ELIMINATION BY SUBTRACTION.

System 2:

The above system of equations can be simplified using the SUBSTITUTION METHOD.

System 3:

The above system of the equation can be simplified using ELIMINATION BY SUBTRACTION.

System 4:

The above system of the equation can be simplified using ELIMINATION BY SUBTRACTION.

System 5:

The above system of the equation can be simplified using ELIMINATION BY MULTIPLICATION.

Answer:

4x-12

Step-by-step explanation:

8-4(-x+5)

8+4x-20

4x-12

Answer:

512

Step-by-step explanation:

the number of subsets of the set {1, 2, 3, ..., 9} is : 2^9 = 512

The student's score on a 5th test for the student's average score on the 5 tests to be 80 is (E) 88.

Average is given by the formula -

Average = sum of all the values ÷ number of values

Taking the case of four tests first, to find the total marks.

Total marks = 78 × 4

Performing multiplication

Total marks = 312

Now, let us assume the student's marks on fifth test be x. So,

80 = (312 + x)/5

Rewriting the equation -

312 + x = 80 × 5

Performing multiplication on Right Hand Side

312 + x = 400

x = 400 - 312

Performing subtraction on Right Hand Side

x = 88

Thus, the student should score 88 marks now.

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At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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The number of whole cup of milk that Charlene would use for all 8 packages would be = 8 cups of whole milk.

A square is a type of quadrilateral that has four sides with four angle 90° at each edge.

The number of chocolate square mixture Charlene would use for the party = 8 packages.

The number of packages that require a cup of milk = 1

Therefore the number of whole cups of milk that would be used for the whole 8 packages would be = 8×1 = 8 cups of whole milk.

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Answer:

6-43/4-21/8

6(-68-21/8)

48-107/8

-59/8

Answer: See attached

Step-by-step explanation:

    Given:

y = -x² + 6x - 5

    Since this is a quadratic function, we will have a parabola.

    Because our x² value is negative, this parabola will be a "frowny face" instead of a "smiley face" like the parent function.    

    The - 5 means we shift the function 5 units to the right from the parent function.

    See attached for our graph.

    What parent function am I mentioning?

The parent function of y = -x² + 6x - 5 is y = x²

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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De acuerdo con la información podemos inferir que la población se refiere a los habitantes de la ciudad y la muestra es 40,000 personas.

Para identificar la información faltante debemos tener en cuenta la información del enunciado. En este caso nos dicen que quieren implementar una revista en una ciudad determinada y para identificar los temas de la revista debemos hacer una encuesta.

En este caso, la entrevista se realiza a 40,000 personas por lo que esta sería la muestra debido a que no podríamos realizar la encuesta a cada una de las personas que es habitante de la ciudad.

Nota: Esta pregunta está incompleta. Aquí está la información completa:

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I put a step by step on the picture, I thought it would be easier than words. Hope this helps!

5−33−32+39+3

Not sure?

Answer:

(6, -8)

Step-by-step explanation:

big brain

Answer:

A(6,-8)

Step-by-step explanation:

To determine the solutions graphically, you want to select a point that lies in both the red and blue sections simultaneously, in this case, the purple section. The only point that satisfies this property is choice A.

If this helped, a brainliest would be greatly appreciated!

Answer:

540 cubic inches.

Step-by-step explanation:

The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

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Answer:

65c

Step-by-step explanation:

Answer:

y - (-1) = -3(x-10)

y+1= -3x+30

y= -3x+30-1

y= -3x+29

Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Step-by-step explanation:

Hope this helps.
If you reflect in the y-axis, it would look like the following.

Answer:

? = 5

Step-by-step explanation:

Parallel lines are made with 2 lines having the same slope but different y-intercept.

Answer:

5

Step-by-step explanation:

Parallel lines have same slope

y= 5x+2

y= 5x+3

Answer:

C. Between 4 and 5.......

"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

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Answer:

Ans) 42.7%

Step-by-step explanation:

For a continuous probability distribution, a curve known as probability density function contains information about these probabilities.

in the given range -

The probability that a continuous random variable = equal to the area under the probability density function curve

The probability that the value of a random variable is equal to 'something' is 1.

As per the diagram,

Weight of chocolate bar between 4 ounces and 7 ounces is highlighted in the blue part. That area is said to be 0.42739 and the total area under the curve is 1.

Hence required probability

=0.42739/1=0.42739

Ans) 42.7%

Round to nearest tenth of a percent

The correct option is (B) That'is

\( \bf \implies{{3x}^{3} - {2x}^{2} + 10x - 12}\)

Step 1) : Operations of functions

\( \bf \longrightarrow{f(x) + g(x)} \\ \bf \longrightarrow( {3x}^{3} - {2x}^{2} + 4x - 5) + (6x - 7)\)

Step 2) : Simplify or expand

\(\bf \longrightarrow( {3x}^{3} - {2x}^{2} + 4x - 5) + (6x - 7)\)

\(\bf \longrightarrow {3x}^{3} - {2x}^{2} + 4x - 5 + 6x - 7\)

\(\bf \longrightarrow {3x}^{3} - {2x}^{2} +( 4x + 6x) + (- 5 - 7)\)

\(\bf \longrightarrow {3x}^{3} - {2x}^{2} +( 4 + 6) \times x+ (- 5 - 7)\)

\(\bf \longrightarrow {3x}^{3} - {2x}^{2} +10x - 12\)

Answer:

Step-by-step explanation:

21-26. a = v - u / t

=> a = 47 - 19 / 5

=> a = 28 / 5

=> a = 5.6 m/s²

27-32. avg. speed = distance / time

=> 40 m / 10 s

=> 4 m/s

33-38. velocity = distance / time

=> v = 150 / 40

=> v = 15 / 4

=> v = 3.75 m/s