a sphere has a radius of 2.7cm what is its volume to the nearest cubic centimeter

The volume and the surface area of the prism is 6 and 22 square inches²

First, lets find the volume of the prism

Volume:

[tex]\text{Volume}=\text{(Area of the base)}\times\text{height}[/tex]

[tex]\text{Volume}=(3\times2)\times1[/tex]

[tex]\text{Volume}=6 \ \text{square inches}^2[/tex]

Since the volume of the prism is 6, now to find the Surface area of the cubes.

[tex]\text{Surface area}= \text{Total area of the 2-dimensional surfaces to make 3-dimensional }[/tex]

[tex]\text{Surface area}=2\times3=6, \ 3\times1=3, \text{and} \ 1\times2=2[/tex].

[tex]\text{Surface area}=6(2)+3(2)+2(2)=22 \ \text{square inches}^2[/tex]

The surface area of the prism is 22.

Therefore, the volume and the surface area of the prism is 6 and 22 square inches²

Answer:

in image

Step-by-step explanation:

if it helped you please mark me a brainliest :))

Answer: 12800 cm³

Step-by-step explanation:

Area of Rectangular Prism = [tex]lwh[/tex]

A = 32 x 25 x 16

A = 12800

After answering the provided question, we can conclude that Therefore, the coordinates of M' are (11, -8).

In mathematics, a coordinate is a number or combination of integers that indicates the location of a point or object in space. Coordinates are frequently used to define a point or object's position in a specific coordinate system, such as the Rectilinear or polar coordinate systems. In the Cartesian coordinate system, a point is located by its distance from the origin along the x-axis and its distance first from origin along the y-axis. These distances are represented by two digits, the x-coordinate and indeed the y-coordinate. The point's position in the plane is specified by the two coordinates.

(x', y') = (x, y) - (a, b)

a) To find the coordinates of K', we need to use the above formula with (a, b) = (-6, 2) and (x, y) = (3, 4) (the coordinates of K in the original figure)

(x', y') = (x, y) - (a, b)

= (3, 4) - (-6, 2)

= (3 + 6, 4 - 2)

= (9, 2)

Therefore, the coordinates of K' are (9, 2).

(x', y') = (x, y) - (a, b)

= (5, -6) - (-6, 2)

= (5 + 6, -6 - 2)

= (11, -8)

Therefore, the coordinates of M' are (11, -8).

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Answer: x < -35

Step-by-step explanation:

To calculate the mean, we first need to find the midpoint of each class interval. We can do this by adding the lower and upper limits of each interval and dividing by 2. We can then multiply each midpoint by its corresponding frequency and add up the products. Finally, we divide by the total frequency to get the mean:

Class interval   Midpoint    Frequency   Midpoint x Frequency

----------------------------------------------------------------

1-5                3          2             6

6-10               8          5            40

11-15              13          8           104

16-20              18         10           180

21-25              23         14           322

26-36              31          6           186

21-35              28          4           112

36-40              38          1            38

----------------------------------------------------------------

Total frequency:   50

Mean = (6 + 40 + 104 + 180 + 322 + 186 + 112 + 38) / 50 = 921 / 50 = 18.42

Class interval   Midpoint   Mean   Midpoint - Mean   (Midpoint - Mean)^2   Frequency   (Midpoint - Mean)^2 x Frequency

--------------------------------------------------------------------------------------------------------------

1-5                3       18.42     -15.42            238.1764           2              476.3528

6-10               8       18.42     -10.42            108.5764           5              542.8820

11-15              13       18.42      -5.42             29.3764           8              235.0112

16-20              18       18.42      -0.42              0.1764          10                1.7640

21-25              23       18.42       4.58             20.9764          14              293.6704

26-36              31       18.42      12.58            158.4964           6              950.9784

21-35              28       18.42       9.58             91.9364           4              367.7456

36-40              38       18.42      19.58            383.4464           1              383.4464

----------------------------------------------------------------------------------------------------------

Total frequency:   50                                                                                   3251.8512

To calculate the standard deviation, we first need to find the variance, which is the sum of the squared deviations divided by the total frequency:

Variance = (476.3528 + 542.8820 + 235.0112 + 1.7640 + 293.6704 + 950.9784 + 367.7456 + 383.4464) / 50

= 65.0378

Then, we take the square root of the variance to get the standard deviation:

Standard deviation = sqrt(65.0378) = 8.06

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Triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:

AB || DC, as required.

What is the congruent angle?

When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.

Corresponding Parts of Congruent Triangles are Equal

AD || BC, AD = CB

Given

1 = 4

From statements 1 and 5, we can conclude that:

ACD is congruent to CAB because they are corresponding angles of parallel lines AD and BC.

If Lines are Parallel, then Alternate Interior Angles are Equal.

ACD = CAB

From statement 4, we know that angles ACD and CAB are equal because AD is parallel to BC. Therefore:

ACD = CAB

Reflexive Property of Equality

AC = AC

From statement 2, we know that segment AC is equal to itself because of the reflexive property of equality. Therefore:

AC = AC

If Alternate Interior Angles are Congruent, then Lines are Parallel.

2 = 3

From statement 3, we know that if alternate interior angles are congruent, then the lines are parallel. Therefore, since ACD = CAB (statement 4) and AC = AC (statement 2), we can apply the SAS (Side-Angle-Side) congruence theorem to triangles ACD and CAB to conclude that they are congruent.

SAS (Side-Angle-Side)

AB || DC

Hence, As a result, since triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:

AB || DC, as required.

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Answer:

60°

Step-by-step explanation:

We know that a straight line would be 180 °.

we can see that  the line is split into 3 equal sides .

180° ÷ 3 = 60°

Answer:

Step-by-step explanation:

if an equation needs only one step to isolate the variable, it is 1-step. For example, 4x=16, which means x=4. Generally I’m not sure of a way other than that to know if an equation is one step or multi-step.

-4(x+5)-2=6x

So, use distributive property.

-4x-20-2=6x

Add 4x to both sides.

-20-2=10x

Solve -20-2.

-22=10x

Divide 10 from both sides.

x=-10/22

Simplify

x=-5/11

Answer:

The circumference of a circle is calculated using the formula `C = 2πr`, where `r` is the radius of the circle. Since you have given the radius as 4 and asked to use 3.14 for π, we can calculate the circumference as `C = 2 x 3.14 x 4 = 25.12`.

The area of a circle is calculated using the formula `A = πr^2`, where `r` is the radius of the circle. Using the same values for π and r as before, we can calculate the area as `A = 3.14 x (4)^2 = 50.24`.

So, for a circle with a diameter of 8 and a radius of 4 (using 3.14 for π), its circumference is approximately **25.12** and its area is approximately **50.24**.

Answer:

a) discrete ; only from a particular building that stays the same

b) continuous ; the population of a country fluctuates and therefore shows trends

c) discrete ; information of a particular place

d) continuous ; there are trends of apple masses because there are different types of apples

Step-by-step explanation:

The angle marked x is 28°

The fοrmula fοr a simple straight line is Y = mX + b, where Y is the respοnse (dependent) variable, X is the predictοr (independent) variable, m is the estimated slοpe, and b is the estimated intercept.

We have,

A, B & C lie in a straight line.

D, B & E lie οn a different straight line.

∠CBE = 62°.

x =?

Because < ABD and <CBE are οppοsite vertex angle

<ABD = <CBE

And because ∠CBE = 62°

∠ABD = 62°.

1 x = 90°- 62°

= 28

Hence, the angle marked x is 28°

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Step-by-step explanation:

A dilation is a transformation that enlarges or reduces an object by a certain scale factor, and it is centered at a fixed point. In this case, we want to dilate the point (-3, 0) by a scale factor of 2, and the center of dilation is at the origin (0, 0).

To perform the dilation, we first need to find the distance between the point (-3, 0) and the center of dilation (0, 0), which is simply the magnitude of the vector (-3, 0), or 3.

Next, we need to multiply this distance by the scale factor of 2 to get the new distance after dilation, which is 6.

Finally, we need to find the point that is 6 units away from the origin along the same line that passes through the origin and the original point (-3, 0). This can be done by multiplying the direction vector of this line by the distance of 6 and adding the result to the center of dilation (0, 0). The direction vector is (-3, 0), normalized to have unit length, which is (-1, 0).

So the image of (-3, 0) after dilation by a scale factor of 2 centered at the origin is:

(-1 * 6, 0 * 6) + (0, 0) = (-6, 0)

Therefore, the image point is (-6, 0).

Answer:

.50 chance that she gets a chocolate chip cookie or 50 percent.

Step-by-step explanation:

half of all the cookies in the jar are chocolate chip cookies. 12/24 meaning that there is a 50/50 chance that she'll get a chocolate chip cookie

.50

Answer:

12

Step-by-step explanation:

Green beads

=60/100x20

=12

Answer:

45 minutes

Step-by-step explanation:

We Know

Kristiana went to a yoga class at 12:30.

She went to lunch with her friends for 1hr and 35 minutes

She finished lunch at 2:50

How long was her yoga class?

We take

12:30 + 1:35 = 2:05

Then we take

2:50 - 2:05 = 45 minutes

So, her yoga class was 45 minutes.

The function f with its inverse function [tex]f^{-1}[/tex] is equal to the identity function. The value of [tex]f^{-1}(4)f[/tex] is equal to 4.

To determine the value of [tex]f^{-1}[/tex](4)f−1(4)f, we would need to know the function f and its inverse function [tex]f^{-1}[/tex].

In this case, we are asked to find [tex]f^{-1}[/tex](4)f−1(4)f, start superscript minus 1, end superscript, left parenthesis 4, right parenthesis. This means we need to find [tex]f^{-1}(4)[/tex] and then plug that value into the original function f.

Now, [tex]f(f^{-1}(4))[/tex] can be simplified as follows:

[tex]f(f^{-1}(4)) = 4[/tex]

This is because [tex]f^{-1}(4)[/tex] is the input that produces an output of 4, and then f is applied to that input to produce the same output.

Multiplying [tex]f^{-1}(4)[/tex] by f is equivalent to evaluating the function f at the point [tex]f^{-1}(4)[/tex]. Thus, we have:

[tex]f(f^{-1}(4)) = 4[/tex]

This means that the composition of the function f with its inverse function [tex]f^{-1}[/tex] is equal to the identity function. Therefore, the value of [tex]f^{-1}(4)f[/tex] is equal to 4.

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Answer:

i think the right answer is 9/21

Step-by-step explanation:

hope it will help you!!

The greatest number of gift bags Ms. Bryant can make with 72 pencils and 54 pens is 18, with 4 pencils and 3 pens in each bag.

To find the greatest number of gift bags that Ms. Bryant can make, we need to find the greatest common factor (GCF) of the numbers of pencils and pens she has.

We can start by listing the factors of each number:

Factors of 72: [tex]1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72[/tex]

Factors of 54: [tex]1, 2, 3, 6, 9, 18, 27, 54[/tex]

To find the GCF, we look for the largest factor that is common to both lists. In this case, the largest common factor is 18.

This means that Ms. Bryant can make 18 gift bags, each containing 4 pencils and 3 pens, with no pencils or pens left over.

Therefore, the greatest number of gift bags Ms. Bryant can make with the given number of pencils and pens is 18.

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Answer:

Your friend's error is that having two equal discriminants doesn't necessarily mean that the two quadratic equations will have the same roots. The discriminant of a quadratic equation determines whether the roots are real, complex, or equal. If two quadratic equations have the same discriminant, then they have the same nature of roots, but that does not mean that their roots are equal.

As an example, consider the following two quadratic equations:

1. x^2 + 4x + 4 = 0

2. x^2 + 6x + 9 = 0

Both equations have the same discriminant: (b^2 - 4ac) = 16 - 16 = 0, but their roots are different. The first equation has one real root: x = -2, while the second equation has only one root, which is repeated twice: x = -3.

Therefore, it is incorrect to conclude that two quadratic equations have the same roots just because they have the same discriminants.

Triangular prism formulas

volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length.

area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.

The better buy for david is churro at the swap

To determine which is the better buy for David, we need to compare the cost per churro for each purchase.

For the farmers market purchase, David bought 3 churros for $2.1, so the cost per churro is:

Cost per churro at farmers market = 2.1/3 = 0.7

For the swap meet purchase, David bought 5 churros for $3.20, so the cost per churro is:

Cost per churro at swap meet = 3.2/5 = 0.64

Since the cost per churro at the swap meet is lower than the cost per churro at the farmers market, buying churros at the swap meet is the better buy for David.

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The vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).

The vertex of a parabola in the form of y = a[tex]x^{2}[/tex] + bx + c can be found using the formula x = -b/2a for the x-coordinate of the vertex and then substituting this value into the equation to find the y-coordinate.

For the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7, we can see that a = 3 and b = -12. We can use the formula to find the x-coordinate of the vertex:

x = -b/2a = -(-12)/(2*3) = 2

So the x-coordinate of the vertex is 2. To find the y-coordinate, we can substitute x = 2 into the equation:

g(2) = 3 [tex](2)^{2}[/tex]- 12(2) + 7 = -5

Therefore, the vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).

So the correct answer is (c) (2, −5).

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Answer:An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Step-by-step explanation:basically its more than 90 degrees

Answer:

An obtuse triangle is a triangle where one of the interior angles measures more than 90°

if you invest $2,500 at a weekly compounding rate of 4.5% for 4 years, you will have approximately $3,157.22 to use as a down payment on your Can-Am Spyder.

How to solve investment?

If you invest $2,500 at a 4.5% weekly compounding rate, it will grow to a considerable amount in 4 years. To calculate this, we need to use the compound interest formula:

A = P(1 + r/n)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have:

P = $2,500

r = 4.5% = 0.045

n = 52 (since compounding is weekly)

t = 4 years

Plugging in these values, we get:

A = $2,500(1 + 0.045/52) in power (52*4) = $3,157.22

So, if you invest $2,500 at a weekly compounding rate of 4.5% for 4 years, you will have approximately $3,157.22 to use as a down payment on your Can-Am Spyder.

It's important to note that this calculation assumes that the investment vehicle will have a steady and reliable return rate for the entire 4 years. There is always some level of risk involved with investing, so it's important to do your research and make informed decisions about where to put your money.

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Answer: Well look at it closely so it will help you understand more of it.

Step-by-step explanation: I read it over and over and over again and I think this will help.

Angle in a semi-circle is a right angle then, angle x is 90°, Z is 100° and y is 53° (refer below figure)

The six trigonometric functions of an angle in a right-angled triangle are connected by a set of fundamental identities known as the "Circle identities" in trigonometry.

In a semicircle AGE, angle at the circumference is 90 degree.

then, angle x = 90°

and arc Z° from the center of circle is a triangle AOB, see below figure,

40° + Z° + 40° = 180°

Then, Z° = 100°

Similarly, arc 74° from center of circle is a triangle EOG;

74°+ y° + y° = 180°

Then, y° = 53°

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Answer/Step-By-Step Explanation:

Part A:

To determine the measure of angle A (m/A), we can use the Law of Cosines, which states that:

c^2 = a^2 + b^2 - 2ab*cos(A)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

Substituting the given values, we have:

(32)^2 = (16)^2 + (16√5)^2 - 2(16)(16√5)*cos(A)

Simplifying:

1024 = 256 + 1280 - 512√5*cos(A)

512√5*cos(A) = 512

cos(A) = 1/√5

Using a calculator, we find:

A ≈ 63.43 degrees

Therefore, m/A ≈ 63.43 degrees.

Part B:

To use the unit circle to find tan A, we first draw a unit circle with its center at the origin of a coordinate plane. We then draw a ray from the origin through the point (1,0) on the circle, which corresponds to the angle of 0 degrees.

Next, we draw another ray from the origin through the point on the circle that corresponds to angle A. This ray intersects the circle at a point (x,y), where x = cos(A) and y = sin(A).

Since cos(A) = 1/√5, we have:

x = cos(A) = 1/√5

To find y, we use the Pythagorean theorem:

x^2 + y^2 = 1

Substituting x = 1/√5, we get:

(1/√5)^2 + y^2 = 1

y^2 = 4/5

y = ± 2/√5

Since angle A is in the first quadrant, we take y = 2/√5.

Therefore, tan(A) = y/x = (2/√5)/(1/√5) = 2.

Part C:

To calculate the area of triangle AABC, we can use Heron's formula, which states that:

Area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a+b+c)/2

Substituting the given values, we have:

s = (16+16√5+32)/2 = 24+8√5

Using this value of s, we can calculate the area:

Area = √[(24+8√5)(8√5-8)(8√5)(24-8√5)]

Simplifying:

Area = √[4096] = 64

Therefore, the area of triangle AABC is 64 square inches.

In this problem, we use the tangent function to solve for angle A, understand that the unit circle cannot be directly used to find the tangent of A, and finally find the area of the triangle using the formula 1/2*base*height.

Part A: Assuming triangle AABC is a right triangle, we can determine m∠A by using the tangent function (tan ∠A = opposite side / adjacent side). Here, the opposite side is 'b' and the adjacent side is 'a'. So, m∠A = tan⁻¹ (b/a) = tan⁻¹ (16 5/16). To get the correct result, we then use a calculator with the inverse tangent or arctan function.

Part B: The unit circle is a fundamental tool in trigonometry. But in this case, having calculated m∠A in Part A, we cannot directly use the unit circle to find tan A as tan A is not represented on the unit circle.

Part C: The area of a triangle can be calculated using the formula 1/2*base*height. In a right triangle, this can be represented as 1/2*a*b: 1/2*16*16 5 = 130 square inches.

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The object would weight 42 pounds on Earth.

In physics, weight is a measure of the force exerted on an object due to gravity. It is a vector quantity, which means that it has both magnitude (numerical value) and direction.

Let's denote the weight of the object on Earth as W and set up a proportion:

Weight on Earth / Weight on Moon = Gravitational force on Earth / Gravitational force on Moon

Using the given information, we can substitute the weights and simplify:

W / 7 = 180 / 30

W / 7 = 6

Multiplying both sides by 7, we get:

W = 7 ×6 = 42

Therefore, the object would weigh 42 pounds on Earth.

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The it is used to understand the likelihood of getting a particular outcome or event from a population.It is important to note that the probabilities for parametric probability distribution models are expressed as cumulative probabilities. Cumulative probabilities are used to evaluate the probability of a particular event or outcome.

Probabilities for parametric probability distribution models are expressed as cumulative probabilities.Parametric probability distribution refers to a type of probability distribution in which the probability distribution is defined by the probability distribution's parameters. The parameters are usually numeric values that define the distribution's probability density function (PDF) or probability mass function (PMF).The probability distribution is usually used to model a population's characteristics.

It is used to help understand the probability of obtaining a particular set of results from a population.Cumulative probabilities Cumulative probability refers to the probability of obtaining a score equal to or lower than a particular value in a given distribution. It is a probability value that is used in statistical analysis, which is usually represented by the area under the probability distribution's curve.The cumulative probability can be expressed as follows:P(X ≤ x)Where;X: random variablex: score or valueCumulative probabilities are used to evaluate the probability of a particular event or outcome.

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