Additional Activities
Directions: Use a non-standard unit of the same material and
size. Which unit will give the greater number for the volume of the
container using ping-pong balls and monggo seeds? Visualize the
volume of each box, explain your answer. Write your answers on a
sheet of paper
.
2.
1.
Ping-Pong balls
Monggo seeds​

Answer:

-4374

Step-by-step explanation:

Given :

a1 = 2 ; r = - 3

The nth term of a geometric series :

A(n) = ar^(n-1)

The 8th term :

A(8) = 2(-3)^(8-1)

A(8) = 2(-3^7)

A(8) = 2(−2187)

A(8) = - 4374

Answer:

7.4 cm

Step-by-step explanation:

Volume of sphere

v = (4/3)πr³

Volume of hemisphere will be half that

v = (2/3)πr³

(2/3)πr³ = 839

multiply both sides by 3/2

πr³ = 1,258.5

Divide both sides by π

r³ = 400.5929917623

Take the cube root of both sides

r = 7.3717022001

Rounded

r = 7.4 cm

Answer:

The equation of the parabola is y = x²/4

Step-by-step explanation:

The given focus of the parabola = (0, 1)

The directrix of the parabola is y = -1

A form of the equation of a parabola is presented as follows;

(x - h)² = 4·p·(y - k)

We note that the equation of the directrix is y = k - p

The focus = (h, k + p)

Therefore, by comparison, we have;

k + p = 1...(1)

k - p = -1...(2)

h = 0...(3)

Adding equation (1) to equation (2) gives;

On the left hand side of the addition, we have;

k + p + (k - p) = k + k + p - p = 2·k

On the right hand side of the addition, we have;

1 + -1 = 0

Equating both sides, gives;

2·k = 0

∴ k = 0/2 = 0

From equation (1)

k + p = 0 + 1 = 1

∴ p = 1

Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;

(x - 0)² = 4 × 1 × (y - 0)

∴ x² = 4·y

The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;

y = x²/4.

Answer:

[tex]Total = 4.8 * 10^{10}[/tex]

Step-by-step explanation:

Given

[tex]h = 1.2 * 10^8[/tex] --- households

[tex]g = 400[/tex] --- gallons

Required

The number of households

To do this, we simply multiply the average households by the gallons.

[tex]Total = g* h[/tex]

[tex]Total = 400 * 1.2 * 10^8[/tex]

[tex]Total = 480 * 10^8[/tex]

Rewrite as:

[tex]Total = 4.8 * 10^2 * 10^8[/tex]

[tex]Total = 4.8 * 10^{10}[/tex]

Answer:

0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Rate of 18 customers per hour.

This is [tex]\mu = 18n[/tex], in which n is the number of hours.

10 minute interval:

An hour has 60 minutes, so this means that [tex]n = \frac{10}{60} = \frac{1}{6}[/tex], and thus [tex]\mu = 18\frac{1}{6} = 3[/tex]

What is the probability that more than 4 customers arrive in a 10 minute interval?

This is:

[tex]P(X > 4) = 1 - P(X \leq 4)[/tex]

In which:

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex] = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 = 0.8152[/tex]

And

[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - 0.8152 = 0.1848[/tex]

0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.

Answer:

It is rational number.

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Answer:

A. The slope of Function A is greater than the slope of Function B.

Step-by-step explanation:

The slope of a function can be defined as rise/run. In Function A, the rise/run is 4. The slope in Function B is much easier to see: it is 2. Because 4 is greater than 2, Function A has a greater slope than Function B.

Answer:

1.  1/3

2. 0

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

Because you want to know the total percent the price increased so you add the amounts. 30% plus 10% makes 40%

Answer:

A.) m = 1.5 | B.) p = -1 | C.) t = 2

Step-by-step explanation:

A.)

[tex]4(m+3)=18\\4m+12=18\\4m=6\\m=3/2=1.5[/tex]

B.)

[tex]-2(p+5)+8=0\\-2p-10+8=0\\-2p-2=0\\-2p=2\\p=-1[/tex]

C.)

[tex]3+5(t-1)=8\\3+5t-5=8\\5t-2=8\\5t=10\\t=2[/tex]

Answer:

(a)=

4(m+3)=18

4m+12=18

4m=18-12

4m=6

m=

[tex] \frac{6}{4} [/tex]

(b)=

-2(p+5)+8=0

-2p-10+8=0

-2p=0+10-8

-2p=2

p=

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

(c)=

3+5(t-1)=8

3+5t-5=8

5t=8-3+5

5t=10

t=

[tex] \frac{10}{5} = 2[/tex]

[tex]please \: mark \: as \: brainliest \: because \: i \: spent \: much \: time \: on \: this \: question[/tex]

Answer:

f(-3) = -1/3

Step-by-step explanation:

-3 is less than -2 so we use the first function  1/x

f(-3) = 1/-3

Answer:

-1/3

Step-by-step explanation:

-3 is less than -2, so use the first one, 1/x and substitute -3 in

1/(-3)=-1/3

Answer:

Step-by-step explanation:

New Total equals Previous Total plus the Check value

New Total minus Previous Total   equals   the Check value

Her new total is  -  Tasta's bank account was = Check value

Answer:

Perimeter: 18.28

Area: 22.28

Step-by-step explanation:

1. Approach

An easy method that can be used to solve the given problem is the partition the given figure into two smaller figures. One can divide this figure into a square and a semi-circle. After doing so, one can find the area of the semi-circle and the area of the square. Finally, one can add the two area together to find the final total area. To find the perimeter of the figure, one can add the lengths of three of the sides of the square and then one can add half of the circumference of the circle to the result. The final value will be the perimeter of the entire figure.

2. Find the circumference of the semi-circle

The circumference of a circle is the two-dimensional distance around the outer edge of a circle, in essence the length of the arc around a circle. The formula to find the circumference of a circle is as follows,

C = 2(pi)r

Since a semi-circle is half of a circle, the formula to find its circumference is the following,

C = (pi)

Where (pi) is the numerical value (3.1415) and (r) is the radius of the circle. By its definition, the radius of a circle is the distance from a point on the circle to the center of the circle. This value will always be half of the diameter, that is the distance from one end of the circle to the other, passing through the center of the circle. The radius of a circle is always half of the diameter, thus the radius of this semi-circle is (2). Substitute this into the formula and solve for the circumference;

C = (pi)r

C = (pi)2

C ~ 6.28

3. Find the area of the semi-circle

The formula to find the area of a circle is as follows,

A = (\pi)(r^2)

As explained earlier, a semi-circle is half of a circle, therefore, divide this formula by (2) to find the formula for the area of a semi-circle

A = ((pi)r^2)/(2)

The radius of this circle is (2), substitute this into the formula and solve for the area of a semi-circle;

A = ((pi)r^2)/(2)

A = ((pi)(2^2))/(2)

A = (pi)2

A = 6.28

4. Find the area and perimeter of the square,

The perimeter of a figure is the two-dimensional distance around the figure. Since the semi-circle is attached to one of the sides of a square, one only needs to add three sides of the square to find the perimeter of the square;

P = 4+4+4

P = 12

The area of a square can be found by multiplying the length by the width of the square.

A = l*w

Substitute,

A = 4*4

A=16

5. Find the area and the perimeter of the figure,

To find the perimeter of the figure, add the value of the circumference to the vlalue of the perimeter of the square;

A = C+P

A = 6.28+12

A = 18.28

To find the area of the figure, add the value of the area of the circle to the area of the square;

A = 6.28+16

A = 22.28

Answer:  roughly 151.81788 square meters of metal

=====================================================

Explanation:

The base is a square with side lengths x, so its area is x*x = x^2

Let h be the height of the tank. We have four identical wall panels that have area of xh square meters. The four walls lead to a lateral surface area of 4xh. Overall, the entire tank requires x^2+4xh square meters of metal. We're ignoring the top since the tank is open.

-----------

Let's set up a volume equation and then isolate h.

volume = length*width*height

108 = x*x*h

108 = x^2*h

x^2*h = 108

h = 108/(x^2)

-----------

Plug that into the expression we found at the end of the first section.

x^2+4xh

x^2+4x(180/(x^2))

x^2+(720/x)

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

Depending on what class you're in, the next step here will vary. If you are in calculus, then use the derivative to determine that the local min happens at approximately (7.11379, 151.81788)

If you're not in calculus, then use your graphing calculator's "min" feature to locate the lowest point on the f(x) = x^2+(720/x) curve.

This lowest point tells us what x must be to make x^2+(720/x) to be as small as possible, where x > 0.

In this context, it means that if the square base has sides approximately 7.11379 meters, then you'll need roughly 151.81788 square meters of metal to form the open tank. This is the least amount of metal required to build such a tank, and that will have a volume of 108 cubic meters.

Answer:

Fail to reject the null hypothesis

[tex]CI = (-4.278, 0.478)[/tex]

Step-by-step explanation:

Given

[tex]n_1=n_2 = 18[/tex]

[tex]\bar x_1 = 12.7[/tex]    [tex]\bar x_2 = 14.6[/tex]

[tex]\sigma_1 = 3.2[/tex]    [tex]\sigma_2 = 3.8[/tex]

[tex]\alpha = 0.05[/tex]

Solving (a): Test the hypothesis

We have:

[tex]H_o : \mu_1 - \mu_2 = 0[/tex]

[tex]H_a : u1 - u2 \ne 0[/tex]

Calculate the pooled standard deviation

[tex]s_p = \sqrt\frac{(n_1-1)\sigma_1^2 + (n_2-1)\sigma_2^2}{n_1+n_2-2}}[/tex]

[tex]s_p = \sqrt\frac{(18-1)*3.2^2 + (18-1)*3.8^2}{18+18-2}}[/tex]

[tex]s_p = \sqrt\frac{419.56}{34}}[/tex]

[tex]s_p = \sqrt{12.34}[/tex]

[tex]s_p = 3.51[/tex]

Calculate test statistic

[tex]t = \frac{x_1 - x_2}{s_p*\sqrt{1/n_1 + 1/n_2}}[/tex]

[tex]t = \frac{12.7 - 14.6}{3.51 *\sqrt{1/18 + 1/18}}[/tex]

[tex]t = \frac{-1.9}{3.51 *\sqrt{1/9}}[/tex]

[tex]t = \frac{-1.9}{3.51 *1/3}[/tex]

[tex]t = \frac{-1.9}{1.17}[/tex]

[tex]t = -1.62[/tex]

From the t table, the p value is:

[tex]p = 0.114472[/tex]

[tex]p > \alpha[/tex]

i.e.

[tex]0.114472 > 0.05[/tex]

So, the conclusion is that: we fail to reject the null hypothesis.

Solving (b): Construct 95% degree freedom

[tex]\alpha = 0.05[/tex]

Calculate the degree of freedom

[tex]df = n_1 + n_2 - 2[/tex]

[tex]df = 18+18 - 2[/tex]

[tex]df = 34[/tex]

From the student t table, the t value is:

[tex]t = 2.032244[/tex]

The confidence interval is calculated as:

[tex]CI = (x_1 - x_2) \± s_p * t * \sqrt{1/n_1 + 1/n_2}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/18 + 1/18}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/9}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * 1/3[/tex]

[tex]CI = -1.90 \± 2.378[/tex]

Split

[tex]CI = (-1.90 - 2.378, -1.90 + 2.378)[/tex]

[tex]CI = (-4.278, 0.478)[/tex]

Answer:

616

Step-by-step explanation:

A fraction that is equivalent to 38 is 616

Answer:

16 slices

Step-by-step explanation:

Given :

Number of pizzas ordered = 4

Number of slices per pizza = 4

If 4 pizzas are each sliced into 4 parts ; the we have :

Pizza 1 = 4 slices

Pizza 2 = 4 slices

Pizza 3 = 4 slices

Pizza 4 = 4 slices

Total slices = (4 +4 +4 +4) = 16 slices

The sum of the measures of angle LMN and angle NMP is 180 degrees. The measure of ∠LMN is 153°.

In Euclidean geometry, an angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively.

L, m n is a straight angle, and we want to find the measure of angle, l, m, p, and m p, and since we are told that l m n is a straight angle.

∠LMN + ∠NMP = 180°

The straight line is 180°

180 - 18 = 162

162 = 18g

g = 9

Hence, ∠LMN = (15 x 9 + 18)° = 153°

Therefore, the measure of ∠LMN is 153°.

To learn more about angles, refer to the link:

https://brainly.com/question/14684647

#SPJ1

Answer:

Step-by-step explanation:

Total number of outcomes:

Number of combinations of getting 6 heads:

Required probability is:

Correct choice is D

Answer:

option D

Step-by-step explanation:

Total sample space

                               =  [tex]2^{15}[/tex]

Number of ways 6 heads can emerge in 15 flips

                                                                          = [tex]15C_6[/tex]  

Probability:

               [tex]=\frac{15C_6}{2^{15}}[/tex] [tex]= 0.1527[/tex]

Probability to the nearest percent : 15.3%

Answer:

Step-by-step explanation:

Given the data :

Using 6 classes :

Class interval ____ Frequency

21 - 30 _________ 6

31 - 40 _________ 10

41 - 50 _________ 5

51 - 60 _________ 0

61 - 70 _________ 1

71 - 80 _________ 2

Answer:

i think it is 46

Step-by-step explanation:

Answer:

2.9lbs

Step-by-step explanation:

there are 14oz in a pound so 14/16 is 0.875. Rounded up to .9lbs.

Answer:

6144π ft³ ; 19292.2 ft³

Step-by-step explanation:

The volume of the cylinder Given above :

Volume of cylinder, V = πr²h

r =Radius = 16 ; h = 24 ft

V = π * 16² * 24

V = 256 * 24 * π

V = 6144π

Using π = 3.14

V = 6144 * 3.14 = 19292.16

Answer:

15π in

Step-by-step explanation:

In order to solve this, we need to know that the circumference of a circle can be found by using the following formula...

Circumference = dπ   (where d is the diameter of the circle)

Therefore the circumference equals...

Circumference = dπ = 15π in

[tex]\boxed{Given:}[/tex]

Diameter of the circle "[tex]d[/tex]" = 15 in.

[tex]\boxed{To\:find:}[/tex]

The circumference of the circle (in terms of π).

[tex]\boxed{Solution:}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:15\:π\:in.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]

[tex] = \pi \times 15 \: in \\ \\ = 15 \: \pi \: in[/tex]

Therefore, the circumference of the circle is 15 π in.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

Answer:

4/8

Step-by-step explanation:

d = 2n

n+3 = 7

d-3 = 5

substitute '2n' for 'd' in d-3=5

2n-3 = 5

2n = 8

n = 4

d = 2(4)

4/8

Answer:

z = 1.77.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X, which is also the area of the normal curve to the left of Z. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Find z such that 3.8% of the standard normal curve lies to the left of z

Thus, z with a z-score of 0.038. Looking at the z-table, this is z = 1.77.

Answer:

1. Term.

2. Common difference.

3. Arithmetic sequence.

4. Sequence.

Step-by-step explanation:

1. Term: an individual quantity or number in a sequence. For example, 1, 2, 3, 5, 6. The first term is 1 while 5 is the fourth term.

2. Common difference: the fixed amount added on to get to the next term in an arithmetic sequence. For example, 2, 4, 6, 8 have a common difference of 2 i.e (6 - 4 = 2).

3. Arithmetic sequence: a sequence in which a fixed amount such as two (2) is added on to get the next term. For example, 0, 2, 4, 6, 8, 10, 12.... is an arithmetic sequence.

4. Sequence: a set of numbers that follow a pattern, with a specific first number. For example, 1, 2, 3, 4, 5, 6 is a sequence.

Answer:

f(x)= -25x+4

y-inter x=0

y= -25(0)+4

=4

x-inter y=0

0= -25x+4

-4= -25x

x=4/25

9514 1404 393

Answer:

  Part A: 2 ft²

  Part B: draw a diagonal (AC, for example); 1 ft²

Step-by-step explanation:

Part A:

The area of a parallelogram is given by the formula ...

  A = bh

where 'b' is the length of the base, and 'h' is the perpendicular distance between the bases.

Using the numbers shown on the diagram, the area is ...

  A = (3 ft)(2/3 ft) = 3·2/3 ft²

  A = 2 ft² . . . . . area of the parallelogram

__

Part B:

Typically, a polygon is partitioned into triangles by drawing diagonals from one of the vertices. It does not matter which one. (In a quadrilateral, only one diagonal can be drawn from any given vertex.) Here, the "base" of each triangle is the same as the base of the parallelogram: 3 feet. The "height" of each triangle is the same as the height of the parallelogram: 2/3 ft.

The area of a triangle is given by the formula ...

  A = 1/2bh

  A = 1/2(3 ft)(2/3 ft) = (1/2)(3)(2/3) ft²

  A = 1 ft² . . . . . . . . area of each triangle

_____

Additional comment

It should be no surprise that the area of each of the two congruent triangles is 1/2 the area of the parallelogram.