A prism is filled with 30 cubes with 1/2 unit side lengths. What is the volume of the prism in cubic units?

Answer:

General equation of line : [tex]y = mx+c[/tex]   --1

Where m is the slope or unit rate

Table 1)

p    d

1      3

2     6

4     12

d = Number of dollars (i.e.y axis)

p = number of pound(i.e. x axis)

First find the slope

First calculate the slope of given points

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]   ---A

[tex](x_1,y_1)=(1,3)[/tex]

[tex](x_2,y_2)=(2,6)[/tex]

Substitute values in A

[tex]m = \frac{6-3}{2-1}[/tex]

[tex]m = 3[/tex]

Thus the unit rate is 3 dollars per pound.

So, It matches the box 1 (Refer the attached figure)

Equation 1 : [tex]p=3d[/tex]

[tex]\frac{p}{3}=d[/tex]

Since p is the x coordinate and d is the y coordinate

On Comparing with 1

[tex]m = \frac{1}{3}[/tex]

Thus the unit rate is [tex]\frac{1}{3}[/tex] dollars per pound

So, It matches the box 2 (Refer the attached figure)

Equation 2 : [tex]\frac{1}{3}d=3p[/tex]

[tex]d=9p[/tex]

Since p is the x coordinate and d is the y coordinate

On Comparing with 1

[tex]m =9[/tex]

Thus the unit rate is 9 dollars per pound

So, It matches the box 3 (Refer the attached figure)

Table 2)

p        d

1/9      1

1         9

2        18

d = Number of dollars (i.e.y axis)

p = number of pound(i.e. x axis)

[tex](x_1,y_1)=(\frac{1}{9},1)[/tex]

[tex](x_2,y_2)=(1,9)[/tex]

Substitute values in A

[tex]m = \frac{9-1}{1-\frac{1}{9}}[/tex]

[tex]m = \frac{8}{frac{8}{9}}[/tex]

[tex]m = 9[/tex]

Thus the unit rate is 9 dollars per pound

So, It matches the box 3 (Refer the attached figure)

Answer: See image attached

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

4x⁶-9 = (2x³)² - (3)²

The answer is:

The area of the base of the pyramid is:

[tex]BaseArea=108mm^{2}[/tex]

We are given the volume and the height of the hexagonal pyramid, so, to calculate the base of the area, we need to use the following formula:

[tex]Volume=\frac{1}{3}*BaseArea*Height[/tex]

So, we are given the following information:

[tex]Volume=144mm^{3}\\\\Height=4mm[/tex]

Then, substituting the given information and isolating the base area, we have:

[tex]Volume=\frac{1}{3}*BaseArea*Height[/tex]

[tex]144mm^{3} =\frac{1}{3}*BaseArea*4mm\\\\144mm^{3}*\frac{3}{4mm}=BaseArea\\\\BaseArea=108mm^{2}[/tex]

Hence, the area of the base of the hexagonal pyramid is equal to:

[tex]BaseArea=108mm^{2}[/tex]

Have a nice day!

Answer:

False

Step-by-step explanation:

False.  An inscribed angle is formed by two chords (inside a circle).

Note:  A central angle is an angle formed by two radii that share an endpoint.

The statement about an inscribed angle being formed by two radii is false. An inscribed angle has its vertex on the circle and is formed by two intersecting chords, whereas a central angle has its vertex at the center of the circle and is formed by two radii.

The statement that an inscribed angle is an angle formed by two radii that share an endpoint is false. An inscribed angle in a circle is actually formed by two chords that intersect on the circle. The vertex of the inscribed angle lies on the circle and its sides are made up of two chords of the circle. By contrast, an angle formed by two radii that share an endpoint is called a central angle. The central angle's vertex is the center of the circle, and it intercepts an arc.

Answer:

the answer is D:  the median of box plot B is greater than the median of box plot A.

Step-by-step explanation:

Answer: D. The median of box plot B is greater than the median of box plot A.

Step-by-step explanation:

We know that in a box-whisker plot, the vertical present in the box represents the median value of data and the length of box along the number line represents the interquartile range.

In the given picture, it can be seen that the box B is longer than box A.

It mean that the interquartile range of box plot B is greater than the interquartile range of box plot A.

Also, the vertical line in box A is present between 15 and 20 on number line but in box B it is present between 25 and 30.

It means that the median of box plot B is greater than the median of box plot A.

Answer:

the answer is: a great circle

In spherical geometry, lines are called geodesics, which are represented by great circles on the surface of a sphere. These circles are the spherical equivalents of straight lines in Euclidean geometry and highlight the unique properties of spherical geometry, such as the different rules for angles and parallel lines.

In spherical geometry, lines are referred to as geodesics. Unlike in Euclidean geometry where lines are the shortest distance between two points on a plane, in spherical geometry, geodesics are the shortest paths on the surface of a sphere and are represented by great circles. Great circles are the largest circles that can be drawn on a sphere, with their centers coinciding with the center of the sphere. This concept is crucial in areas such as cartography and navigation where the Earth's surface needs to be understood as a sphere rather than a flat plane.

For example, in creating a triangle on the Earth's surface with one corner at the north pole and the other two at the equator separated by 90 degrees of longitude, the sum of its interior angles exceeds 180 degrees. This defies a fundamental rule of Euclidean geometry, indicating the unique properties of spherical geometry where traditional parallel lines do not exist and the axioms of Euclidean geometry are not entirely applicable.

Answer:

99 cm^2

Step-by-step explanation:

Solution 1: Don't decompose and instead use the trapeziod area theorem. (b1+b2)/2 * h. Using this we plug in the two bases and get (23+10)/2 *6 -->

16.5*6=99cm2

Solution 2: You follow the rules and decompose the trapeziod. Split it into two triangles and a rectangle. The area of the triangle on the left is (b*h)/2 which is equal to (3*6)/2 which is 9 cm2. Spliting the trapeziod gives the rectangle dimensions of 10x6. 10*6= 60cm2. Finally we must find the area of the triangle on the right. The height is 6cm in the diagram and the base would be the full base of the trapeziod(20+3)-(10+3) --> 23-13=10. Using the area formula for the triangle gives us 10*6/2 = 30cm2. To find the full area we must add all the shapes up, 9+60+30 = 99cm2

Answer:

11.2 feet

Step-by-step explanation:

The width of the actual train car, to the nearest foot, is 11 feet.

To find the width of the actual train car, we need to use the scale factor provided.

Given:

- Width of the model train's car = 2.4 inches

- Scale = 1:56

To find the actual width, we'll use the scale factor:

[tex]\[ \text{Actual width} = \text{Model width} \times \text{Scale factor} \][/tex]

First, we need to convert the width of the model train's car from inches to feet because the scale factor is given as a ratio. There are 12 inches in a foot.

[tex]\[ \text{Model width} = \frac{2.4 \text{ inches}}{12 \text{ inches/foot}} = 0.2 \text{ feet} \][/tex]

Now, we can find the actual width:

[tex]\[ \text{Actual width} = 0.2 \text{ feet} \times 56 = 11.2 \text{ feet} \][/tex]

Answer:

[tex]x^2-y^2[/tex]

Step-by-step explanation:

Given the expression [tex](x+y)(x-y)[/tex]

We can distribute this using the FOIL technique

This would leave us with

[tex]x^2+xy-xy-y^2[/tex]

Then we can combine like terms to leave us with

[tex]x^2-y^2[/tex]

Steps:

(x+y)(x-y)

x^2-xy+xy-y^2

Multiplying the brackets together.

negative and positive= negative

= x^2-y^2

Answer is x^2-y^2

Answer:

will i dont know if this i right but there are 7 sets on the data table that has 2 1/4 on it so i hope this help i am not shore though the answer is 7

Step-by-step explanation:

The answer would be 7

Answer:

it has to be 8 because I subtracted and that was my answer for It

10.5 is the standard deviation for the data set to the nearest tenth hope this helps;)

Answer: the answer is 10.5

Answer:

7

Step-by-step explanation:

The wording of this question is ambiguous, but 7 * 7 = 49, at least that's my reasoning.

Answer:

Step-by-step explanation: 7 and -7 i learned about it the other day but i’m almost positive it’s -7

Answer:

(2x - 7y)(2x + 7y)

Step-by-step explanation:

4x^2-49y^2 is the difference of two squares:  (2x)² - (7y)².

This is a case of "special products and factoring."

Since a² - b² = (a - b)(a + b),

(2x)² - (7y)² = (2x - 7y)(2x + 7y)

Solution:

The given Equation is 4x² - 49y²

Spilt it in the form of a² - b² :

☞4x² - 49y²

☞ (2x)² - (7y)²

☞ ( 2x + 7)(2x -7 )

Answer:

More information: { Identity Used }

☞ a² - b² = (a + b)(a-b)

☞ (a + b)² = a² + b² + 2ab

Answer:

The positive zero is 11

Step-by-step explanation:

Given in the question an equation,

f(x) =x² - 121

We are asked to find the positive zero of f(x)

means x > 0 for which f(x) = 0

so,

 x² = 121

Take square root on both sides of the equation

√x² = √121

  x =  ±11

which means that x = 11 and x = -11

Since x > 0 so we will reject x =-11 and we will accept x = 11

Answer: 11

Step-by-step explanation:

You need to substitute [tex]f(x)=0[/tex] into the function given:

[tex]f(x) =x^2-121\\0 =x^2-121[/tex]

Now you need to solve for the variable "x", to do this, first you must add 121 to both sides of the function:

[tex](121)+0=x^2-121+(121)\\121=x^2[/tex]

Now apply square root to both sides of the function. Then, you get:

[tex]\±\sqrt{121}=\±\sqrt{x^2}\\\\\±\sqrt{121}=x\\\\x_1=11\\x_1=-11[/tex]

The value of the positive zero of the function is 11.

Answer:

0.75 hr

Step-by-step explanation:

Recall that distance = rate times time.

Thus, time = distance / rate.

Here, time = 63.75 miles / 85 mph  =  0.75 hr

Next time, please share the possible answer choices.  Thank you.

(Table) Answer:

rice and chicken=20

rice and beef=10

total rice= 30

pasta and chicken=40

pasta and beef=30

total pasta=70

total chicken=60

total beef=40

total total=100

Answer:

If 10 minutes block, then it can be rented for 20 minutes. If no blocks, then 27.27 minutes

Step-by-step explanation:

Initial setup cost is $6.

Every 10 minutes, $5.5 is charges, so each minute  [tex]\frac{5.5}{10}=0.55[/tex] is charged.

Let time used be t, so we can set up an equation as:

21 = 6 + 0.55t

Where t is in minutes

we solve for t to find out how many minutes we can rent for $21:

[tex]21 = 6 + 0.55t\\21-6=0.55t\\15=0.55t\\t=\frac{15}{0.55}=27.27[/tex]

since it is charged PER 10 MINUTES, so we can rent it for 10, 20 , 30 minutes etc.

WE CANNOT RENT FOR 30 minutes as we dont have enough money (only for fractional amount of a little over 27 minutes). Thus, we will have to have some money left over and rent for 20 minutes.

For $21, you can rent approximately 20 minutes of time at the local copy center when there's a $6 setup charge and each 10-minute period costs an additional $5.50.

The question is asking how much time can be rented for $21 at a local copy center, where there's a $6 setup charge and an additional $5.50 for every 10 minutes. To figure this out, we first need to subtract the setup charge from the total amount of money that can be spent. So, $21 - $6 = $15. Next, we need to see how many 10 minute increments can be rented with $15. Since each 10 minute increment costs $5.50, we divide $15 by $5.50 to get approximately 2.72. Since we can't rent time in fractions of a minute, we round this down to 2. Therefore, we can rent about 20 minutes of time for $21.

https://brainly.com/question/34407434

#SPJ11

Answer:

1296.85 ft

Step-by-step explanation:

Answer:

The maximum distance riders travel in one full ride is:

                        1296.192 feet

Step-by-step explanation:

It is given that the diameter(d) of carousel is: 32 feet.

This means that the distance travelled in one revolution is equal to the circumference(C) of the circle.

We know that the circumference of circle is given by:

[tex]C=\pi\times d\\\\\\C=3.14\times 32\\\\\\C=100.48\ feet[/tex]

Also, Time of one full ride is:  3 minutes.

Speed of one full ride is: 4.3 revolutions per minute.

This means that the number of revolutions made is calculated as:

Number of revolution=Speed×Time

Number of revolution=4.3×3=12.9 revolutions.

Hence, total distance traveled in one full ride is:

Number of revolution made×Distance covered in one revolution

=  12.9×100.48

= 1296.192 feet

Answer:

Dot Plot

Step-by-step explanation:

Just start marking off the numbers from left to right until you get to the middle.

The equation of the circle is (x - 1)^2 + (y - 2)^2 = 17.

The equation of a circle can be written in the form:

(x - h)2 + (y - k)2 = r2

Where (h, k) is the center of the circle and r is the radius.

In this case, the center of the circle is (1, 2) and it passes through the point (0, 6).

So, the distance between the center and the point is equal to the radius of the circle.

Using the distance formula, we can find the radius:

r = sqrt((0 - 1)2 + (6 - 2)2) = sqrt(1 + 16) = sqrt(17)

Therefore, the equation of the circle is:

(x - 1)2 + (y - 2)2 = 17

Answer:

n = 1 if you meant "(4/5)n - (3/5) = (1/5)n"

Step-by-step explanation:                                                                              

There's some ambiguity here.  Did you mean (4/5)n or did you

              4

mean --------- ?  Please use parentheses to eliminate this ambiguity.

              5n    

I'm going to assume that you meant to type in (4/5)n - (3/5) = (1/5)n.

Then we have (3/5)n = 3/5, or n = 1

The simplified form of the equation (4/5)n - (3/5) = (1/5)n is n=1. This is obtained by solving for n since it is an algebraic equation.

Given that,

(4/5)n - (3/5) = (1/5)n

Taking terms with n to one side and constant to other side of the equation,

(4/5)n - (1/5)n = (3/5)

(4-1/5)n = (3/5)

(3/5)n = (3/5)

⇒n = 1

Hence the simplified form of the equation (4/5)n - (3/5) = (1/5)n is n=1.

Learn more about solving algebraic equations here:

brainly.com/question/2170884

Answer:

P = 6.4 m

Step-by-step explanation:

Hello,

The perimeter is the sum o each side of that square, so:

Psquare = 4*(lenght of side)

P = 4*(1.6m)

P = 6.4 m

PD: PI IS NOT NECESSARY, WORKS ONLY FOR CIRCLE

Best regards

Answer:

2 hours

Step-by-step explanation:

Given in the question that,

speed of Aja = 3 miles/h

speed of Pete  = 4 miles/h

we know that Aja is 2 miles away from Pete  

Both will have covered same distance at the time they will catch up.

suppose time = x

               distance covered = y

Formula to use

distance = speed x time

Equation 1

3x  = y - 2

3x + 2 = y

Equation 2

4x = y

Equate both equation

3x + 2 = 4x

2 = 4x -3x

2 = x

Answer:

Pete will catch up Aja after 2 hours

Step-by-step explanation:

We can represent thsi problem as as system of equations.

Let

x =  be the time in which both Aja and Pete starte biking, (in hours)

y = the number of miles traveled by each

Aja begins 2 miles ahead of Pete and bikes at an average speed of 3 miles per hour. This means

y_Aja =  3*x + 2

Pete bikes at an average speed of 4 miles per hour.

y_Pete =  4*x

Then, we can find the intersection point between the graphs, so we find the solution.

Please see attached picture below

Pete will catch up Aja after 2 hours

Answer:

Sin E=0.50

Step-by-step explanation:

Here we are given that DE || AB, and DB and AE are traverse lines to them meeting at point F.

By the properties of parallel lines intersected by a transverse we know that the alternate interior angles are equal.

If we extend DE and AE on both sides , we can see that A and E are equal as they forms alternate interior angles.

Hence

A=E

Sin A = Sin E

0.50=Sin E

Answer:

I got sin E = 0.5

Thus answer choice C being the correct choice

Hope this helps ;)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Given

11x = 11 - 55xz²

Collect the terms in x together by adding 55xz² to both sides

11x + 55xz² = 11 ← factor out x on the left side

x(11 + 55z²) == 11 ← divide both sides by 11 + 55z²

x = [tex]\frac{11}{11+55z^2}[/tex] ← factor out 11 on the denominator

x = [tex]\frac{11}{11(1+5z^2)}[/tex] ← cancel 11 on numerator/denominator

x = [tex]\frac{1}{1+5z^2}[/tex] → D

Answer:

If x=0, then f(0) = -15

If f(x) = 27, then x = 3

Step-by-step explanation:

Find where the x column on the table has a 0 and find the corresponding f(x) value which is -15.

Do then same for the other question but find where f(x) on the table is equal to 27 and find the corresponding x value which is 3

If x=0, then f(0) =  -15

If f(x) = 27, then x =  3

We are given a table of values as follows:

             x              f(x)

             -3              33

             -2              17  

              0              -15

              2               -7

              3               27

This means that x is the independent variable and f(x) is the dependent variable corresponding to the variable x.

Hence, from the table of values we have:

If x=0, then f(0) =  -15

If f(x) = 27, then x =  3

Answer:

The measure of SWX is 108.

Step-by-step explanation:

TX and QS are not perpendicular.

QRT and TRU are complementary (add to 90) not supplementary (add to 180)

The measure of SWX is 108 because angles on a line add to 180, and RWS is 72. 180 - 72 = 108

Answer:

The measure of <SWX is 108°

The second answer is actually Complementary.

He rest of the answers are pretty obvious no’s.

Answer:

y-1/3x=17/3

Step-by-step explanation:

ax+by=c is standard form

first I'll start with slope interecept form and then we can change it to standard

y=mx+b

y=1/3x+b

4=1/3(-5)+b

4=-5/3+b

12/3+5/3=b

17/3=b

y=1/3x+17/3

to change to standard

y-1/3x=17/3

Answer:

a. congruent

b. complementary

c. supplementary

d. congruent

Hope this helps.