1. the surface area of the rectangular prism
5 cm
20 cm
4cm

Answer:

[tex]\text{C. }60[/tex]

Step-by-step explanation:

Question from image:

"The digits 1, 2, 3, 4, and 5 can be formed to arrange 120 different numbers. How many of these numbers will have the digits 1 and 2 in increasing order? For example, 14352 and 51234 are two such numbers."

Let's start by taking a look with the number 1. There are four possible places 1 could be, because there needs to be space for the 2 after it.

Checkmarks mark where the 1 can be, the x marks where it cannot be.

[tex]\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{X}[/tex]

Let's start with the first position:

[tex]\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}\:\underline{\#}[/tex]

There are four places the 2 can be. For each of these four places, we can arrange the remaining 3 digits in [tex]3!=6[/tex] ways. Therefore, there are [tex]4\cdot 6=\boxed{24}[/tex] possible numbers when 1 is the first digit of the number.

Continue this process with the remaining possible positions for 1.

Second position:

[tex]\underline{X}\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}[/tex]

There are three places the 2 can be, since the 2 must be behind the 1. For each of these three places, the remaining 3 digits can be arranged in [tex]3!=6[/tex] ways. Therefore, there are [tex]3\cdot 6=\boxed{18}[/tex] possible numbers when 1 is the second digit of the number.

The pattern continues. Next there will be 2 places to place the 2. For each of these, there are [tex]3!=6[/tex] ways to rearrange the remaining 3 digits for a total of [tex]2\cdot 6=\boxed{12}[/tex] possible numbers when 1 is the third digit of the number.

Lastly, when 1 is the fourth digit of the number, there is only 1 place the 2 can be. For this one place, there are still [tex]3!=6[/tex] ways to rearrange the remaining three numbers. Therefore, there are [tex]1\cdot 6=\boxed{6}[/tex] possible numbers when 1 is the fourth digit of the number.

Thus, there are [tex]24+18+12+6=\boxed{60}[/tex] numbers that will have the digits 1 and 2 in increasing order, from a set of 120 five-digit numbers created by the digits 1 through 5, where no digit may be repeated.

Never, B is the middle colinear point so it cant measure longer than AC which is the full line segment.

Step-by-step explanation:

B) opposite sides are congruent !!!!!!

Answer:

The population of town A = 18,000

The population of town B = 15,000

The population of town C = 20,000

Step-by-step explanation:

Given;

A:B = 6:5

B:C = 3:4

total population = 53,000

A + B + C = 53,000

[tex]\frac{A}{B} = \frac{6}{5} \\\\A = \frac{6B}{5} \\\\\Also;\\\\\frac{B}{C} = \frac{3}{4} \\\\C = \frac{4B}{3} \\\\then;\\\\\frac{6B}{5} +B+ \frac{4B}{3} = 53,000\\\\multiply \ through \ by \ "15"\\\\18B + 15B + 20B = 795,000\\\\53B = 795,000\\\\B = \frac{795,000}{53} \\\\B = 15,000[/tex]

Now solve for A and C;

[tex]A = \frac{6 \times 15,000}{5} = 18,000\\\\C = \frac{4 \times 15,000}{3} = 20,000[/tex]

Answer:

a. P(x = 5) = 0.24

b. P(x ≥ 6) = 0.43

c. P(x < 4)= 0.14

Step-by-step explanation:

According to the Question,

⇒We use Binomial Probability Formula

[tex]P(X = x ) = \frac{n!}{x!((n-x)! } * p^{x} * (1-p)^{n-x}[/tex]

Where, p=0.52 & n=10

a. The probability that the number of U.S. adults who have very little confidence in newspapers is ​exactly​ five . So, (x=5)

Thus, [tex]P(X = 5 ) = \frac{10!}{5!((10-5)! } * 0.52^{5} * (1-0.52)^{10-5}[/tex]

On Solving Above Equation we get,

P(5)=0.2441 ≈ 0.24

b. The probability that the number of U.S. adults who have very little confidence in newspapers is at least 6 . So, (x≥6)

Then,

P(x≥6) = P(6)+P(7)+P(8)+P(9)+P(10)

P(x≥6) = [tex]\frac{10!}{6!((10-6)! } * 0.52^{6} * (1-0.52)^{10-6}[/tex] + [tex]\frac{10!}{7!((10-7)! } * 0.52^{7} * (1-0.52)^{10-7}[/tex] +[tex]\frac{10!}{8!((10-8)! } * 0.52^{8} * (1-0.52)^{10-8}[/tex] + [tex]\frac{10!}{9!((10-9)! } * 0.52^{9} * (1-0.52)^{10-9}[/tex]+[tex]\frac{10!}{10!((10-10)! } * 0.52^{10} * (1-0.52)^{10-10}[/tex]

On solving above equation we get,

P(x≥6) =  0.4270 ≈ 0.43

c. The probability that the number of U.S. adults who have very little confidence in newspapers is less than 4 . So, (x<4)

Then,

P(x < 4)=P(3) + P(2)+P(1)+P(0)

P(x<4) = [tex]\frac{10!}{3!((10-3)! } * 0.52^{3} * (1-0.52)^{10-3}[/tex] + [tex]\frac{10!}{2!((10-2)! } * 0.52^{2} * (1-0.52)^{10-2}[/tex]+ [tex]\frac{10!}{1!((10-1)! } * 0.52^{1} * (1-0.52)^{10-1}[/tex] + [tex]\frac{10!}{0!((10-0)! } * 0.52^{0} * (1-0.52)^{10-0}[/tex]

On solving we get,

P(x < 4)= 0.1410 ≈ 0.14  

Answer:

D

8x^2-12x+5

thanx for youer sug

Answer:

[tex]8x^2-12x+5[/tex]

Step-by-step explanation:

This is the same as saying h(g(x)). All you do is take the g(x) equation and plug that in for x in the h(x) equation.

h(x) = 4x+1                                           Plug in g(x) equation for x

h(g(x)) = [tex]4(2x^2-3x+1)+1[/tex]                Distribute the 4 and simplify

h(g(x)) = [tex]8x^2-12x+5[/tex]  

Answer:

take a break from social media , find a peaceful spot to study ,be engaged , take notes and listen during discussion make use of ur extra time wisely

hope it's helpful

Answer:

Step-by-step explanation:

let the speed of Landon=x

speed of Eduardo=x+9

5x+5(x+9)=135

divide by 5

x+x+9=135/5=27

2x+9=27

2x=27-9

2x=18

x=18/2=9

speed of Landon=9 mph

speed of Eduardo=9+9=18 mph

Answer:

I think it is of the last option

Answer:

15×5 =75

Step-by-step explanation:

1 inch reprsnt 5

Answer:

175°

Step-by-step explanation:

If angle x = 058° and angle y = 127° then the bearing A from point O is 360 minus angle x plus angle y.

Solution:

360° - (058° + 127°) = 175°

This is because the complete turn from north to north is 360°.

Answer:

x = 25

Step-by-step explanation:

The angles in a triangle add up to 180°, so we can write an equation to model the situation:

55 + 75 + 2x = 180

Now, we can simplify and solve:

130 + 2x = 180

2x = 50

x = 25

Answer:

x = 25

Step-by-step explanation:

The angles in a triangle add up to 180 degrees.

Using this, create an equation:

55 + 75 + 2x = 180

Solve for x:

55 + 75 + 2x = 180

130 + 2x = 180

2x = 50

x = 25

So, x = 25

Answer:

6cm

Step-by-step explanation:

Area of the trapezoid = Area of the square + Area of the triangle

Area of the square= Area of the trapezoid - Area of the triangle

Area of the square= 60 - 24

Area of the square= = 36 square metres

Since Area of the square= L²

L is the length of the side of the square

L² = 36

L = √36

L = 6cm

Hence the required length is 6cm

Answer:

I don't know.

Answer:

It's (-3, -2)

I did the math, don't worry

Answer:

7/5 is the scale factor

Step-by-step explanation:

The graph of the function f ( x ) = x² - 2x + 3 is plotted

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as A

Now , the value of A = f ( x )

f ( x ) = x² - 2x + 3   be equation (1)

Now , the function is a parabolic equation with the vertices at ( 1 , 2 )

Therefore , the function is f ( x ) = x² - 2x + 3  and the graph is plotted

Hence , the parabolic function is f ( x ) = x² - 2x + 3

To learn more about equation of graph of polynomials click :

https://brainly.com/question/16957172

#SPJ7

Answer:

D

Step-by-step explanation:

notice how everything goes up by 3? that's a sequence.

Answer:

Barb is correct she won by 10 points

Darius's=480

Barb=490

Answer:

Step-by-step explanation:

[tex]6\sqrt{20} + 8\sqrt{5} -5\sqrt{45}[/tex]

[tex]12\sqrt{5} + 8\sqrt{5} -15\sqrt{5}[/tex]

[tex]5\sqrt{5}[/tex]

Answer:

Step-by-step explanation:

I imagine that you are simplifying this, since there is nothing else you can do with it. You are in the section in algebra where you're learning how to simplify radicals. ALWAYS think prime factorization when it comes to numbers. For example, the square root of 5...the prime factorization of 5 is simply 5 * 1. So we know that √5 is as simple as it can be. It would benefit us if we could simplify either of the other 2 radicals down to the same radicand so we could add or subtract them.

The prime factorization of 20 is

20--> 5   *   4

                  4--> perfect square (2×2). So the simplification of 6√20 is 6×2√5 which is 12√5.

The prime factorization of 45 is

45--> 5   *   9

                   9--> perfect square (3×3). So the simplification of 5√45 is 5×3√5 which is 15√5.

Put it all together to get

12√5 + 8√5 -15√5 which simplifies to

5√5

Answer:

84%

Step-by-step explanation:

each liter is 1000 cubic centimetre, so you have a total density of 3000, but instead think of 3 liters being 100% density and think of alcohol as 80% density, there are 4 times at much 80% than 100% liquid.

with 3 liters of alcohol, 3 liters of water is now 90% density or 0.9 gram per centimetre. add another 3 liters and it is 2/3, so the grams per centimetre would be 8.66667 or 8 2/3's

if you add another 3 liters, THEN it is 85%

add 12 liters in total and the final answer 84%

Answer:

9 pounds

Step-by-step explanation:

1 lb = 16 ounces

144/16 = 9 pounds

Answer:

1

Step-by-step explanation:

Answer:

all 3

Step-by-step explanation:

its not right or wrong you can do all 3 if you like

Answer:

C. 8

Step-by-step explanation:

Options

A. 5

B. 6

C. 8

D. Can't say without knowing the number of participants

Number of sweet distributed = Total number of sweets - left over sweets

= 1025 sweets - 1 left over sweet

= 1024 sweets

Number of participants = Number of sweets distributed / number of sweets given to each participant

A. 5

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1024 /5 Sweets

= 204.8 participant

B. 6

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1024/6

= 170.67 participant

C. 8

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1,024/8

= 128 participant

D. Can't say without knowing the number of participants

From the options given, the number of sweets given away to each participant could be 8

Number of sweets given to each participants is 32.

Since, A sports teacher had 1025 sweets and he had one sweet left after distributing.

So, number of sweets he distributing is, [tex]1025-1=1024[/tex]

Since, distributing these equally amongst all the participants

Therefore, number of sweets given to each participants is, [tex]=\sqrt{1024}=32[/tex]

So, total number of participants is 32 and number of sweets given to each participants is 32.

Learn more about square root here:

https://brainly.com/question/11388449

Answer:

C

Step-by-step explanation:

For any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

[tex]\sqrt{x^2+(y-5)^2}[/tex] = | y + 5 | ← square both sides

x² + (y - 5)² = (y + 5)² ← expand parenthesis on both sides

x² + y² - 10y + 25 = y² + 10y + 25 ( subtract y² - 10y + 25 from both sides )

x² = 20y

Answer:

A. 70°

Step-by-step explanation:

There are two ways to solve this problem:

(1) The sum of all the angles of a quadrilateral equals 360°.

The equation for this problem would be:

110° + 110° + 70° + m∠A = 360°

Simplify:

290° + m∠A = 360°

m∠A = 70°

(2) Trapezoid ABCD is an isosceles trapezoid, because m∠B and m∠C, opposite angles of the same base of the trapezoid, are congruent.

Therefore m∠A and m∠D must also be congruent.

m∠A = m∠D = 70°

Answer:

489.40 cm³

Step-by-step explanation:

Since the cross section is parallel to their respective bases, hence:

Area of the cylinder cross section = area of the circular base = πr²

where r is the radius of the cylinder base.

Area of other cross section = area of rectangle base = 3.8 cm * 8.1 cm

Since both cross sections have same area, hence:

Area of cylinder cross section = Area of rectangle base

πr² = 8.1 * 3.8

r² = 9.8

r = 3.1 cm

Volume of the cylinder = πr²h = π(3.1)²(15.9) = 489.40 cm³

Step-by-step explanation:

4(2.8*4.5)=50.4

50.4/12= 4.2

4.2 means 5 tins of paint

£52.5 =price

Step-by-step explanation:

i have explained in the paper.

Goodluck

Answer:

I need more information to answer this. Please provide more context

Step-by-step explanation:

SOHCAHTOA

SIN: Opposite/hypo

COS: Adj/Hyp

TAN: Opp/Adj