A mathematical model is a simplified description of a system or a process. In your opinion, how are mathematical models helpful? What are the advantages and disadvantages of using a model?

Answer:

150

Step-by-step explanation:

bc is along a straight line with section 4 straight lines are 180° if bc is 30° then 180°-30°=150°

Answer:

The measure of ∠4 is 150°

Step-by-step explanation:

Given the figure in which BD is the diameter of circle and

m∠1=100°

m(arc BC)=∠3=30°

we have to find the measure of ∠4.

As BD is a straight line as BD is diameter therefore

∠4 and ∠3 forms a linear pair

⇒ ∠4 and ∠3 are supplementary i.e these angles adds up to 180°

∠4 + ∠3 = 180°

∠4+30°=180°

∠4=180°-30°=150°

Hence, the measure of ∠4 is 150°

The recursive rule tells you that

[tex]t_2=t_1+3[/tex]

[tex]t_3=t_2+3=(t_1+3)+3=t_1+2\cdot3[/tex]

[tex]t_4=t_3+3=(t_1+2\cdot3)+3=t_1+3\cdot3[/tex]

and so on, with the general rule

[tex]t_n=t_1+(n-1)\cdot3[/tex]

Then with [tex]t_1=1[/tex], you have

[tex]t_n=1+3(n-1)\implies\boxed{t_n=3n-2}[/tex]

The answer is 19/50 or 38%.

Hope this helps!

Answer:

The probability that a student buys a drink is 0.47.

Step-by-step explanation:

Given : At a high school movie night, the refreshment stand sells popcorn and soft drinks. Of the 100 students who came to the movie, 62 bout popcorn and 47 bought a drink. 38 students bought both popcorn and a drink.

To find : What is the probability that a student buys a drink?          

Solution :

Total number of students are T=100 who came to the movie.

Student who bought popcorn = 62

Student who bought drink = 47

Students who bought both popcorn and a drink = 38

We have to find the probability that a student buys a drink.

Favorable outcome F=47                      

Probability is [tex]P=\frac{F}{T}[/tex]

[tex]P=\frac{47}{100}[/tex]    

[tex]P=0.47[/tex]    

Therefore, The probability that a student buys a drink is 0.47.

[tex]\bf \begin{array}{ccll} workers&bricks\\ \cline{1-2} 14&36000\\ x&54000 \end{array}\implies \cfrac{14}{x}=\cfrac{36000}{54000}\implies \implies \cfrac{14}{x}=\cfrac{2}{3} \\\\\\ 42=2x\implies \cfrac{42}{2}=x\implies 21=x[/tex]

Answer:

21 workers would be your answer.

Answer:

The surface area is [tex]1,536\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The surface area is equal to

[tex]SA=B+PH[/tex]

where

B is the area of the ceiling

P is the perimeter of the base

H is the height of the walls

substitute the given values

[tex]SA=(20)(24)+2(20+24)(12)[/tex]

[tex]SA=480+1,056=1,536\ ft^{2}[/tex]

Mrs. Karabin will be painting a total of 1536 square feet in her garage. This includes 1056 square feet for the walls and 480 square feet for the ceiling.

To solve this, we need to calculate the surface area for the walls and ceiling of the garage. Because all sides of this garage are rectangular, we can find the area by multiplying the length by times width for each side.

For the walls: There are two walls that are 12 feet high and 24 feet long and two walls that are 12 feet high and 20 feet wide. So, we calculate (12x24)x2 + (12x20)x2 = 576 + 480 = 1056 square feet.

For the ceiling: The ceiling is 20 feet wide and 24 feet long, so we calculate 20x24 = 480 square feet.

Adding these together, Mrs. Karabin will be painting 1056 (for the walls) + 480 (for the ceiling) = 1536 square feet in total.

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The correct answer is C. you multiply the 16x5

Answer:B) 40 sq units

Step-by-step explanation:

use formula [tex]\frac{1}{2}[/tex] base × height

= (0.50)(16) × (5)

= 40 sq units

1/3

2 of the books are math books and there are 6 books. This is 2/6. Now, divide both sides of the fraction by 2 to simplify it. This gives you a final answer of 1/3.

Answer:

432ft²

Step-by-step explanation:

The dimensions for one wall= 12' by 9'

Area of the wall is given by = width × height

Given width of room = 12' and height of wall =9 feet

Area for one wall= 12×9=108ft²

Area for four walls= 108 × 4=432ft²

Answer:

They will cover 432 feet²

Step-by-step explanation:

* Lets study the information in the problem

- The room has floor with dimensions 12 feet by 12 feet

- The height of the room is 9 feet

- The room has floor and ceiling with same dimensions

- The room has four walls with dimensions 12 feet and 9 feet

- The need to cover the 4 walls

- Each wall shaped a rectangle with base 12 feet and height 9 feet

- The area of the rectangle = base × height

* Now lets solve the problem

∵ The base of the wall = 12 feet  

∵ The height of the wall = 9 feet

∵ The area of the wall = base × height

∴ The area of one wall = 12 × 9 = 109 feet²

- The room has four identical walls

∴ The area of the 4 walls = 4 × 108 = 432 feet²

* They will cover 432 feet²

- The attached figure for more understand

For this case we have a function of the form [tex]y = f (x)[/tex], where:

[tex]f (x) = \frac {5 + x} {6 + 3x}[/tex]

We must evaluate the function at[tex]x = a-1[/tex]

So:

[tex]g (a-1) = \frac {5+ (a-1)} {6 + 3 (a-1)}\\g (a-1) = \frac {5 + a-1} {6 + 3a-3}\\g (a-1) = \frac {4 + a} {3 + 3a}[/tex]

Thus, the value of the function is:

[tex]\frac {4 + a} {3 + 3a}[/tex]

Answer:

[tex]g (a-1) = \frac {4 + a} {3 + 3a}[/tex]

Answer:

V=2

Step-by-step explanation:

p=8/v

substitute p=4,

4=8/v

multiply both sides by v,

4(v)=8(v)/v

4v=8

divide 8 by 4,

v=2

Answer: choice c. 2 edge 2023

Step-by-step explanation:

Answer:

16%

Step-by-step explanation:

THERE

Answer: 16%

Step-by-step explanation:

Given: Mean : [tex]\mu = 200\text{ pounds}[/tex]

Standard deviation : [tex]\sigma=50\text{ pounds}[/tex]

The formula for z score is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

Now, for x=250

[tex]z=\dfrac{250-200}{50}=1[/tex]

The P-value [tex]= P(z>1)=1-P(z<1)[/tex]

[tex]=1-0.8413=0.1587\approx16\%[/tex]

Hence, the percent of the adult pandas weigh over 250 pounds is about 16%.

Answer:

28 minutes

Step-by-step explanation:

Speed = distance / time

Your speed is 1 lawn / 57 minutes.  Your friend's speed is 1 lawn / 54 minutes.  Working together, your combined speed is:

1/57 + 1/54

So the time it takes working together is:

Speed = distance / time

1/57 + 1/54 = 1 / t

t = 27.7 minutes

Rounded to the nearest whole number, it takes 28 minutes.

Answer:

Step-by-step explanation:

It's a parallelogram.

The formula of an area of a parallelogram:

[tex]A=bh[/tex]

b - base

h - height

We have

[tex]b=17\dfrac{1}{5}yd=17\dfrac{1\cdot2}{5\cdot2}yd=17\dfrac{2}{10}yd=17.2yd\\\\h=12\dfrac{1}{2}yd=12.5yd[/tex]

Substitute:

[tex]A=(17.2)(12.5)=215\ yd^2[/tex]

10^6/10^-3 = 10^6-(-3) = 10^6+3 =

10^9

Answer:

[tex]One\: Billion[/tex]

Step-by-step explanation:

According to the Quotient-to-Power Exponential Rule, whenever you divide similar bases, you keep the base and subtract the exponents:

[tex]1000000000 = {10}^{9} = \frac{{10}^{6}}{{10}^{-3}}[/tex]

I am joyous to assist you anytime.

Answer:

4

Step-by-step explanation:

In a 45-45-90 triangle, the length of the hypotenuse is √2 times the legs.

s√2 = 4√2

s = 4

Each leg is 4 units long.

Each length of the side of the triangle is 4 units long.

We have given that side is s and hypotenuse is 4root2.

and also the angle is 45-45-90degrees.

We have to determine the length of the sides

In a 45-45-90 triangle, the length of the hypotenuse is √2 times the legs.

45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2 .

s√2 = 4√2

s = 4

Therefore each length of the side of the triangle is 4 units long.

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Answer:

The function is a linear function

The function is translated 3 units to the left,then stretched vertically

by factor 2, then translated 5 units down

Step-by-step explanation:

* Lets revise some transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

- If the function f(x) stretched vertically, then g(x) = k · f(x), where

 k > 1 (multiplying each of its y-coordinates by k)

- If the function f(x) compressed vertically, then g(x) = k · f(x), where

 0 < k < 1 (multiplying each of its y-coordinates by k)

* Now lets solve the problem

∵ f(x) = 2(x + 3) - 5

- The greatest power of the function is 1 (degree of the function)

∴ f(x) is linear function

- The parent function f(x) = x

∵ f(x) changed to f(x + 3)

∴ f(x) translated 3 units to the left

# Each x-coordinate of the points on the function subtracted by 3

∵ f(x + 3) changed to 2f(x + 3)

∵ 2 > 1

∴ f(x + 3) stretched vertically by factor 2 (k = 2)

# Each y-coordinate of the points on the function multiplied by 2

∵ 2f(x + 3) changed to 2f(x + 3) - 5

∴ 2f(x + 3) translated 5 units down

# Each y-coordinate of the points on the function subtracted by 5

Answer:

what is 1/20 as a decimal and a percentage: 0.05 and 5%

what 1/10 as a decimal and a percentage : 0,1 and 10%

what 12 1/2% as a decimal and a percentage: 12.5% it's already as a percentage, as a fraction 1/8

what is 0.2 as a fraction and a percentage: 1/5 and 20%

what is 25% as a decimal and fraction: 0.25 and 1/4

what is 30% decimal and fraction :  0.3 and 3/10

what is 1/3 as a decimal and percentage : 0.33 and 33%

what's is 0.375 as a fraction and percentage : 3/8 and 37.5%

what is 0.4 as a fraction and percentage : 4/10 and 40%

what is 1/2 as a decimal and percentage : 0.5 and 50%

what is 0.6 as a fraction and percentage : 3/5 and 60%

what is 0.625 as a fraction and percentage: 5/8 and 62.5%

what is 66 1/2% as a decimal and fraction: 0.665 and 665/1000, 133/200

Step-by-step explanation:

These are basically 3 problems, so I won't explain two items for every one of your 13 similar questions.  Here's the explanation for every 3 cases asked in your questions... and the answers.  All you have to do is replace the numbers in the explanations for the ones in each other question asking the same thing.

To express a fraction in percentage, you simply have to put the fraction with a denominator of 100..., for example:

[tex]\frac{1}{20} * \frac{5}{5}  = \frac{5}{100}[/tex]

So, 1/20 is 5%.

[tex]\frac{1}{2} * \frac{50}{50}  = \frac{50}{100}[/tex]

And 1/2 is 50%

To express a percentage as a fraction, you take that percentage and place it over a denominator of 100 and you simplify, like this:

[tex]\frac{12.5}{100} = \frac{1}{8}[/tex]

[tex]\frac{30}{100} = \frac{3}{10}[/tex]

To convert a decimal number to a fraction, the easiest way is to express this number up to the 2nd decimal... then take that as a %.  

Examples:

0.2 you can say 0.2 = 0.20...  so it's 20 hundredths, or 20 per 100... so 20%

0.375, it's already expressed in more than hundredths, so you simply move the dot 2 spots right to get 37.5%

what is 1/20 as a decimal and a percentage: 5% (see above)

what 1/10 as a decimal and a percentage : 10% (save as above)

what 12 1/2% as a decimal and a percentage: 12.5%, it's already as a percentage, if you mean as a fraction... 1/8 (see above)

what is 0.2 as a fraction and a percentage: 1/5 and 20% (see above)

what is 25% as a decimal and fraction: 0.25 and 1/4

what is 30% decimal and fraction :  0.3 and 3/10

what is 1/3 as a decimal and percentage : 0.33 and 33%

what's is 0.375 as a fraction and percentage : 3/8 and 37.5%

what is 0.4 as a fraction and percentage : 4/10 and 40%

what is 1/2 as a decimal and percentage : 0.5 and 50%

what is 0.6 as a fraction and percentage : 3/5 and 60%

what is 0.625 as a fraction and percentage: 5/8 and 62.5%

what is 66 1/2% as a decimal and fraction: 0.665 and 665/1000, 133/200

Answer:

Option B is correct

Step-by-step explanation:

We have function f(x)=(x+3)2

The domain of the function is the set of values for which the function is defined and real.

In our case if x belong to all real numbers the function will be real and defined as given in Option B as function has no undefined points.

All other options are subset of real numbers.

So, option B is correct.

Answer:

y=0

Step-by-step explanation:

For the x axis, the value of y is zero

y=0

Answer:

(6x² - 5)(x² + 2)

Step-by-step explanation:

Given

6[tex]x^{4}[/tex] - 5x² + 12x² - 10 ( factor the first/second and third/fourth terms )

= x²(6x² - 5) + 2(6x² - 5) ← factor out (6x² - 5) from each term

= (6x² - 5)(x² + 2)

Answer:

(x^2 + 2)(6x^2 – 5)

Step-by-step explanation:

6x^4 – 5x^2 + 12x^2 – 10

=(6x^4 – 5x^2) + (12x^2 – 10)

=x^2 (6x^2 – 5) + 2(6x^2 – 5)

=(x^2 + 2)(6x^2 – 5)

Answer

(x^2 + 2) and (6x^2 – 5) are factors of the expression 6x^4 – 5x^2 + 12x^2 – 10

Answer:

9,000

Step-by-step explanation:

multiply the mass value by 1000

Answer:

9000 grams!!!

I hope this helped! :)

Try this option:

1.

[tex]\frac{10-4}{(-3)*(-5)+8*2}=6[/tex]

2.

[tex]\frac{8+2-4}{\frac{10}{-5}-(-3)} =6[/tex]

Answer:

5

Step-by-step explanation:

4 - 1 = 3

3 + 2 = 5

Hope this helps :)

Have a great day !

5INGH

Hi, hope you’re having a good day!

You have to follow PEMDAS (in US) which is Parentheses, Exponent, Multiplication or Division (left to right) Addition or Subtraction (left to right)

4-1=3

3+2=5

So, the answer is 5!

Hope this helped, thanks for taking your time to read this! ❤️❤️

It’s going to be b which is positive 5 and negative 3

Answer:

The product of 7 and t and 7 multiplied by t

Step-by-step explanation:

Answer:

[tex]h(-9)=-\frac{2}{33}[/tex]

Step-by-step explanation:

The given expression is [tex]h(r)=\frac{2}{3r-6}[/tex]

We want to find the value of h(-9).

We substitute r=-9 to obtain:

[tex]h(-9)=\frac{2}{3(-9)-6}[/tex]

We multiply out to obtain:

[tex]h(-9)=\frac{2}{-27-6}[/tex]

We simplify the denominator to obtain:

[tex]h(-9)=\frac{2}{-33}[/tex]

This is the same as:

[tex]h(-9)=-\frac{2}{33}[/tex]

The value of h(-9) is 0. Function substitution is a mathematical technique that involves replacing a variable with an expression or function, simplifying calculations and solving equations by making them more manageable.

To find h(-9), you simply substitute -9 for r in the function h(r):

h(-9) = (2/3) * (-9) - 6

Now, calculate it step by step:

h(-9) = (-18/3) - 6

Since -18/3 is -6, the equation simplifies to:

h(-9) = -6 - 6

Now, add -6 and -6:

h(-9) = -12

So, the value of h(-9) is -12.

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Answer:

5/4

Step-by-step explanation:

Use the slope formula

Answer:

9.43398

Step-by-step explanation:

The formula is square root of (x2-x1)^2 + (y2-y1)^2.  

So if you plug in the equation, it is 9.43398.

Answer:

15

Step-by-step explanation:

Write a proportion:

60 cups / 12 gallons = x cups / 3 gallons

Cross multiply:

12x = 180

Divide:

x = 15

He should use 15 cups.

Jesse should use 15 cups of mushrooms to make 3 gallons of mushroom soup, based on the restaurant's recipe. Devon will be making 37.5 liters of soup for the party of 100 guests.

To solve Jesse's question about how many cups of mushrooms he should use to make 3 gallons of mushroom soup, we need to find the proportion between the amount used in the restaurant's recipe and the desired amount for Jesse's smaller batch.

The restaurant uses 60 cups of mushrooms to make 12 gallons of soup. To find out how many cups are needed for 1 gallon, we divide the number of cups by the number of gallons:

60 cups / 12 gallons = 5 cups per gallon

Jesse wants to make 3 gallons of soup. Multiplying the amount needed for one gallon by 3 gives us the answer:

5 cups/gallon × 3 gallons = 15 cups of mushrooms.

Devon, on the other hand, is preparing soup for a party. Calculating the total amount for 100 guests using 375 milliliters per person, we get:

375 milliliters/guest × 100 guests = 37500 milliliters.

Since 1 liter is equivalent to 1000 milliliters, we can convert the milliliters to liters:

37500 milliliters / 1000 = 37.5 liters of soup for 100 guests.

Answer:

Step-by-step explanation:

A function has a root only if cuts the x axis .

If it cuts once it means it has one real root, if twice then two roots and so on .

Here in the graph of G(x) shown ,it never crosses the x axis so we can say that there is no real root of the given function G(x).

It means the option A which states G(x) has zero roots is correct.

Let [tex]v[/tex] be the speed of train A, and let's set the origin in the initial position of train A. The equations of motion are

[tex]\begin{cases}s_A(t) = vt\\s_B(t) = -\dfrac{8}{7}vt+450\end{cases}[/tex]

where [tex]s_A,\ s_B[/tex] are the positions of trains A and B respectively, and t is the time in hours.

The two trains meet if and only if [tex]s_A=s_B[/tex], and we know that this happens after two hours, i.e. at [tex]t=2[/tex]

[tex]\begin{cases}s_A(2) = 2v\\s_B(2) = -\dfrac{16}{7}v+450\end{cases}\implies 2v = -\dfrac{16}{7}v+450[/tex]

Solving this equation for v we have

[tex]2v = -\dfrac{16}{7}v+450 \iff \dfrac{30}{7}v=450 \iff v=\dfrac{450\cdot 7}{30} = 105[/tex]

So, train A is travelling at 105 km/h. This implies that train B travels at

[tex]105\cdot \dfrac{8}{7} = 15\cdot 8=120 \text{ km/h}[/tex]

train A travels at 210 km/h and train B travels at 240 km/h.

The student's question involves finding the speeds of two trains moving towards each other when certain conditions are provided. We know that the two trains are 450 km apart and meet after 2 hours. Train B travels at 8/7 the speed of train A.

Let's denote the speed of train A as v km/h. Then, the speed of train B would be 8/7 * v km/h. Since they meet after 2 hours, we can add their distances to equal the total distance between them.

Speed of train A: v km/h
Speed of train B: 8/7 × v km/h
Total distance: 450 km
Time to meet: 2 hours

The total distance both trains cover can be expressed as:
(Speed of train A + Speed of train B) × Time = (v + 8/7 × v) × 2 hours

Since the sum of the two distances covered by the trains is the initial distance between them which is 450 km, we get:
(1 + 8/7)v * 2 = 450 km

We simplify this equation to find the value of v. The equation becomes:
15/7  v × 2 = 450 km
v = (450 × 7) / (15 × 2)
v = 210 km/h

Now, we find the speed of train B by multiplying the speed of train A by 8/7:
Speed of train B = 8/7 × 210 km/h = 240 km/h

Therefore, train A travels at 210 km/h and train B travels at 240 km/h.