A tortoise moves forward 15 meters in one hour. It turns around and crawls 10 meters in the
next hour. Finally, in the third hour, it turns around again and crawls 8 more meters. How
much did the tortoise walk in total in 3 hours?

Answer:

1: 16

2: 4940

3: 24

4: 25

5: 9

Step-by-step explanation:

A permutation is a method of calculating the number of possible outcomes. It follows the following general formula;

[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]

There (n) is the number of objects, and (r) is the number of objects selected.

1. Arranging 4 pots with different plants in a row

In order to solve this, one needs two pieces of information, the number of objects, and the number of objects selected. One is given the number of objects; (4), but when the problem states "in a row" it never specifies how many plants are in a row. Thus, let one assume that a "row" can have an infinite amount of space, but in this case, only (4) space will be used. Therefore there are (4) objects with (4) objects selected. However, the drawback is that the combination formula doesn't work when the two parameters (n) and (r) are the same. Hence, to solve this special case, one simply multiplies the two numbers to get the answers:

[tex]n*r\\\\=4*4\\\\=16[/tex]

2. Forming a four-digit ATM pin

One is given that there are (4) digits in the ATM pin, this is the number of objects selected. One is also given that number of objects, there are (10) digits including (0). Set up the permutation and solve;

[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]

[tex]_1_0P_4=\frac{10!}{(10-4)!}\\\\=\frac{10!}{6!}\\\\=\frac{10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}\\\\=10*9*8*7\\\\=4940[/tex]

3. Securing a motorcycle with a three-digit combination lock using the numbers (1), (2), (3), and (6).

There are (4) digits to choose from on the lock. But there are (3) numbers that can be selected.

[tex]_4P_3=\frac{4!}{(4-3)!}\\\\=\frac{4!}{1!}\\\\=\frac{4*3*2*1}{1}\\\\=4*3*2*1\\\\=24[/tex]

4. Displaying 3 identical small vases, 1 figure, and a photo frame in a row.

There are (5) objects, and (5) spaces (read problem (1) for an explanation for the objects being put in a row). Thus, this is a special case; multiply the two numbers to get the result;

[tex]n*r\\=5*5\\=25[/tex]

5. 3 girls sitting around a circular table

There are (3) subjects, and (3) spaces in this problem. Apply the same logic applies to a row in this problem. Therefore, this is another special case; multiply the two numbers to get the result;

[tex]n*r\\=3*3\\=9[/tex]

Answer:

y=|x -3| -1

Step-by-step explanation:

Answer:

maybe 12 because

Step-by-step explanation:

30/25=1.2

10×1.2=12

Answer:

$ 100 + $ 60 y

Step-by-step explanation:

The dental clinic Dentes Felizes calculates the value of its services based on a fixed fee of R$ 100.00 and R$ 60.00 for each filling.

Let the total number of fillings is y.

The total cost of fillings = $ 60 x y =  $ 60 y

The total cost of the treatment = $ 100 + $ 60 y

Answer:

B. 13.95 meters

Step-by-step explanation:

The question is just asking you to talk the amount of time taken, and divide it in half.

d= 0.5(27.9)

Answer:

5 units!

Step-by-step explanation:

Because Rectangle Perimeter = 2(a+b)

a=2w-1, b=w

2(2w-1+w)=28

3w-1=14

3w=15

w=5

So the answer is 5! 5! 5! A!A!A!

Fighting!! o(≧o≦)o

Answer: The ratio that represents the cosine of ∠T is [tex]\frac{56}{65}[/tex]

Step-by-step explanation:

We are given:

UV = 56 units

VT = 33 units

UT = 65 units

∠V = 90°

Cosine of an angle is equal to the ratio of base and the hypotenuse of the triangle. ΔTUV is drawn in the image below.

[tex]\cos \theta=\frac{\text{base}}{\text{hypotenuse}}[/tex]

Base of the triangle is UV and the hypotenuse of the triangle is TU

Putting values in above equation, we get:

[tex]\cos \theta=\frac{UV}{TU}=\frac{56}{65}[/tex]

Hence, the ratio that represents the cosine of ∠T is [tex]\frac{56}{65}[/tex]

Answer:

-5 + 3(7.2 - 3.2) equals 7.

Step-by-step explanation:

The order of operations states the order in which different mathematical operations should be done first, you can use the mnemonic PEMDAS to remember the order to complete each operation. PEMDAS states that the order must be followed as Parenthesis, Exponents, Multiplication/Division, and Addition/Subtraction. In the expression -5 + 3(7.2 - 3.2), the three mathematical operations being used are subtraction, multiplication, and parenthesis, so based on PEMDAS, the order to complete them is parenthesis, multiplication, and subtraction. -5 + 3(7.2 - 3.2) = -5 + 3(4) = -5 + 12 = 7, so that is your final answer.

[tex]\displaystyle\bf -5+3(7.2-3.2)=7\\\\1)\:7.2-3.2=4\\\\2)\:4\cdot3=12\\\\3)\:12-5=7[/tex]

Answer:

-27/7

Step-by-step explanation:

put x into the equation

Answer:

1

Step-by-step explanation:

Let the number be n.

We are given:

n/12=q1+(7/12) where q1 is the quotient

n/6=q2+(?/6) where q2 is the quotient and ? is the remainder value we are trying to find.

? must be a integer between 0 and 5, inclusive. A remainder cannot be bigger than or equal to the divisor.

Let's rewrite the first equations

Multiply equation 1 on both sides by 2:

n/6=2q1+7/6

Remainder cannot be 7.

Rewrite again.

6 goes into 7 1 time with remainder 1.

n/6=2q1+(1+1/6)

n/6=(2q1+1)+1/6

So q2=2q1+1 and the remainder is 1 when dividing n by 6.

For fun. What is a number n with such conditions on it?

So what number has remainder 7 when divided by 12 and a remainder 1 when divided by 6.

n=12q1+7

n=6q2+1

If q1=1, we find a number right away that works.

19/12=1+7/12

19/6=3+1/6

Answer:

hope that is helpful

Step-by-step explanation:

W= VI

W= VI

I. I

V= W

I

Answer:

V = [tex]\frac{W}{I}[/tex]

Step-by-step explanation:

Given

W = VI ( isolate V by dividing both sides by I )

[tex]\frac{W}{I}[/tex] = V

Answer:

75 in^2

Step-by-step explanation:

The surface area is the sum of the areas

Area of the square:

A = s^2 = 5^2 =25

Area of one triangle

A = 1/2 bh = 1/2 (5)(5) = 25/2

There are 4 triangles

4* (26)/2 = 50

The sum is 25+50 = 75

Hi!

[tex]P_{\square}=5^2=25 \ in.^2\\\\P_{\triangle}=\frac{1}{2}\cdot5\cdot5=\frac{1}{2}\cdot25=12,5 \ in.^2\\\\P_c=25+4\cdot12,5=25+50=\boxed{75 \ in.^2}[/tex]

Answer:

b ≈ 48.6°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin b = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{12}[/tex] , then

b = [tex]sin^{-1}[/tex] ([tex]\frac{9}{12}[/tex] ) ≈ 48.6° ( to 1 dec. place )

Answer:

1/2×d1×d2

=1/2× (4+4)(6+3)

=36

Answer:

y=n^2+3n+4

Step-by-step explanation:

Sequence,S: 8,14,22,32 ,44, 58, 74...

First differences of S: 6,8,10,12,14,16,...

Second differences of S: 2,2,2,2,2,2,....

It is indeed a quadratic since the 1st differences that are the same are the second differences.

So the 1st term is 8. If the 0th term was listes it would be 4 since 8-4=4 and 6-4=2.

This means our quadratic it is in the form

y=an^2+bn+c where c=4.

So we have y=an^2+bn+4.

Now we can find a and b using two points from our sequence to form a system of equations to solve.

(1,8) gives us 8=a(1)^2+b(1)+4

Simplifying gives 8=a+b+4

Subtracting 4 on both sides gives: 4=a+b

(2,14) gives us 14=a(2)^2+b(2)+4

Simplifying gives 14=4a+2b+4

Subtracting 4 on both sides gives 10=4a+2b

So we have the following system to solve:

4=a+b

10=4a+2b

I'm going to solve using elimination/linear combination style.

Dividing second equation by 2 gives the system as:

4=a+b

5=2a+b

Subtract the 2nd equation from the first gives:

-1=-1a

This implies a=1 since -1=-1(1) is true.

If a+b=4 and a=1, then b=3. Because 3+1=4.

So the equation is y=1n^2+3n+4 or y=n^2+3n+4.

Answer:

p = 0

Step-by-step explanation:

1 - 4p - 2p = 1 - 5p

-6p + 1 = -5p + 1

-p + 1 = 1

-p = 0

p = 0

Answer:

142 [tex]cm^3\\[/tex]

Step-by-step explanation:

You have to do [tex](7*5)+(5*3)+(7*3)+(7*3)+(5*7)+(3*5)[/tex].

This equals 142 [tex]cm^3\\[/tex].

Answer:

The answer is 142cm

Step-by-step explanation:

ANSWER :

- ( x+ 2 ) + 4

-x - 2 + 4

-x + 2

Answer:

−x+2

Step-by-step explanation:

-(x+2)+4 Distribute the negative sign (-) outside of the parenthesis with x and 2 and that will turn into -x-2+4.

Add -2 and 4 and that will turn into -x+2.

Answer:

1 option is correct nd your answer is also correct

Answer:

each member needs to put in 91.70 dollars in.

Step-by-step explanation:

you add the costs of all the tools needed. in this case the two controllers and wheels which adds up to 275.1.

then you divide by the amount of people which is three. so 275.1/3 and you get 91.7

Answer:

condition

Step-by-step explanation:

An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).

This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.

On the other hand, an observational study can be defined as a type of study in which a researcher observes and measures the effect of a diagnostic test, risk factors, or treatments on individuals without intervening, changing or manipulating who are or aren't exposed to it (controlled conditions).

Hence, the main purpose of doing an experiment over an observational study is to learn whether a certain condition causes a certain response.

Cause and effect can be defined as the relationship between two things or events in which an occurrence of one (cause) leads to the occurrence of another (effect).

Answer:

9 < x

6 - f

t × 6

1/2n

Step-by-step explanation:

Given expressions:

9 less than x

Less than (<)

9 less than x = 9 < x

6 minus f

Minus (-)

= 6 - f

t multiplied by 6

Multiplication (×)

= t × 6

one half of a number n

One half = 1/2

one half of a number n

= 1/2 × n

= 1/2n

= n/2

Answer:

A) 5

Step-by-step explanation:

We are given that:

[tex]x^2+kx+6=(x+n)(x+3)[/tex]

Where k and n are constants.

And we want to find the value of k.

We can expand the right-hand side:

[tex]\displaystyle =x(x+n)+3(x+n)\\ \\ = x^2+nx+3x+3n \\ \\ = x^2 + (n+3)x+3n[/tex]

Hence:

[tex]x^2+kx+6=x^2+(n+3)x+3n[/tex]

The coefficients of each term must be equivalent. In other words:

[tex]k=n+3\text{ and } 6=3n[/tex]

Solve for n:

[tex]n=2[/tex]

Now, we can solve for k:

[tex]k=(2)+3=5[/tex]

Our answer is A.

Answer:

The median is 9

Step-by-step explanation:

The median is the number in the middle. The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.

Answer:

188 m

Step-by-step explanation:

[tex] \tan(12) = \frac{40}{x} \\ x = \frac{40}{ \tan(12) } \\ x = 188[/tex]

Answer:

I think that the other answer is WRONG

tan(12) = [tex]\frac{x}{40}[/tex]

x = tan(12)*40 = 8.5

Step-by-step explanation:

[tex]\frac{sin\left(78\right)}{40}=\frac{sin\left(12\right)}{x}[/tex] = 8.5

Answer:

B is the answer because the graph is translated 2 down. the translation cannot be included within the radical sign, so it can't be C

Answer:

A: The y-intercept of f(x) is equal to the x-intercept of g(x)

Step-by-step explanation:

From the equation of f(x) given, we have;

f(x) = -4(1.09)^(x)

Now,the y-Intercept will be the point where x = 0.

Thus;

f(0) = -4(1.09)^(0)

f(0) = -4

Now,from the table given for g(x), we can see that at x = 0,g(x) = -4.

Thus,it means that the y-intercept of f(x) is equal to the x-intercept of g(x)

Answer:

Answer:

Radius of the circular garden

= 210 sq

=105m

Radius of the region covering the garden and the path =105m+7m

=112m

Area of the region between two concentric circles

with radius of outer circle R, and inner circle r =π(R sq−r sq)

Hence, the area of the path

=π(112sq−105 sq)= 7/22

(12544−11025)

= 33418/7

=4774m sq

HOPE THIS WILL HELP YOU MATE