25. Higher Order Thinking How are the ratios 24 laps 1 hour different? 192 laps 8 hours alike? How are they different?​

Answer:

a₅ = 80 , [tex]a_{n}[/tex] = 5[tex](2)^{n-1}[/tex]

Step-by-step explanation:

to find a term in the geometric sequence multiply the previous term by r

a₁ = 5

a₂ = a₁ × 2 = 5 × 2 = 10

a₃ = a₂ × 2 = 10 × 2 = 20

a₄ = a₃ × 2 = 20 × 2 = 40

a₅ = a₄ × 2 = 40 × 2 = 80

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

here a₁ = 5 and r = 2 , then

[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]

Answer:

x/2 = 19-11

x/2 = 8

x = 8×2

x= 16

Answer:

x=16

Step-by-step explanation:

x/2 + 11 = 19

*2     *2    *2    Multiply 2 on both sides to make x stand by itself

x+22 = 38

  -22   -22

x=16

Check

Plug in 16 instead of x.

16/2 + 11 = 19

8+11=19

19=19

Hope it helps:)

Answer:

Step-by-step explanation:

Distance around = 2*160 + 2*360

= 320 + 720

= 1080 feet.

The distance around the field is 1040 feet.

It is required to find the distance around the field.

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that:

A football field is 160 feet wide and 360 feet in length.

A  football field is in the shape of rectangle.

So, we know that ,

Perimeter of rectangle= 2(length +breadth)

Distance around

= 2(160 + 360)

=2(520)

= 1040 feet.

Hence,  the distance around the field is 1040 feet.

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[tex] \boxed{ \sf{ \color{purple}\huge Answer :}}[/tex]

[tex] \: \: [/tex]

[tex] \large \tt \purple↪ \: \: \: \: \: 5x - 16 = x + 10 [/tex]

[tex] \: \: [/tex]

[tex]\large \tt \purple↪ \: \: \: \: \:5x - x = 10 + 16 [/tex]

[tex] \: [/tex]

[tex]\large \tt \purple↪ \: \: \: \: \: 4x = 26[/tex]

[tex] \: [/tex]

[tex]\large \tt \purple↪ \: \: \: \: \: x = \cancel\frac{26}{4} [/tex]

[tex] \: \: [/tex]

[tex] \underline{ \boxed{\large \tt \purple↪ \red{ \: \: \: \: x = \frac{13}{2} }}}{ \large✓}[/tex]

[tex] \: \: [/tex]

hope helps ~

The larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60. This can be obtained by forming algebraic equation and finding

Given that one number is 4 more than another,

⇒x = y + 4              (equation (1))

Their sum is 60,

⇒x + y = 60

y + 4 + y = 60      (From (1))

2y + 4 = 60

2y = 56 ⇒ y = 28

x = y + 4 = 28 + 4 ⇒x = 32

Hence the larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60.

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Answer:

240.5 cm and 139.5 cm, respectively

Step-by-step explanation:

101 cm / 2 = 50.5 cm

The right edge of the mirror is 50.5 cm to the right of the center line.

The right end of the wall is 190 cm from the center line.

190 cm - 50.5 cm = 139.5 cm

139.5 cm + 101 cm = 240.5 cm

240.5 cm and 139.5 cm, respectively

x would be the side-length of a square that has the same area as a rectangle with width b and length a.

√(a*b) = x

Notice that you have two "lengths" which are a and b.

And you want to find x such that:

a/x = x/b

Now, notice that w e can rewrite the above expressions as:

a*b  = x*x

This means that x would be the side-length of a square that has the same area as a rectangle with width b and length a.

Now, if you know the values of a and b (you can get these by using a ruler for example)

Then you can replace them in the equation:

a*b = x*x

√(a*b) = x

And find the value of x that meets the given condition.

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Using the properties of logarithms, it is found that the San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.

As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are [tex]R_1, R_2, R_1 > R_2[/tex], the ratio of the intensities is given by:

[tex]R = 10^{\frac{R_1}{R_2}}[/tex]

For this problem, the intensities are:

[tex]R_1 = 7.8, R_2 = 5.6[/tex]

Hence the ratio is:

[tex]R = 10^{\frac{7.8}{5.6}} = 24.71[/tex]

The San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.

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Answer:

10 years old

Step-by-step explanation:

Let m = mother's age

Let f = father's age

Let d = Dina's age

m = 4d               d = f-35                f = m+5

Substitute the middle equation in to the first equation

m = 4(f - 35) Use the distributive property

m = 4f - 140 subtract 4f from both sides

*m -4f = -140

In equation 3 above, subtract m from both sides  to get

f = m+5

f - m = 5  rearrange so that the  m term is first

*-m + f = 5  

Now add the equations together that have *

m -4f = -140

-m + f = 5

     -3f = -135  Divide both sides by -3

f = 45  This is the father's age.  To find Dina's age, plug 45 into the second equation above:

d = f -35

d = 45 -35

d = 10.

To find the mom's age, use the third equation:

f = m+5

45 = m + 5

40 = m

You can check this by plugging the answers you found and you can see that all three equations are solved.

m = 4d                        d = f - 35                 f = m + 5

40 = 4(10)                    10 = 45 - 35            45 = 40 + 5

40 = 40                       10 = 10                     45 = 45

Answer:

404 inches

Step-by-step explanation:

Since a room of 2cm is to be left of either side of the TV, thus, the permissible required length of the TV is 136-2 = 134cm

Use Pythagoras Theorem,

h² = 134² + 86² = 17956 + 7396 = 25352

h = √25352 = 159.22 ≈ 159cm = 404.41 inches ≈ 404 inches.

Answer: A

Step-by-step explanation:

[tex]m\angle ABC=59^{\circ}[/tex] by the inscribed angle theorem.

Answer:

29 years

Step-by-step explanation:

[tex]f(x)= 200(0.5)^\frac{140}{50}}[/tex]

From here I'll just use a calculator & get 28.7, or 29 years.

Answer:

Step-by-step explanation:

The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse

Answer:

Step-by-step explanation:

Comment

The radius is 33 feet. The height is really a radius. The diameter consists of 2*r

r = diameter / 2

diameter = 66 feet

r = 66 /2 = 33

So you have 2 ways of finding the radius.

Solution

Area of a full circle = pi r^2

Area of a full circle = pi * 33^2

Area of a full circle = 1089 pi    

Area of a semicircle = area of a full circle / 2

Area of a semicircle = 1089 * pi /2

Area of a semicircle = 544.5 * pi

Answer

Exact answer in terms of pi is 544.5 * pi

Approximate answer using 3.14 for pi = 3.14*544.5 = 1709.73

Answer:

Area=

πr2

2

Step-by-step explanation:

3.14159⋅(33)2

2

=1710.5958

Answer:

(y+17)÷18=22.5

y+17=22.5×18

y+17=405

y=405-17

y=388

The coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).

The midpoint of AB,  given any points A (x₁, y₁) and B(x₂, y₂) is given as point M = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).

In the question, we are given that the midpoint of PQ is (-3, 1) and point Q is (7, 5).

We are asked to find the coordinates of point P.

We assume the coordinates of point P as (x, y).

Thus, the midpoint of PQ = ({(x + 7)/2}, {(y + 5)/2}),

that is, (-3, 1) = ({(x + 7)/2}, {(y + 5)/2}).

Thus, we can show that:

(x + 7)/2 = -3,

or, x + 7 = -6,

or, x = -6 - 7 = -13.

(y + 5)/2 = 1,

or, y + 5 = 2,

or, y = 2 - 5 = -3.

Thus, the coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).

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The answers are as follows:

a. There are 6 ways of tossing a coin and then drawing a marble from the bag. (Tree diagram is shown in the diagram below) The probability is 1/12.

b. These are independent events since tossing a coin does not affect the drawing of marble from the bag.

c. From the tree diagram, the probability of tossing a head and drawing a red marble is 1/6(since they are independent events).

d. The probability of drawing two blue marbles if the first marble is not replaced is 1/5(since they are dependent events).

It is given that a bag contains,

Number of white marbles(W) = 1

Number of Blue marbles (B) = 3

Number of Red marbles (R) = 2

Thus, there are 6 marbles in the bag. So, the sample space for drawing a marble = 6

a. Finding all the possible outcomes using a tree diagram:

The possible outcomes from the tree diagram are

(H, W), (H, B), (H, R), (T, W), (T, B),  and (T, R)

The probability of tossing head or tail = 1/2

The probability of drawing a marble from the bag = 1/6

So, the compound probability = (1/2)(1/6) = (1/12)

The sample space for this is 12.

b. Independent or dependent events:

These are independent events since the tossing of a coin does not affect the drawing of marble from the bag.

c. Finding the probability of tossing a head and drawing a red marble:

The probability of tossing a head = 1/2

The probability of drawing a red marble = 2/6 = 1/2

Since they are independent events,

The required probability = (1/2)(1/2) = 1/4

d. Finding the probability of drawing two blue marbles if the first marble is not replaced:

The probability of drawing a blue marble from the bag(1st attempt) = 3/6

The probability of drawing another blue marble from the bag (2nd attempt) = 2/5 (From the leftover marbles after the first attempt)

Since they are dependent events, the probability of the 2nd event is calculated only after the first event is calculated.

So, the required probability = (3/6)(2/5) = 1/5

Thus, all the probabilities are calculated.

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Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

According to the statement

we have given that the Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal.

and we have to find that the expected value of the difference between the number of days.

So, the total number of days in a year is 365 days.

Chance to get a prime number on a die = 3/6

Chance to get a prime number on a die = 1/2.

and chances to get a composite number = 2/6

chances to get a composite number = 1/3

and chances to get a 1 on a die = 1/6.

Then the expected value =

so, expected value = 365(1/6) + 365(1/3) + 365(1/2)

then after calculating

Expected value = 1+2+1

then the value become is 4

and by this way he eat 171 days sweet cereal and other days he eat unsweetened.

So, Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

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An equivalent ratio of the given ratio 6/7 is; 12/14

To find equivalent ratios, we will just multiply the given ratio by any number that is equivalent to 1 such as 2/2, 3/3, 4/4, 5/5 e.t.c

Now, we want to find equivalent ratio of 6/7. Applying the procedure above, we can say that;

Equivalent ratio = (6/7) * (2/2) = 12/14

Thus, an equivalent ratio of 6/7 is; 12/14

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The population standard deviation of the data set is 1.414.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.

Mean = (8 + 9 + 10 + 11 + 12) / 5 = 10

Sum of squared differences: (8 - 10)² + (9 - 10)² + (10 - 10)² + (11 - 10)² + (12 - 10)² = 10

√10/5 = 1.414

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Answer:

Step-by-step explanation:

Add 4% food tax:

Total amount of purchase is:

Subtract $30 paid in cash:

Answer:

$5.25

Step-by-step explanation:

Cost of gasoline

⇒ 9.25 × $3.15 = $29.1375

Cost of gum

$1.10 plus 4% food tax:

⇒ $1.10 × 1.04 = $1.144

Total cost of purchases

Gasoline + gum + Windshield wiper fluid

⇒ $29.1375 + $1.144 + $4.97 = $35.2515 = $35.25 (nearest cent)

If $30.00 was paid by cash and the rest was paid for by debit card:

Debit card charge = $35.25 - $30.00 = $5.25

The probability of on- time arrival in class given that the subject is biology is 82.4%.

Given the following table relating to subject on tie assignment submission and on time arrival in class.

Subject              On time submission                    On time arrival

Physics                    89.7%                                             82.3%

Maths                       88.2%                                            88.7%

Chemistry                89.4%                                             83.1%

Biology                     90.1%                                              82.4%

Total                         88.5%                                             84.7%

We have to find the probability of on time arrival in class given that the subject is biology.

We have been given the corresponding percentages and percentages in itself shows some quantity. Percentage is the ratio of total favourable outcome to total outcome.

From the table the probability of on time arrival in class given that the subject is biology is 82.4%

Hence the probability of on- time arrival in class given that the subject is biology is 82.4%.

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Question is incomplete as it should includes the following table:

Subject              On time submission                    On time arrival

Physics                    89.7%                                             82.3%

Maths                       88.2%                                            88.7%

Chemistry                89.4%                                             83.1%

Biology                     90.1%                                              82.4%

Total                         88.5%                                             84.7%

Answer:

82.4%.

Step-by-step explanation:

Answer:

[tex]y=7x[/tex]

I hope this helps and that you can give a brainliest!

Step-by-step explanation:

If x and y vary directly, that means that y is directly proportional to x. So, the parent function is y = kx.

So, by plugging in the given y=42 when x=6 into this parent function, we get:

42=6k

If we solve for k, we end up with 7.

Now if we plug in the value of k back into the parent function of this scenario, we get:
[tex]y=7x[/tex]

In Bayes Theorem, apart from the already starting information, some new information so that you can update or transform the original probabilities so you now have better information.

What is Bayes Theorem?

The Bayes' theorem was named after Thomas Bayes and it is used in probability theory and statistics as one of the fundamental theorems. It estimates the likelihood of an event based on knowledge of circumstances that might be connected to it in the past.

The Formula for Bayes' Theorem

The Bayes' theorem is given as,

P(A|B) = P(A).P(B|A) / P(B)

Here, for two events A and B,

P(A|B) is the probability for likelihood of A when B is true

P(B|A) is probability for likelihood of B when A is true

P(A) is the independent probability of event A

P(B) is the independent probability of event B

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The total number of 5 digit palindrome that we have is 900.

This is the term that is used to refer to a number or a word phrase that is the same way when it is written from the front and from the back.

Examples of palindrome numbers are

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Answer:

-7, 8.

Step-by-step explanation:

x^2 - x - 56 = 0

Let's see if we can factor this function:

We need 2 numbers whose product is -56 and whose sum is -1 ( which is the coefficient of x).

They are  -8 and 7 , so the factors are:

(x - 8)(x + 7) = 0

x - 8 = 0 giving x =  8 and

x + 7 = 0 giving x = -7.

The zeros are -7, 8

Answer:

A

Step-by-step explanation:

Answer:

[tex]400m^3[/tex]

Step-by-step explanation:

Use the formula [tex]V=\frac{1}{3}Ah[/tex]

Where h=the height of the pyramid (12cm)

A=the base area of the pyramid, also known as the area of the square (10cm*10cm=100cm)

So, inserting this into the equation:

[tex]V=\frac{1}{3} (100)(12)[/tex]

[tex]V=\frac{1}{3} (1200)[/tex]

[tex]V=400m^3[/tex]

Answer: 3n ants

Step-by-step explanation:

         If there are n ants one month, and the ants triple every month, then next month there will be 3n ants.

         We can multiply 3 by n to show it tripling.

      To test this, 3(10,000) = 30,000 and 3(270,000) = 810,000, which corresponds to what you've filled out in the table.