boat traveled downstream a distance of 60 mi and then came right back. If the speed of the current was 6 mph and the total trip took 4 hours find the average speed of the boat relative to the water.

Answer:

Step-by-step explanation:

Comment

If you know this formula

tn = t1 + (n - 1)*d then you don't even have  to count how many odd numbers there are. If you don't know the formula, then you have to count how many odds there are between 1 and 25 inclusive. Just to save you the trouble, there are 13.

Givens

1 = t1

25 = tn

d = 2

Solution

25 = 1 + (n - 1)*2                 Subtract 1 from both sides?

25-1 = 1-1 + (n - 1)*2            Combine

24 = (n  -  1) * 2                   Divide by 2

24/2 = (n - 1)*2/2                

12 = n - 1                               Add 1 to both sides

12 + 1 = n - 1 + 1                     Combine

13 = n

Answer

So you have 13 cards that  will bring success.

Answer:

We know that

The costs of repair for each of the four crashes were

$2529, $1889, $2610, $1073

Here we have to compute the mean, median, and mode cost of repair.

Mean = total cost

the no of crashes

Mean = $2529 + $1889 +$2610 +$1073

4

Mean = $2025.25

Therefore the mean = 2025.25

Then we have to find median.

Now first we have to arrange the data in ascending order (smallest to highest).

$1073,$1889,$2529,$2610

Add the two middle numbers and then divide by two, to get the average:

$1889+$2529 = $4418

Median = $4418/2 = $2209

Therefore the median = $2209

Here there is no mode cost.

The correct answer is the fourth option.

Step-by-step explanation:

easy how thick it is we need a picture

Answer:

22-3d=x

Step-by-step explanation:

where d is the days that it melts and the amount of snow x is the snow that is left.

Answer:

$4

Step-by-step explanation:

Company $0.50

Store. $ 4.50

Price up $ X

4.50

- 0.50

------------

4.00

X= $4.00

Answer:

n = [tex]\frac{1}{36}[/tex]

Step-by-step explanation:

n × 18 = [tex]\frac{1}{2}[/tex]

To find the value of n we have to divide both sides by 18.

Let us solve it now.

18n = [tex]\frac{1}{2}[/tex]

[tex]\frac{18n}{18}[/tex] = [tex]\frac{1}{2}[/tex] ÷ 18

n =  [tex]\frac{1}{2}[/tex] ÷ 18

n = [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{18}{1}[/tex]

n =  [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{18}[/tex]

n = [tex]\frac{1}{36}[/tex]

Answer: -2

Step-by-step explanation:

[tex]g(-3)=0\\\\g(-2)=-2\\\\\frac{g(-3)-g(-2)}{-3-(-2)}=\frac{0-(-2)}{-1}=\boxed{-2}[/tex]

The correct option is Option D: Yes, the graph passes the vertical line test.

The function is a relationship between two distinct sets X and set Y which can be many-one or one-one. here set X is called the domain and set Y is called the codomain.

The vertical line test states that

If we draw a straight vertical line( which is also parallel to the y-axis) and it touches the graph at only one point at all locations, then that relation is said to be a function and this relation will be also one-one.

So here in this function shown in the graph.

If we draw a vertical line parallel to the y-axis in this at any location then it crosses the graph only once. So, it passes vertical line test. And this graph is a function. Therefore option D is correct.

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0.21094 is the probability that the surgery is successful on exactly 3 patients.

It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

According to the given question,

Let Y = The number of patients who respond yes: [tex]Y - Bin (n,p)[/tex]

Given , [tex]n = 4 , p = 0.75 , q = 1 - p = 0.25[/tex]

[tex]P (Y = 3) = \left(\begin{array}{ccc}4\\3\\\end{array}\right) (0.75)^{2}(0.25)^{4-3} \\ = 0.21094\\\\[/tex]

The probability that the surgery is successful on exactly 3 patients is 0.21094

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Using the combination formula, it is found that there are 495 ways to choose a 4-topping sandwich.

The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

4 toppings are chosen from a set of 12, hence the number of ways is given by:

[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]

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Answer:

4 inches

Step-by-step explanation:

Given information:

Let y = height of snow on the lawn

Let t = time in hours

⇒ y = 2 + 0.5t

To find how much snow is on the lawn after 4 hours of snowing, substitute t = 4 into the found equation and solve for y:

⇒ y = 2 + 0.5(4)

⇒ y = 2 + 2

⇒ y = 4 inches

Therefore, Amadou will have 4 inches of snow on his lawn after 4 hours of snow falling.

After 4 hours of continuous snowfall at a rate of 0.5 inches per hour, Amadou would have 4 inches of snow on his lawn. After t hours of snow falling at the same rate, he would have 2 + 0.5t inches of snow on his lawn.

After 4 hours of snow falling at a constant rate of 0.5 inches per hour, Amadou would have:

Snow accumulation = Initial snow + (Snowfall rate × Time)

Snow accumulation = 2 inches + (0.5 inches/hour × 4 hours)

Snow accumulation = 2 inches + 2 inches

Snow accumulation = 4 inches of snow.

After t hours of snow falling, the amount of snow on Amadou's lawn would be:

Snow accumulation = Initial snow + (Snowfall rate × Time)

Snow accumulation = 2 inches + (0.5 inches/hour × t hours)

Snow accumulation = 2 + 0.5t inches of snow.

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Answer:

x² - 4 = 0

x² = 4

x =± √4

x = +2 or x = -2.

Answer:

2 and -2 (±2)

Step-by-step explanation:

Step 1: Move -4 to the other side of the equal sign; we get x² = 4.

Step 2: A lot of people miss the negative answer! The square root of 4 is equal to both positive 2 and negative 2.

Answer:

-8/3

Step-by-step explanation:

Slope = (-1-7)/(6-3) = -8/3

Answer:

-8/3

Step-by-step explanation:

You can use the slope formula which is (y2 - y1) / (x2 - x1). So using these values we get

(-1 - 7) / (6 - 3) = -8/3

Answer:

Answer:

A,B,D

Step-by-step explanation:

The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

y = x³ - 5x + 2

The maximum is at dy/dx = 0, hence:

3x² - 5 = 0

x = -1.29 or x = 1.29

y = (-1.29)³ - 5(-1.29) + 2 = 6.3

The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29

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The sign of the leading coefficient can be found using the graph of a polynomial function.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have given the graph of polynomial functions:

In the first graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → -∞

Degree of a function = 3

In the second graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → -∞

Degree of a function = 4

In the third graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → ∞

Degree of a function = 4

In the fourth graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → ∞

Degree of a function = 3

Thus, the sign of the leading coefficient can be found using the graph of a polynomial function.

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Answer:

9

Step-by-step explanation:

a^2+b^2=c^2

a^2+12^2=15^2

a^2=225-144

a=sqrt(81)

a=9

An example of independent events is P(Police Officers and choose cars).

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent if we have:

P(A ∩ B) = P(A)P(B)

                    Police Officers         Firefighters

Cars               12                             3

Trucks            9                              4

SUVs              15                             2

Let  P(A) = Firefighters choose cars

P(B) = Firefighters choose Trucks

P(A ∩ B)  =  Police Officers choose cars

Thus,

P(A ∩ B) = P(A)P(B)

12 = (4) ( 3)

Hence,  an example of independent events is P(Police Officers and choose cars).

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Answer:

20

Step-by-step explanation:

492/99x100=21.43

nearest tenth percentage is 20

Answer:

X = ABC+ AB+ ABC

X = AB(C+1+C)

X = AB(2C+1)

a) Corresponding angles of similar figures are congruent, so [tex]\angle B \cong \boxed{\angle Z}[/tex]

b) Scale factor = (image)/(preimage). Since we are looking for ABCD to WZYX, this means that WZYX is the image and ABCD is the preimage. Thus, the scale factor is [tex]\frac{25}{10}=\boxed{5/2}[/tex]

c) Since the scale factor is 5/2,

[tex]\frac{20}{t}=\frac{5}[2}\\\\40=5t\\ \\ t=\boxed{8}[/tex]

Domain: (-∞,∞)

Range: (-∞,-3]

Step-by-step explanation:

A quadratic equation graphs a parabola. Therefore there will be arrows on the bottom of the graph as it will go down forever. The domain (min x-values to max x-values) is

(-∞,∞) because the graph keeps on going down and to the right and left. The range (min y-values to max y-values) is (-∞,-3] because the lowest y-value the graph goes to is -∞ nd the highest y-value is -3.

The Venn diagram to illustrate this information is given in the image attached.

The number of children who took plantain and beans only are:

Let  beans = a

Rice = b

Plantain = P

So:  a + b = 24 - 9 - 5 = 10

Note that 24 children took plantain.

9 children took only Plantain.

5 took the 3 food items.

So:

b + c = 18 -2 - 5 = 11

a + c = 21 - 3 - 5 = 13

P∩B = a + 5

= 6 + 5 = 11

R ∩ B = C + 5

=7 + 5 = 12

None of the three items of food =  

50 - (3 + 2 + 9 + 6 + 4 + 7 + 5)

= 50 - 36

=14

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Answer:

4/25

Step-by-step explanation:

4/5 ÷ 5 = 4/5 × 1/5 = 4/25