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dalvyx [7]
2 years ago
11

If a person rows to his favorite fishing spot 21 miles downstream in the same amount of time that he rows 7 miles

Mathematics
1 answer:
klio [65]2 years ago
8 0

28 miles upstream requires 28/7 = 4 hours.

28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.

How long does it take him to cover 28 miles?

Apply the distance formula:

d = rt

where

d is distance

r is rate or speed

t is time

21 = t*(r+7)  = rt+ 7t

7 = t *(r-7)   = rt - 7t

            28 = 2rt

             14 = rt

             21 = rt + 7t

             21 = 14 + 7t

               7 = 7t

                 t=1

              21 = (r+7)*1 = r+7

                r = 14

The speed of the boat is 14 mph. With the current (downstream), the speed is 14+7 = 21 mph, so 21 miles are traveled in 1 hour. Against the current (upstream), the speed is 14-7 = 7 mph, which means 7 miles are traveled in the same 1-hour time frame.

28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.

28 miles upstream requires 28/7 = 4 hours.

To learn more about sequences refer to:

brainly.com/question/340538

#SPJ9

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One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for t
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Hi, did you forget to attach the two-way table to the question? I can't seem to see it, so I can't answer your question

8 0
3 years ago
What is the measure of
Nastasia [14]

Answer:

70

Step-by-step explanation:

The sum of the angles of a triangle should always add up to 180 degrees.

In this problem, they have given us 2 angle measures of the triangle - 40 degrees and 70 degrees. To figure out the third angle, we simply need to figure out how many more degrees we need for reaching the 180 degrees.

I'm just going to do some simple math:

40 + 70 = 110 (sum of the 2 angles)

180 - 110 = 70 (subtracting 180 by the sum of the 2 angles)

3 0
2 years ago
A researcher wanted to see if giving a selective serotonin reuptake inhibitor (anti-depressant) would decrease the number of sel
Delvig [45]

Answer:

a. The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

b. z=-1.6

c. SEM = 2.212

Step-by-step explanation:

The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

<u>Sample mean</u>

<u />M=\dfrac{1}{8}\sum_{i=1}^{8}(27+25+32+40+43+37+35+38)\\\\\\ M=\dfrac{277}{8}=35

<u>Sample variance and standard deviation</u>

<u />s^2=\dfrac{1}{(n-1)}\sum_{i=1}^{8}(x_i-M)^2\\\\\\s^2=\dfrac{1}{7}\cdot [(27-(35))^2+(25-(35))^2+(32-(35))^2+(40-(35))^2+(43-(35))^2+(37-(35))^2+(35-(35))^2+(38-(35))^2]\\\\\\

s^2=\dfrac{1}{7}\cdot [(58.141)+(92.641)+(6.891)+(28.891)+(70.141)+(5.64)+(0.14)+(11.39)]\\\\\            s^2=\dfrac{273.875}{7}=39.125\\\\\\s=\sqrt{39.125}=6.255

b. If the population mean is 45, the z-score for M=35 would be:

z=\dfrac{M-\mu}{\sigma}=\dfrac{35-45}{6.255}=\dfrac{-10}{6.255}=-1.6

c. The standard error of the mean (SEM) of this group is calculated as:

SEM=\dfrac{s}{\sqrt{n}}=\dfrac{6.255}{\sqrt{8}}=\dfrac{6.255}{2.828}=2.212

4 0
3 years ago
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. 3 sin(x2)
sweet [91]

The value of the given statement according to the mid point theorem is 5.

According to the statement

we have given that the equation and we have to integrate it with the help of the mid point theorem.

So, For this purpose, we know that the

The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

So, The given equation is

\int\limits^6_0 {Sinx } \, dx

where n = 4

And

The mid point formula is a with limits a to b is

f(x) dx ≈ Δx (f (x₀ + x₁)/2) + (f (x₁ + x₂)/2) + ... (f (xₓ₋₂ + xₓ₋₁)/2) + (f (xₓ₋₁ + x)/2))

Then

Where Δx = (b-a)/n

Recall that

a= 0

b= 64 and

n=4, therefore,

Δx = (64-0)/4 = 16

The next step requires that the interval [0,64] be divided into 4 sub-intervals with length = Δx =16

Hence, we've got, 0, 16, 32, 48, 64.

From this point, we calibrate the respective functions as follows:

f (x₀ + x₁)/2) = f ((0+16)/2) = f(8) = Sin (8) = 0.98935824662

(f (x₁ + x₂)/2) = f((16+32)/2) = f(24) =Sin (24) = -0.905578362

(f (x₂ + x₃)/2) = f((32+48)/2) = f(40) = Sin (40) = 0.74511316047

(f (x₃ + x₄)/2) = f((48+64)/2) = f(56) = Sin (56) = -0.52155100208

At this point, we sum up the above values derive the product of the total and Δx = 16

sin (x) dx = 16(0.98935824662 - 0.905578362 +  0.74511316047 - 0.52155100208)

= 16 (0.30734204301)

= 4.91747268816

\int\limits^6_0 {Sinx } \, dx = 5

So, The value of the given statement according to the mid point theorem is 5.

Learn more about Mid point theorem here

brainly.com/question/9635025

#SPJ4

4 0
1 year ago
Given the vector equation ????(t)=(4−3t)????+(−5+t)????+(3−t)????, rewrite this in terms of the parametric equations for the lin
Anit [1.1K]

Answer:

The parametric equations for the line.x(t)=

y(t)=

z(t)=

is  

 \= r (t) =  \left \{ {{x(t)= 4-3t} \atop {y(t)= -5+t}}  \atop {z(t)=3-t}} \right \}

Step-by-step explanation:

From the question we are told that

      the given equation is

                \= r(t) =  (4-3t) + (-5 + t) + (3-t)

This given equation can be represented as

             \= r (t) =  [4 -3t , -5+t,3-t]

Generally this equation can be represented in terms of the parametric equations as follows

   \= r (t) =  \left \{ {{x(t)= 4-3t} \atop {y(t)= -5+t}}  \atop {z(t)=3-t}} \right \}

This above equation is obtained by assigning each component of r(t) to each  line

4 0
3 years ago
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