A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank. Write and solve a system of equations to find the family’s paddling speed in still water. Let s equal the families paddling speed and c represent the current
a.
s + c = 2.75
s - c = 1.5
2.125 mi/h
c.
s + c = 2.75
c - s = 1.5
.60 mi/h
b.
2.75s = c
1.5s = c
1.725 mi/h
d.
2.75c = s
1.5c = s
30 mi/h

Answer:

8

-5

12

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The average rate of change of a function f(x) on interval [a, b] is the slope of the line through points (a, f(a)) and (b, f(b)). The slope formula tells you that is ...

  m = (f(b) -f(a))/(b -a)

1) The rate of change in the interval [1, 2] is ...

  rate of change = (2³ -1³)/(2 -1) = (8 -1)/1 = 7

__

2) rate of change = ((√4 -8) -(√1 -2))/(4 -1) = (-6-(-1))/3 = -5/3

__

3) rate of change = (11 -(-1))/(5 -2) = 4

Answer:

Reflection over y=x

Step-by-step explanation:

Answer:

40 + 5 = 45

45 ÷ 9 = 5

Therefore, he will have 5 boxes of rocks.

Answer:

2.70 decimeters

Step-by-step explanation:

1 cm = 0.1 decimeter

27 * 0.1 = 2.7

Answer:

number 3 is 30, number 4 is 46 and the last one is 55

Answer:

3. 30°

4. 46°

5. 55°

Step-by-step explanation:

You add the two known angle measures and subtract that number from 180, since all the angle measures will add up to 180°. Hope this helped!

Answer:

Part A: The equation of the planet's orbit is simply the equation of a circle with radius 70 (half the diameter) and center at the origin. The standard form equation of a circle with radius r and center at (h,k) is (x-h)^2 + (y-k)^2 = r^2. In this case, h and k are both 0, so the equation of the planet's orbit is simply x^2 + y^2 = 70^2.

Part B: The equation of the comet's path is a parabola with directrix x=100 and vertex at (85, 0). The standard form equation of a parabola with directrix x=p, vertex at (h,k), and focus at (h,k+f) is y = (4f/p^2)(x-h)^2 + k. In this case, p=100, h=85, k=0, and f is the distance from the vertex to the focus. We can find f by using the equation f = sqrt(p^2+4ah), where a is the distance from the vertex to the directrix. In this case, a=50, so f = sqrt(100^2+45085) = 50. Plugging this value into the equation for the parabola, we get y = (4*50/100^2)(x-85)^2 + 0. Simplifying this gives us y = (2/25)(x-85)^2.

Part C: To find the points where the planet's orbit intersects the path of the comet, we need to find the points where the x and y coordinates of the two equations are equal. Setting the two equations equal to each other gives us (2/25)(x-85)^2 = x^2 + y^2 - 70^2. Expanding the left side and rearranging the terms gives us x^2 - 170x + 15129 = 0. We can use the quadratic formula to find the solutions for x: x = (170 +/- sqrt(170^2 - 4115129))/2. This simplifies to x = 85 +/- sqrt(40900). Therefore, the points of intersection are (85 + sqrt(40900), 0) and (85 - sqrt(40900), 0). Rounding these values to the hundredths place gives us (92.84, 0) and (77.16, 0).

The given function will be represented by a straight line graph, as shown below in the attachment.

On a coordinate plane, functions can be graphed. To graph a function, first select several input values and compute the outputs. The x value is the independent variable, and the y value is the dependent variable. Plot the points and connect them with a line or a curve, depending on whether the function is linear or curvilinear.

Linear functions are written as y = mx + b, where m is the slope of the line and b is the y-intercept. A linear function's graph is a straight line that represents a constant rate of change between two variables. All other functions are curvilinear or non-linear.

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The fraction 20/3 rounded to the nearest hundredth is 6.67.

We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, A fraction 20/3, First we'll convert this fraction into a decimal.

So, 20/3 is equal to 6.666666....

Therefore,  20/3 to the nearest hundredth of a foot is equal to 6.67.

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Answer:

Below

Step-by-step explanation:

S = dt        S = distance    d = rate = 6.5 m/ hr    t = time = 30 min = 1/2 hr

S = (6.5 m/hr) *(1/2 hr) = 3.25 miles

The value of distance you will run will be;

⇒ Distance = 3.25 miles

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

You are going to run at a constant speed of 6.5 miles per hour for 30 minutes.

Here,

Speed = 6.5 miles per hour

Time = 30 minutes

        = 30/60 hour

        = 1/2 hour

We know that;

⇒ Speed = Distance / Time

Substitute all the values we get;

⇒ 6.5 = Distance / (1/2)

⇒ 6.5 × 1/2 = Distance

⇒ Distance = 3.25 miles

Thus, We get;

⇒ Distance = 3.25 miles

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Answer:

[tex]\frac{29}{6}[/tex]

Step-by-step explanation:

Multiply the denominator by the whole number.

6 × 4 = 24

Add the answer from step 1 to the numerator.

24 + 5 = 29

Write answer from step 2 over the denominator

[tex]\frac{29}{6}[/tex]

Answer:

true

Step-by-step explanation:

Therefore ,option 3 is hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.

Any three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.

Here,

From the provided figure, it is clear that there are two triangles.

ABC and EFG are the triangles.

AB = EF

AC = FG

BC = EG

As a result, the triangles ABC and EFG are congruent according to the triangle's SSS theorem, and angle A is equal to angle D.

Therefore ,D and E are hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.

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Answer:

From lowest to highest, the numbers would follow the following order:

1) 4.606, 2) 4.64, 3) 4 + 13/20, 4) 47/10.

Step-by-step explanation:

Given that the numbers 47/10, 4.606, 4 + 13/20 and 4.64 are presented, to order these from lowest to highest, the following calculations must be performed:

47/10 = 4.70

4,606

4 + 13/20 = 4 + 0.65 = 4.65

4.64

Therefore, from lowest to highest, the numbers would follow the following order:

1) 4.606, 2) 4.64, 3) 4 + 13/20, 4) 47/10.

Answer:

600 pounds of gunk

Step-by-step explanation:

Given data:

Initial volume of water = 200 gallons

Initial mass of gunk = 100 pounds

dumping rate of pipe( contaminated water into tank ) = 16 gallons per minute

concentration of Gunk = 0.6 pounds / gallon

removal rate of second pipe = 14 gallons per minute

Determine how much gunk will be in the tank when the tank is full

Amount of gunk when tank is full = 599.99 pounds ≈ 600 pounds ≈

Attached below is a detailed solution

Sodium has two radioactive cosmogenic isotopes (22Na, half-life = 2.605 years; 24Na, half-life = ~ 15 hours) that have been used as tracers in hydrologic studies.

Sodium-24, a radioactive isotope having a half life of 15 hours is used medically in blood studies and it decays by beta decay.

Na has received considerable attention in hydrologic research because it is a mobile element that participates in precipitation and dissolution reactions in ground water (clay formation, albitization of plagioclase). Their short half-lives (i.e. high decay rate) make their measurement relatively easy by common radioanalytical techniques.

Substantial concentrations of 22Na and 24Na have been measured in precipitation (Roedel, 1970; Perkins et al., 1970). However, no studies have as yet been published documenting the cosmogenic sodium systematics in ground or surface waters.

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Answer:

Not a function

Step-by-step explanation:

please help!!! HURRY!!

Answer:

Step-by-step explanation:

10,14,18

Answer:

Given a GP where:

Formula for nth term:

Recursive formula

Explicit formula:

Answer: solve the same variables

Step-by-step explanation:

1. 3y + 4.1

2. 4x +

3. 5x + 22½

4. 4y²

5. + 25

6. 0



Answer:

147.33

Step-by-step explanation:

mupitply 26*17 and then dived my 3

Answer:

The formula to generate 70% confidence interval is: [tex][\overline{x} - 0.013, \overline{x} + 0.013][/tex], in which [tex]\overline{x}[/tex]  is the sample mean.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.7}{2} = 0.15[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.15 = 0.85[/tex], so Z = 1.037.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Assume that body masses of Goldfinch birds follow a normal distribution with standard deviation equal to 0.04 oz.

This means that [tex]\sigma = 0.04[/tex].

Sample of 10 birds:

This means that [tex]n = 10[/tex].

The margin of error is of:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 1.037\frac{0.04}{\sqrt{10}}[/tex]

[tex]M = 0.013[/tex]

The lower end of the interval is the sample mean of [tex]\overline{x}[/tex] subtracted by M.

The upper end of the interval is the sample mean of [tex]\overline{x}[/tex] added to M.

Then, the formula to generate 70% confidence interval is: [tex][\overline{x} - 0.013, \overline{x} + 0.013][/tex], in which [tex]\overline{x}[/tex]  is the sample mean.

Answer:

it's 30

Step-by-step explanation:

30+4_2= dakukabilat

Answer:b

Step-by-step explanation:

Answer:

[tex]\frac{6}{10}, \frac{7}{10}, \frac{8}{10},\frac{9}{10}[/tex] (in general, the numerator has to be greater than half the denominator)

Step-by-step explanation:

There are an infinite number of fractions greater than 1/2, but we can generally form a rule to figure out whether a fraction is greater than 1/2, which will help us find those fractions!

Let's first just express a fraction in the form: [tex]\frac{a}{b}[/tex], and we have to ask our self, what determines whether this is 1/2? Well we know if we have 1/2, and multiply it by two, then we have a whole, or one, but the only case where we have a whole, or one, in fraction form, is where the numerator and denominator are equal.

This means, multiplying the numerator "a" by 2, will result in it being equal to the denominator "b". From here, it can be determined that for the fraction: [tex]\frac{a}{b}[/tex], to be 1/2, then the numerator "a" has to be half the denominator "b". But this is just telling us what "a" and "b" need to be, for the fraction to be equal to 1/2, not greater than 1/2. This is still useful, since in general the following is true: [tex]\frac{a+1}{b}[/tex], if we add one to the numerator, the fraction becomes bigger. So if we want the fraction to be bigger than 1/2, the numerator "a" just needs to be bigger or larger than the half the denominator "b".

Let's select a denominator, and from there find numerators that make the fraction bigger than 1/2. For this example let's just select "9". In this case, for a fraction to be 1/2, the numerator just has to be larger than 9/2 or 4.5, but since we can't have decimals in fractions, or at least proper fractions, we just need the numerator to be greater than or equal to 5 (5 is included, since it's still bigger than 4.5)

[tex]\frac{4}{5}[/tex] is actually the only proper fraction, since 5/5 would just simplify to one.

Let's do another example, in this case let the denominator be 10. For the fraction to be considered greater than 1/2, the numerator, has to be greater than half the denominator, 10/2 = 5.

[tex]\frac{6}{10}, \frac{7}{10}, \frac{8}{10},\frac{9}{10}[/tex] would all be valid answers (although some do simplify further). But all of them represent fractions which have a greater value than 1/2

Answer:

The Answer is B

Step-by-step explanation:

Answer:

722 cm ^2

Step-by-step explanation: