4) Janet runs half a mile in 1/3 of an hour.
How many miles can she run in one hour?
How far can she run in 4 hours?
I

your

Step-by-step explanation:

jsbsbnajdbdnsnsazxxss

Answer:

(0, 3 ), (5, 0), (10, -3), (15, -6)

Step-by-step explanation:

3x − 5y = 15

-5y = 3x + 15

y = \(-\frac{3}{5} x + 3\)

Point 1:  (0, 3 )

  y = -3/5(0) + 3

  y = 0 + 3

  y = 3

  Validate:

   3 = -3/5(0) + 3

   3 = 3

Point 2:  (5, 0)

  y = -3/5(5) + 3

  y = -3 + 3

  y = 0

  Validate:

   0 = -3/5(5) + 3

   0 = 0

Point 3:  (10, -3)

  y = -3/5(10) + 3

  y = -6 + 3

  y = -3

  Validate:

   -3 = -3/5(10) + 3

   -3 = -3

Point 4:  (15, -6)

  y = -3/5(15) + 3

  y = -9 + 3

  y = -6

 Validate:

   -6 = -3/5(15) + 3

   -6 = -6

Answer: For this problem, you cannot go over 10! so remember guys you can graph it however you want for example if you wanted to you could do -3/5(-2) + 3 for the first point but you would have to solve it. the next one would be maybe -3/5(-1) + 3 if you wanted to go up by plus one REMEMBER this is your OWN graph so do whichever number order you want it doesn't matter you can increase by 1 or 2 or 3 but the final point shouldn't be over ten or you will get the problem wrong. Good Luck I hope I get an A and I hope you guys get A's as well. Do ur absolute best on this

Answer:

$13

Step-by-step explanation:

multiply 65 by 80 then divide by 100, you get 52, so subtract 65 from 52 you get 13

Answer:

The system of equations is (x, y) = (13, 12).

Step-by-step explanation:

To evaluate the system of equations:

3x - 2y = 15

7x - 3y = 15

We can use either the substitution or elimination method to solve the system.

Using substitution method:

From the first equation, we can isolate x as follows:

3x - 2y = 15

3x = 2y + 15

x = (2/3)y + 5

Substitute this expression for x into the second equation:

7x - 3y = 15

7[(2/3)y + 5] - 3y = 15

Simplify and solve for y:

(14/3)y + 35 - 3y = 15

(-5/3)y = -20

y = 12

Now that we know y = 12, we can use either equation to solve for x:

3x - 2y = 15

3x - 2(12) = 15

3x - 24 = 15

3x = 39

x = 13

Therefore, the solution to the system of equations is (x, y) = (13, 12).

Rate of the jet in still Air is 716 miles per hour and

wind speed is 80 miles/hour.

The velocity of an item in relation to another observer is known as its relative velocity. It is the pace at which one item's relative location changes in relation to another object over time. When two bodies are travelling in opposing directions, their relative velocity is at its highest. They are approaching one another.

Let ‘X’ be speed of jet and

'Y’ be speed of Wind

Relative velocity when jet travels against wind: X - Y = ( 2544 / 4 ) = 636 miles/hour

Relative velocity when jet travels with wind is: X + Y = ( 3184 / 4 ) = 796 miles/hour

By adding these two equations we will get

2 X = 1432 or X = 716 miles /hour and

or, Y = 796 - 716 = 80 miles/hour

Hence,

Rate of the Jet in still Air is 716 miles per hour and

Wind speed is 80 miles/hour.

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As per area of rectangle, the dimensions of the box that yield the lowest cost is (1,1,6)

Area of rectangle:

The standard formula for area of rectangle is calculated as,

A = length x breadth

Given,

A closed rectangular box with volume 6 cubic feet is made from two different types of cardboard. the top and bottom are made with a heavy-duty cardboard that costs 30 cents per square foot. The sides are made from a light-weight cardboard that costs 5 cents per square foot.

Here find the dimensions of the box that yield the lowest cost.

Here let's consider the dimensions of the rectangular box be length l, breadth is b, and height is h.

Now, from the given information, the total cost can be derived as,

=> C=2lb×48+(2bh+2lh)×8

=> C=96lb+16bh+16lh

=> C=16(6lb+bh+lh) -----------------→(1)

Then the given volume is, V = lbh = 6 ---------------→(2) cubic feet.

Then the equation 2,

=> lbh = 6h = 6/lb

And then we have to substitute the value of h in equation 1, we get

=> C(l,b,h)=16(6lb+6/l+6/b)

Now we need to minimize the resulting function of two variables.

Therefore, we need to partially derivative the above function with respect to l,b. And set these equal to zero.

And the for l=0,b is undefined. So we can eliminate l=0.

Here we have to substitute l=1,b=112⇒1 in equation 2, we get

=> lbh=6(1)(1)h=6h=6h=6

Therefore, the critical point is, (1,1,6)

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To determine how many papers the newspaper boy should order each day, we need to consider his profit margin. His profit is the difference between the revenue earned from selling the papers and the cost of buying them.

The revenue earned is the number of papers sold multiplied by the selling price of $0.50. The cost of buying the papers is the number of papers ordered multiplied by the buying price of $0.30. Let's say he orders x papers each day. The expected value of his revenue can be calculated as x multiplied by the mean of 100 papers,

which is 100x. The expected value of his cost can be calculated as x multiplied by the buying price of $0.30, which is 0.3x. His profit can then be calculated as the difference between his revenue and cost, which is 0.2x (since the selling price of $0.50 minus the buying price of $0.30 is $0.20 profit per paper).

To maximize his profit, he should order the number of papers that gives him the highest expected profit. This occurs at the point where the deviation from the mean is zero. In other words, he should order the number of papers that gives him the highest probability of selling all of them, without having any unsold papers that he needs to throw away.

Using the formula for standard deviation, we can calculate that the probability of selling all 100 papers is 68.3%. The probability of selling 101 papers is slightly lower at 64.2%, while the probability of selling 99 papers is also slightly lower at 64.2%.

Therefore, to maximize his profit, the newspaper boy should order 100 papers each day, since this gives him the highest probability of selling all of them without having any unsold papers. This would give him a daily profit of $10 (100 papers sold x $0.20 profit per paper).

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The resultant moment about a both forces is zero. The statement is true.

A man B exerts a force on the rope, P = 30 lb

To find:

The magnitude of force, F

Consider a statement:

"The resultant moment about A of both forces is Zero."

Diagram attached at the end of the  solution

\($ \theta=\tan ^{-1}\left(\frac{3}{4}\right) \\\)

\(& \theta=36.87^0\)

To prevent the pole from rotating, so that the resultant moment is about A = 0

We will apply the equilibrium Equation \($\sum \mathrm{M}_{\mathbf{A}}=0$\)

Here force \($P \times \sin (45)$\) and \($F \times \sin (\theta)$\) will not produce the moment at A.

Taking clockwise moment as a negative and anticlockwise moment as a positive.

\(& \mathrm{P} \times \cos (45) \times(18)-\mathrm{F} \times \cos (\theta) \times 12=0 \\\)

\(& 30 \times \cos (45) \times(18)=\mathrm{F} \times \cos (\theta) \times 12 \\\)

\($ \mathrm{~F}=\frac{30 \times \cos (45) \times(18)}{\cos (36.87) \times 12} \\\)

F = 39.77 lb

Based on the given parameters,

The magnitude of force, F = 39.77 lb

So there exists the force by considering the resultant moment about an of both forces as zero.

The statement is true.

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The Fourier sine series of the derivative of a function with a jump discontinuity can be expressed in terms of the Fourier cosine series coefficients of the original function.

Let's consider the function f(x) with a jump discontinuity at x = x₀, where f(-x₀) = α and f(+x₀) = β. Since f(x) is continuous except for the jump discontinuity, it can be represented by a Fourier cosine series:

f(x) = A₀ + Σ(Aₙ*cos(nωx))

where A₀ represents the DC component, Aₙ are the Fourier cosine coefficients, and ω is the fundamental frequency.

Now, we want to determine the Fourier sine series of the derivative of f(x), denoted as df/dx. We know that the derivative of the cosine term Aₙcos(nωx) is given by -nωAₙsin(nωx). Thus, the derivative of f(x) can be written as:

df/dx = Σ(-nωAₙ*sin(nωx))

To express df/dx in terms of the Fourier cosine series coefficients, we need to find the Fourier sine series coefficients. These coefficients can be obtained by integrating df/dx over one period and dividing by the appropriate factor. However, since df/dx has jump discontinuity at x = x₀, we need to consider two separate integrals for x < x₀ and x > x₀.

By evaluating the definite integrals, we can express the Fourier sine series of df/dx in terms of the Fourier cosine series coefficients of f(x). This relationship allows us to determine the Fourier sine series representation of the derivative when the original function has a jump discontinuity.

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Answer:

\(m\text{ arc BC} =32\\m\angle 2=16\\m\angle3=74\\m\angle4=74\\m\angle5=16\)

Step-by-step explanation:

Arc BC is the intercepted arc for the central angle COB, so its measure is the same as the central angle.

Angle 2 is an inscribed angle, so its measure is half the measure of the intercepted arc BC.

Angles 3 and 4 are congruent inside an isosceles triangle (OB = OC, both radii), and the sum of all angles in triangle COB is 180 degrees, so

180 - 32 = 148 (sum of angles 3 and 4)

Each of angles 3 and 4 measure half that remaining 148 degrees.

Angle 5 is one of two congruent angles in an isosceles triangle AOC (OA = OC) so its measure is that of angle 2.

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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Answer:

Im pretty sure it is

Step-by-step explanation:

As you can see there is a pattern, +10, +15, then you see 260, you'd need 5 more numbers before getting to 260, in other words, +30, and not +15 or +10. So yes.

Answer:

$30.47

Step-by-step explanation:

100%-15%=85%
85%=0.85
$35.85*0.85=30.47 (to 2d.p)
Hope this helps

The diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.

An average is a mean or the central value obtained by dividing the sum of all data values by the number of data values.

Diver            Crabs observed     Dives     Average Crab per dive

Scuba Sam              33                     11               3

Wet Suit Willy          81                     18              4.5

Deep Diving Dan  104                    26              4

Thus, the diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.

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The polynomial p(x) has option (c) three real zeros because it has a relative maximum at (-2, 4), a relative minimum at (1,1), a relative maximum at (5,7), and a negative leading coefficient.

Since p(x) has a relative maximum at (-2, 4), a relative minimum at (1,1), and a relative maximum at (5,7), it means that the degree of the polynomial must be odd and at least three.

Moreover, we know that p(x) has no other critical points. This means that p(x) does not change sign between these relative extrema, which in turn implies that there are no real zeros between these extrema.

Therefore, the number of real zeros of p(x) is either one or three. To determine the answer, we need to consider the leading coefficient of p(x).

If the leading coefficient is positive, then p(x) must eventually increase on both ends, since the degree is odd. This means that there is exactly one real zero.

If the leading coefficient is negative, then p(x) must eventually decrease on both ends. In this case, since there are three relative extrema, there must be three real zeros.

Thus, we need to find the sign of the leading coefficient of p(x). This can be done by looking at the relative extrema.

Since p(x) has a relative maximum at (-2, 4), we know that the leading coefficient is negative.

Therefore, the correct option is (c) three.

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A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.

A polynomial p(x) has a relative maximum at (-2, 4), a relative minimum at (1, 1), and a relative maximum at (5, 7), with no other critical points. This means there are turning points at these coordinates. Since there are two relative maxima and one relative minimum, the polynomial must have at least 3 turning points.

A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.

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The equation of the following line include the following: E. y = -2x .

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (8 - 0)/(-4 - 0)

Slope (m) = 8/-4

Slope (m) = -2.

At data point (-4, 8) and a slope of -2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 8 = -2(x + 4)  

y - 8 = -2x - 8

y = -2x

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To round intermediate calculations and final answers to 2 decimal places, use the following steps:

1. Identify the number that needs to be rounded.

2. Look at the digit in the third decimal place.

3. If the digit is 5 or greater, round up the previous digit. If the digit is 4 or less, leave the previous digit as it is.

When performing calculations or obtaining results that involve decimal numbers, it is often necessary to round the values to a certain number of decimal places. In this case, we want to round the numbers 130,452.45 and 106,343.98 to 2 decimal places.

To achieve this, we focus on the third decimal place of each number. For 130,452.45, the digit in the third decimal place is 4, which is less than 5. Therefore, we leave the previous digit (2) unchanged, resulting in the rounded value of 130,452.45.

For 106,343.98, the digit in the third decimal place is 9, which is 5 or greater. In this case, we round up the previous digit (3) by adding 1, resulting in 106,344.00 when rounded to 2 decimal places.

Rounding to 2 decimal places ensures that the numbers are presented with a specified level of precision. It is important to follow consistent rounding rules to maintain accuracy and avoid misleading interpretations of the data.

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Answer:

The exponential function represents growth, the percentage rate of increase is 7.8 %

Step-by-step explanation:

Please see the attachment.

The exponential function represents growth, the percentage rate of increase is 7.8 %

Step-by-step explanation:

Do you mean 8 times what is 56?

8×7 is 56

Answer: 4x13x9= 468 ft.

Step-by-step explanation: To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units. The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.

Answer:

27cm

Step-by-step explanation:

so you are dumb for not nowing it

Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

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Answer:

C

Step-by-step explanation:

half of IQR is 17

110 + 17 = 127 (this represents the 3rd quartile)

110 - 17 = 93 (this represents the 1st quartile)

The 3rd quartile represents 75% of the data so 75% of the students complete the test in 127 minutes or less

The term used to describe an error that occurs when numbers are moved to the right or left in an amount column is "Slide".

Slide:

An accounting slide is a mistake that happens when the decimal point of a number is moved to the left or right of where it should be.

For instance, a bookkeeper would enter $1,200.50 in place of $12,005 in the revenue account or $250.75 in place of $2,507.50 in the monthly insurance expenses. In general, bookkeeping mistakes and accounting blunders lead to financial record misstatements.

"Slide" is the name for a mistake that happens when numbers are moved to the right or left in an amount column.

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SOLUTION

The functions are:

Notice that the function f(x) was translated 1 unit to the right and 2 units downward to ge

We are given v = ds/dt, v = 9.8t + 9, s(0) = 17. We need to find the position of a body moving along a coordinate line at time t.

Using the formula of velocity, we can integrate it with respect to t to find the position of the body at any time t. The formula for velocity is:v = ds/dt... (1) Integrating equation (1) with respect to t, we get's = ∫vdt + C ...(2)

Here, C is the constant of integration, and it is found using the given initial position. Given, s(0) = 17Substitute s = 17 and t = 0 in equation (2).17 = ∫(9.8t + 9)dt + C [∵ s(0) = 17]17 = 4.9t² + 9t + C

Therefore, C = 17 - 4.9t² - 9tOn substituting the value of C in equation (2), we get:s = ∫vdt + 17 - 4.9t² - 9t ...(3)Now, we can substitute the given velocity, v = 9.8t + 9, in equation (3).s = ∫(9.8t + 9)dt + 17 - 4.9t² - 9ts = 4.9t² + 9t + 17 - 4.9t² - 9ts = 9t + 17

Hence, the position of the body at time t is 9t + 17 units.

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In a paired design, each pair of observations does not necessarily consist of measuring the same individual twice. Instead, a paired design involves matching pairs of individuals or units based on certain criteria or characteristics and then measuring each individual in the pair under different conditions or at different time points.

This design is often used to compare the effects of different treatments or interventions within the same individuals or to control for individual-specific factors. In a paired design, the pairing could be based on various factors such as age, gender, pre-existing conditions, or other relevant characteristics. For example, in a study evaluating the effectiveness of a new medication, researchers may pair individuals with similar characteristics (e.g., age, gender, severity of the condition) and then administer the new medication to one individual in each pair while providing a placebo to the other individual. By measuring the outcomes within each pair, the researchers can directly compare the effects of the medication and the placebo within the same individuals.

The key aspect of a paired design is that the pairs are matched based on certain criteria, and each pair represents a unique combination of individuals. This allows for a more controlled comparison within the pairs and helps minimize the influence of individual-specific factors on the outcomes of interest.

In summary, a paired design involves matching pairs of individuals based on certain characteristics and comparing the outcomes within each pair. It does not require measuring the same individual twice but rather focuses on comparing different conditions or treatments within matched pairs of individuals.

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Answer:

x+5

Step-by-step explanation:

I thought what 2 numbers if multiplied made 15

also 2x+3 already has a 3

so I'm guessing 3 and 5

then I put them next to each other

(2x+3) ( +5)

I put a x in the second parenthesis as a guess because the area had a 2x^2 in it . that could only happen with 2x * x

so (2x+3) (x+5)