Problem 4. As a cold front passed through Denver, the temperature changed at the same
rate of 6 hours. The total change in temperature was -42 degrees. What was the change in
temperature each hour?

The initial value problem for the concentration of salt in the tank over time will be: dc/dt = [(1 g/L * 2 L/min) - (c * 2 L/min)] / 2000 L

An initial value problem (IVP) in multivariable calculus is an ordinary differential equation with an initial condition that determines the value of the unknown function at a specific location in the domain. In physics or other sciences, modelling a system typically entails addressing an initial value issue.

Let's call the concentration of salt in the tank "c" (in grams/liter).

The initial concentration of salt in the tank is: c(0) = 400 / 2000 = 0.2 g/L

The rate of change of concentration with time "t" (in minutes) can be represented as:

dc/dt = (inflow rate of saltwater - outflow rate of saltwater) / volume of tank

dc/dt = [(1 g/L * 2 L/min) - (c * 2 L/min)] / 2000 L

This is the initial value problem for the concentration of salt in the tank over time.

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The probability of not getting purple marble will be 64%. Then the correct option is A.

What is probability?

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Joseph has a bag filled with 2 red, 4 green, 10 yellow, and 9 purple marbles.

The total number of marbles is given as,

Total marbles = 2 + 4 + 10 + 9

Total marbles = 25

Then the probability of not getting purple marble will be given as,

P = 1 - 9 / 25

P = 1 - 0.36

P = 0.64

P = 64%

Hence, The probability of not getting purple marble will be 64%. Then the correct option is A.

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If the sum of $5000 is invested at rate of 5% per annum simple interest for 2 years then the amount of interest is $500  .

The amount of interest earned for a sum invested at a rate of 5% per annum simple interest for 2 years can be calculated using the formula:

Interest  = (P × R × T)/100 ;

Where:  I = interest  ,  P = principal (initial sum invested) = $5000

r = interest rate = 5%  ;  t = time = 2 years

Substituting the values into the interest  formula, we get:

Interest  = (5000 × 5 × 2)/100

On simplifying , we get Interest is = $500 .

Therefore, the amount of interest earned is $500.

The given question is incomplete , the complete question is

Find the amount of interest earned for time = 2 years , when the sum of $5000 is invested at rate of 5% per annum simple interest ?

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If water is being poured into the trough at a rate of 5 ft^3/min, the rate at which the water level is rising when the depth is 8 inches is 15√3/32 ft/min.

Length (L) = 8 feet

Side = 2 feet

If water is being poured into the trough at a rate of 5 ft^3/min. So

dV/dt = 5 ft^3/min

The depth is 8 inches.

h = 8 inches = 2/3 feet

The formula of volume (V) = √3/4 b^2 · L

Now putting the value

V = √3/4 b^2 · 8

Simplify

V = 2√3b^2

Using the Pythagorean Theorem

b/h = 2/√3

So b = 2/√3 h

Now putting the value of h in the volume V

V = 2√3(2/√3 h)^2

V = 2√3 × 4/3 × h^2

V = 8/√3 × h^2

Differentiating the equation with respect to t

dV/dt = 8/√3 d/dt(h^2)

dV/dt = 8/√3 × 2h dh/dt

dV/dt = 16h/√3 × dh/dt

As dV/dt = 5. So

5 = 16h/√3 × dh/dt

Multiply by √3 on both side, we get

16h dh/dt = 5√3

Divide by 16h on both side, we get

dh/dt = 5√3/16h

As h = 2/3. So

dh/dt = 5√3/(16×2/3)

After solving

dh/dt = 15√3/32 ft/min

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Using ratios, There are total 4 green marbles.

If b is not equal to 0, an ordered pair of numbers, a and b, expressed as a / b, is a ratio. A proportion is an equation that balances two ratios. As an illustration, the ratio could be expressed as follows: The ratio is 1:3 if there is 1 boy and 3 girls. (There are three girls for every one boy) Only one in four men are male, with three out of four being female.

In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of oranges to lemons on a fruit platter would be eight to six if there were eight oranges and six lemons.

Given,

The ratio of blue to orange to green is 4:2:1 ,

bag contains 8 blue marbles,

green marbles = 2x = 8

x = 4

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Answer:

I'm sorry, but I am not sure what you are asking or what this series of numbers and symbols represents. Can you please provide more information or context for me to understand your question?

Answer: x=7[tex]\sqrt{3}[/tex] and y = 14

Step-by-step explanation:

Slope of relationship between length of icicle and time = −0.6;

for every additional hour, the length of the icicle decreases by 0.6 inches

The correct option is D.

The slope of a line is defined as the change in vertical coordinate with respect to the change in horizontal coordinate of that line.

Given,

A student is measuring the length of an icicle, y, every hour, x

At present icicle is 9 inches long

melting at rate of 0.6 per hour

y = 9 - 0.6 x

Where y is the length of the icicle after x hours

comparing with slope intercept form of line: y = m x + c

slope m = -0.6

Hence, - 0.6 is the slope, represents that the length of the icicle decreases by 0.6 inches every hour.

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We can see that:

1. Given

2. Definition of supplementary angles

3. Substitution Property of Equality

4. Subtraction Property of Equality

5. If two angles have the same measure, then they are congruent.

In mathematics, an angle is a measure of the amount of rotation between two lines or planes. It is typically measured in degrees or radians, and can be represented symbolically using the Greek letter theta (θ). An angle can be acute, right, obtuse, or reflex, depending on the degree of rotation. It can also be formed by the intersection of two lines or by the rotation of a line about a point.

Angles are commonly used in geometry and trigonometry to measure and describe the relationships between shapes and figures.

We see here that the above answers are correct.

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Ram obtained 680 marks in his examination.

We have to use the concept of percent-to-decimal conversion to solve this problem.

Ram scored 85% of the total marks, which was 800 of the total. To find the number of marks he obtained, we have to multiply 800 by 85% (0.85).

85% is equivalent to 0.85 when expressed as a decimal. To find the number of marks Ram obtained, we have to multiply the total marks (800) by 0.85,

After multiplying 800 * 0.85 = 680 marks.

So the marks obtained by Ram in his examination are 680.

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Answer: Option D

Step-by-step explanation: to find the common difference, you'll subtract:

  From the sequence  4, 7, 10, 13, ...

d (common difference) = (7 - 4)   or   (10 - 7)   or   (13 - 10)

                                        = 3

As per the proportion the reason behind equal amounts of each color in every bag has the proportion less than the other colors.

The term called proportion is defined as  an equation that defines that the two given ratios are equivalent to each other

Here we know that they may not put equal amount of colors because they put the 2 most popular colors in the bag.

Because of the the popular colors of bag were Blue and Orange. Here as per the proportion of other color bags are less than that of blue and orange.

This is the real reason behind the Mars put more amount in more popular colors and less amount in less popular colors.

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Answer:

The solution fo the inequality x < -3 will be {-83, -6, -4, -3.5}. Then the correct option is C.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

x < -3

The value of the variable 'x' should be less than negative 3.

In option A, zero is greater than -3. So, option A is incorrect.

In option B, 1 is greater than -3. So, option B is incorrect.

In option D, -3 is equal to -3. So, option D is incorrect.

The arrangement of the imbalance x < - 3 will be {-83, - 6, - 4, - 3.5}. Then, at that point, the right choice is C.

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Step-by-step explanation:

Step-by-step explanation:

-5/8 = v + 48/8

-53/8 = v

-6 5/8 = v

Answer:

2 hours and 30 mins

Step-by-step explanation:

is 12 cookies made = 30 mins

then times both sides by 5

then,60 cookies made= 150 mins or 2 hours and 30 mins.

Answer:

150 min = 2,5 hours

Step-by-step explanation:

12 cookies ....... 30 min

1 cookie ........ 30/12 = 2,5 min

60 cookies ...... 2,5 * 60 = 150 min

Answer:

415

Step-by-step explanation:

4.15 ×

[tex]4.15 \: \times {10}^{2} [/tex]

The value of z that satisfies the condition p(-z < z < z) = 0.7372 is 0.8614.

Given: p(-z < z < z) = 0.7372

We are trying to find the value of z that satisfies the above condition.

The given condition p(-z < z < z) means that the value of z lies in the interval (-z, z) such that the probability of this interval is equal to 0.7372.

To find the value of z, we need to use the properties of normal distribution.

If X is a standard normal random variable, then the cumulative distribution function (CDF) of X, denoted by Φ(x), is given by:

Φ(x) = P(X ≤ x) = 1/√2π ∫-∞x e^-t^2/2dt

So, for the given condition, we have:

p(-z < z < z) = Φ(z) - Φ(-z) = 0.7372

We can use a standard normal table or a calculator with the cumulative normal distribution function to find the value of z that satisfies the above equation.

After using the cumulative normal distribution function, we find that z = 0.8614.

Therefore, the value of z that satisfies the condition p(-z < z < z) = 0.7372 is 0.8614.

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Answer:

C

the answer is C, the third graph

The set of ordered pairs of A and C represents a linear function.

The graph of a linear function is a straight line. The following is the form of a linear function.

a + bx = y = f(x).

One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.

Given ordered pairs:

A (-2,8) (0,4) (2,3) (4,2)

B (1,2) (1,3) (1,4) (1,5)

C (-2,7) (0,12) (2,17) (4,22)

D (3,5) (4,7) (3,9) (5,11)​

The definition of a linear function is the relationship between input and output values.

Range refers to the set of output values, and domain refers to the set of input values.

The fact that an input value cannot have two different output values is the most significant attribute of functions (which defines them). Having stated so, observe how sets B and D include pairings that defy this rule.

Therefore, since each input value only produces one output value, the correct solutions are A and C.

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The complete question:

Which set of ordered pairs X Y could represent a linear function of x

A (-2,8) (0,4) (2,3) (4,2)

B (1,2) (1,3) (1,4) (1,5)

C (-2,7) (0,12) (2,17) (4,22)

D (3,5) (4,7) (3,9) (5,11)​

Answer:

B

Step-by-step explanation:

First you are going to have to solve for one of the variables in the terms of the other two. The easiest one of these to start with is x.

If you take the first equation, x+4y-5z=-6 and solve for x you get

x=5z-4y-6

Now you can plug that into another equation and solve for another one of the variables. Lets use equation #2. Plugging in the definition of x into the equation you get;

(5z-4y-6)+4y-4z=-2

Simplify

z-6=-2

Conveniently, the y terms cancelled out. And therefore we know

z=4

(From there, we can determine that B is the right answer because it is the only one that gives z=4. I will walk you through the rest of the answer though)

Taking our new value of z, we can pug that value into our original x equation yielding;

x=20-4y-6

simplify

x=14-4y

Using this information, we can plug it into equation #3

(14-4y)+5y-16=1

simplify

y-2=1

solve

y=3

Now we just plug the new values of y and z into the first equation to get the value of x.

x+12-20=-6

simplify

x-8=-6

solve

x=2

Therefore;

x=2

y=3

z=4

length of the arc of the circle formed by this central angle is 12.56 units.

The formula for calculating arc length is used to determine the length of the arc's curved line (a segment of a circle). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. Arc stability, weld current, and part concentricity are all factors that affect arc length. Arc stability, weld current, and part concentricity are all factors that affect arc length. The commercial welder's job in this situation is to maintain the electrode at a specific distance from the surface so that there is adequate room to prevent stubbing out.

Since, the length of an arc on a circle is:

l = r × θ

Where, r is the radius of the circle and  is the central angle ( in radian ) made by the arc,

Here,

r = 8 unit,

θ = 90° = 90 × (π/180) = π/2

( π radian = 180°)

Hence, the length of the given arc is,

l = 8 × (π/2)

l = 4π

l = 12.56 units

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The sine function graphed is defined as follows:

y = sin(2x) + 2.

The sine function for this problem is defined as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

The difference between the highest and the lowest value of the function is of 3 - 1 = 2, hence the amplitude is obtained as follows:

2A = 3 - 1

2A = 2.

2A = 1.

The period is of π, hence the coefficient B is given as follows:

2π/B = π

B = 2.

A function with amplitude 1, with no vertical shift, would oscillate between -1 and 1, while this function oscillates between 1 and 3, hence the vertical shift C is given as follows:

C = 2.

Hence the function is defined as follows:

y = sin(2x) + 2.

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The equation of the line passing through the points (1,-5) and (3, -17) is y = -6x + 1.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

Points are  (1,-5) and (3, -17)

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

m = -17 + 5 / 3 - 1

m  = -6

The equation of the line is given as

y - y₁ = m (x - x₁)

y + 5 = -6 (x -1)
y = -6x + 1

Thus, the equation of the line passing through the points (1,-5) and (3, -17) is y = -6x + 1.

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Answer:

see below

Step-by-step explanation:

1: 180-90-45 =45

2. 180-90-26 = 64

3. 180-90-60 =30

Answer:

Step-by-step explanation:

1)  tan45 = x/10  

x = 10(tan45) = 10

cos45 = 10/y    

y = 10/(cos45) = 14.14

2) cos26 = 8/x  

x = 8/cos26 = 8.9

3) sin60 = y/12

y = 12(sin60) = 10.4

cos60 = x/12

x = 12(cos60) = 6

4)  Draw a line from top of triangle straight down and perpendicular to the 15 leg, label it z.  This divides the 15 leg into 2 segments: y and (15-y).

cos89 = y/12

y = 12(cos89) = 0.21

sin89 = z/12

z = 12

15 - 0.21 = 14.79

Now you can solve for x:

x² = 14.79² + 12²

x = [tex]\sqrt{362.74}[/tex] = 19

The finest-grain property simply means that all possible distinguishable outcomes are identified separately in probability statistics.

The requirement that outcomes be mutually exclusive says that if one outcome occurs, then no other outcome also occurs.

An outcome is often called a finest grain result of the model in the sense that an outcome ω contains no subsets other than the empty set ϕ and the singleton subset {ω}. A sample space is a set of all the possible outcomes or sample points, denoted as Ω. An outcome ω is often called a finest grain result when even {ω} contains no proper subsets. The outcomes in the sample space are mutually exclusive and collectively constitute the entire sample space.

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Answer:

[tex]28a[/tex]

Step-by-step explanation:

   Usually, the parenthesis in an expression = a(bc) indicates multiplication.

 Similarly, in 4(7a) we multiply -

4*7a = [tex]28a[/tex]

Hence the answer, study Hard

The percent markup is 66.67%.

The markup is the difference between the cost price and the selling price of a product, expressed as a percentage of the cost price.

Let's call the cost price of each shirt "cp". Then, the total cost price of 200 shirts would be 200 * cp.

The selling price of each shirt is $20, so the total revenue from selling 200 shirts would be 200 * $20 = $4000.

From the information given, we know that the total cost price of 200 shirts is $2400.

Therefore, we can set up the following equation to find the cost price of each shirt:

200 * cp = $2400

Dividing both sides by 200, we get:

cp = $12

The markup is the percentage increase from the cost price to the selling price, so it can be calculated as follows:

Markup = (Selling Price - Cost Price) / Cost Price * 100%

= ($20 - $12) / $12 * 100%

= 66.67%

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Answer:

765 [tex]ft^{2}[/tex]

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex]

A = (3.24)[tex]15^{2}[/tex]     [tex]15^{2}[/tex] means 15 x 15

A = (3.14(15)(15)

A  = 765

Answer:

  396 cm

Step-by-step explanation:

You want the distance traveled by a wheel of radius 21 cm in 3 revolutions.

The circumference of the wheel is ...

  C = 2πr

  C = 2π(21 cm) = 42π cm

In 3 revolutions of the wheel, it travels 3 times that distance, or ...

  3(42π cm) = 126π cm ≈ 396 cm

The distance traveled is about 396 cm.

__

Additional comment

The value shown is rounded to the nearest centimeter. The attachment shows the value to higher precision, for the usual approximations of pi.

<95141404393>