Olumide plays the piano and quitar. for every five minutes of piano practice, he spends 8minutes practicing guitar. how many minutes will olumide practice piano if he spends 64 minutes practicing guitar

The differential equation that expresses Newton's Law of Cooling is:

dT/dt = -k(T - A)

The dependent variable in this differential equation is T, representing the temperature of the coffee.

The independent variable in this differential equation is t, representing time in minutes.

The value of the constant A is 70 ∘ F.

The differential equation is:

dT/dt = -k(T - 70)

To solve the differential equation, we can separate the variables T and t and integrate both sides with respect to t:

1/(T - 70) dT = -k dt

Integrating both sides, we get:

ln|T - 70| = -kt + C_1

where C_1 is a constant of integration.

Exponentiating both sides, we get:

|T - 70| = e^C_1 * e^(-kt)

Now, since T cannot be negative, we can drop the absolute value signs, and we get:

T(t) = Ce^(-kt) + 70

where C = ±e^C_1 is another constant of integration.

We are given T(0) = 194 ∘ F and T(1) = 168 ∘ F. Plugging these values into the equation T(t) = Ce^(-kt) + 70, we get the following two equations:

194 = Ce^0 + 70   -->   C = 124

168 = 124e^(-k) + 70

Solving the second equation for k, we get:

k = ln(54/124)

Plugging in the values of C and k, we get:

T(t) = 124e^(-ln(54/124)t) + 70

Simplifying, we get:

T(t) = 54e^(-0.693t) + 70

We want to find the time it takes for the coffee to cool to 130 ∘ F. This means we need to solve for t in the equation T(t) = 130. Plugging in the values we found for C and k, we get:

130 = 54e^(-0.693t) + 70

Subtracting 70 from both sides and dividing by 54, we get:

0.3704 = e^(-0.693t)

Taking the natural logarithm of both sides, we get:

ln(0.3704) = -0.693t

Solving for t, we get:

t = ln(0.3704)/(-0.693) ≈ 1.93 minutes

Therefore, approximately 1 minute and 56 seconds pass until Dr. Wahl should begin drinking the coffee.

learn more about differential equation here

https://brainly.com/question/32645495

#SPJ11

Each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.

Let the cost of an adult-fare bus pass be A student-fare bus pass costs half as much as an adult-fare pass, hence, the cost of a student pass will be $129 - A.

Mathematically, this is represented as:A = 2($129 - A) $A = $258 - 2A 3A = $258 A = $86Therefore, the cost of an adult-fare bus pass is $86.A student pass costs half as much as an adult-fare pass.

Since the cost of an adult-fare pass is $86, therefore the cost of a student pass will be half of $86. Mathematically, this can be represented as:Cost of student pass = 1/2 x $86 = $43

Therefore, each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.

Know more about adult-fare here,

https://brainly.com/question/2263713

#SPJ11

Answer:

VERTICAL AND COMPLEMENTARY

Answer:

294 cubic inches

Step-by-step explanation:

Answer:

x = 94

Step-by-step explanation:

(86 + x)/2 = 90

86 + x = 180

x = 94

The given numbers are in ascending order are, -3.5, -√12, 3.5, √13.

What is ascending order?

Ascending order refers to a list of numbers that are arranged from least to greatest. The numbers are arranged in ascending order in this form. The first figure must be less than the second figure. It is referred to as descending order when the numbers are listed from greatest to least.

Consider, the given numbers

-√12,  √13,  -3.5,  3.5

We have to arrange these numbers in ascending order.

First to find the values of  -√12, and √13,

Here,

-√12 = -3.46

 √13 = 3.6

Now we arrange the numbers -3.46,  3.6, -3.5, 3.5 in ascending order.

⇒ -3.5, -3.46, 3.5, 3.6

⇒ -3.5, -√12, 3.5, √13

Hence, the given numbers are in ascending order are,

-3.5, -√12, 3.5, √13.

To know more about ascending order, click on the link

https://brainly.com/question/1094377

#SPJ1

Answer: 170

Step-by-step explanation:

Answer:

15.6 units (3 s.f.)

Step-by-step explanation:

The distance between 2 points is given by the formula below, where \((x_1, y_1)\) is the first coordinate and \((x_2, y_2)\) is the second coordinate.

\(\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}\)

Using the distance formula above,

distance between A(-3, 1) and B(7, 13)

= \(\sqrt{(13-1)^{2} + [7-(-3)]^{2} } }}\)

= \(\sqrt{12^2+(7+3)^2}\)

= \(\sqrt{244}\)

= 15.6 units (3 s.f.)

Additional:

To learn more about the distance formula, do check out: https://brainly.com/question/8283882

The number of text messages that would result in the same cost per month is 200 text messages.

Based on the information provided above, Pay Per Text Plan charges $10 per month and $0.10 for each text message. Therefore, the total cost, y, can be represented by this equation:

y = 0.10x + 10    .......equation 1.

where:

x represents the number of text messages.

Based on the graph for the Frequent Text Plan, the total cost, y, can be represented by this equation:

y = x(25 - 20)/100 + 20 = 0.05x + 20 ....equation 2.

By equating equation 1 and equation 2, we have the following:

0.05x + 20 = 0.10x + 10

0.10x - 0.05x = 20 - 10

0.05x = 10

x = 10/0.05

x = 200 text messages.

Read more on equation here: brainly.com/question/18912929

#SPJ1

Complete Question:

A customer is comparing two different text message plans at Cellular Bargains. He wants to find out which plan allows the most text messages for the same cost. The Pay Per Text Plan charges $10 per month and $0.10 for each text message. The Frequent Text Plan is modeled by the graph shown above. How many text messages would result in the same cost per month for the two plans?

Answer:

D

or nine times seventy

Answer:

9 x 60

Step-by-step explanation:

yes

Answer:

30.7

Step-by-step explanation:

sin 71° = 29/ ladder length

so length = 29/ sin 71° = 30.7

So,

Let me graph the three points here below:

To classify this triangle by its sides, the first thing we need to do is to find the measure of each segment. For this, we could use the formula for the distance between two points for each one.

Let's start with segment WX.

Now, continue with XY:

And finally, WY:

As you can see, sides WY and WX are equal. So, the triangle has two equal sides and one different.

For this reason, the triangle is an isosceles triangle.

Answer:

B. 1,190 square cm

Step-by-step explanation:

For given prism:

l = 16 cm, w = 7 cm, h = 21 cm

Surface area of of the prism

\(= 2 (lw + wh + hl) \\ = 2(16 \times 7 + 7 \times 21 + 21 \times 16) \\ = 2(112 + 147 + 336) \\ = 2 \times 595 \\ = 1190 \: {cm}^{2} \\ \)

I don't know lol ididjdjdj

Answer:

C = 7.72 ~ 7.7

Step-by-step explanation:

So when you solve this equetion you must 1st find x then c

we can find x by using cos(60)

cos(60) = x/14

x = cos(60) × 14

x = 1/2 ×14

x = 7

so after we find x we are going to solve c by using cos (25)

cos (25) = X/C = 7/c

cos(25) × C = 7

C = 7/cos (25)

C = 7.72 ~ 7.7

so the solution is 7.7

Answer:

1. 45

2. 105

3. 95

4. 85

Step-by-step explanation:

For problems 1 and 4:

Consecutive angles are supplementary in a parallelogram, which means they equal 180.

180 - 135 = 45

180 - 95 = 85

For problems 2 and 3:

Opposite angles are congruent or equal each other in a parallelogram,

Refer to the images attached.

Answer:

4

Step-by-step explanation:

What you have typed is

\( \frac{ {3}^{12} \times {2}^{10} \times {2}^{ - 8} }{ {3}^{12} }\)

=3^12 cancels out

\( \frac{1 \times {2}^{2} }{1} \)

=4

Answer:

54.2

Step-by-step explanation:

we want to find m∠T

Recall the three main trig functions

sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent

we are given the side length opposite of ∠T ( SU ) and the adjacent (TU)

when dealing with the opposite and adjacent we use tan

tan = opposite / adjacent

opposite (SU) = 18 and adjacent (TU) = 13 ( let ∠T = x )

So tan(x) = 18/13

* take the inverse tan of both sides *

arctan(tan(x)) = x

acrtan (18/13) = 54.2

we're left with x = 54.2 meaning that ∠T = 54.2

The number of valid ways to construct the cube is \(4096 - 48 = 4048\)

Each corner of the cube is formed by three wires coming together. Since the wires are soldered together at the ends, each corner must have either 3 silver wires or 3 copper wires coming together.

There are two choices for each wire: it can be silver or copper. Since there are 12 edges in a cube, there are 2 choices for each edge, giving a total of \(2^12 = 4096\) possible arrangements of the edges.

However, not all of these arrangements are valid. We must eliminate the arrangements where at least one corner has two silver wires and one copper wire

There are 8 corners in a cube, and for each corner, there are 3 ways to choose which wire is different from the other two. Once we choose which wire is different, there are 2 choices for its color (silver or copper). Thus, there are \(8 x 3 x 2 = 48\) invalid arrangements.

for such more questions on arrangements

https://brainly.com/question/1427391

#SPJ11

The probability that it takes from 2 to 3 minutes to fill an order is approximately 0.2562 or 25.62%.

Given that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes.

We know that the probability density function (PDF) of exponential distribution is given by:

f(x) = (1/β) * e^(-x/β)

where β is the mean of the distribution.

Therefore, in this case, the PDF is:

f(x) = (1/1.5) * e^(-x/1.5)

To find the probability that it takes from 2 to 3 minutes to fill an order, we need to calculate the area under the PDF curve between 2 and 3 minutes.

P(2 < x < 3) = ∫2^3 f(x) dx

= ∫2^3 (1/1.5) * e^(-x/1.5) dx

= [-e^(-x/1.5)]2^3

= e^(-2/1.5) - e^(-3/1.5)

= 0.2562

Therefore, the probability that it takes from 2 to 3 minutes to fill an order is approximately 0.2562 or 25.62%.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ11

Two measures of central tendency commonly used are the mean and the median.

The mean is the arithmetic average of all the scores in a dataset. It is calculated by summing up all the scores and dividing by the total number of scores. The mean is sensitive to extreme values or outliers, as it takes into account every value in the dataset.

The median, on the other hand, is the middle value when the data is arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values. The median is less affected by extreme values or outliers, as it only considers the position of values relative to each other, rather than their actual values.

When the distribution of scores on the variable is skewed due to an outlier, the median would be a more valid measure of center. This is because the median is not influenced by extreme values and is less affected by the shape of the distribution. It provides a more robust estimate of the central tendency, especially in cases where there are significant outliers pulling the mean away from the typical values.

To know more about measures of central tendency,

https://brainly.com/question/17351419

#SPJ11

7 out of 6 ymto a mixed number is

1¹/6

Answer:

y= -3.5x +10

Step-by-step explanation:

The first thing to do in this equation is solve for m, the slope of the line.

Because we are given that the y-intercept is 10, we know that the graph intercepts at the point (0,10).

We are also given the point (5,-7.5).

Using the two points we can solve for the slope!

To solve for the slope use this formula: \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

(-7.5 -10) / (5 -0)

= -3.5

So our slope, m = -3.5

The other missing value is b, but is very easy to find.

In this example, b is equal to the y-intercept, so b=10.

Now we can plug in the values we found into the original equation

y =mx+b

y= -3.5x +10

Answer:

The value of x = 0    

Step-by-step explanation:

Given

To determine

The value of x = ?

If we closely observe the value of the y-coordinate of the image B'(x, 20), we can see that the y-coordinate of the image B' is 4 times the y-coordinate of the original point (0, 5).

i.e. y → 5×4 =20

It means the coordinates of the image B'(x, 20) can be determined by dilating the original point (0, 5) by a scale factor of 4.

Thus, the x-coordinate of B'(x, 20) can also be obtained by multiplying the x-coordinate of B(0, 5) by 4.

i.e. x → 4×0 = 0

Thus, the rule of dilation is:

P(x, y) = P'(4x, 4y)

Hence,

B(0, 5) → B'(4(0), 4(5)) → B'(0, 20)

Thus,

The value of x = 0           ∵ 0×4 = 0

If Binita is going to buy 450 envelopes. The amount in pounds (£), it will cost Binita to buy the envelopes from Value World is 0.72 pounds.

First step is to calculate the cost for letter2go

Cost =  450 / 25 × 3.29

Cost = 59.22

Second step is to calculate the cost for value world

Cost = 450 /30 × (1.95 ×2)

Cost = 58.50

Now let calculate the cost of buying the envelopes from value world

Cost = 59.22 - 58.50

Cost = 0.72 pounds

Therefore the cost is 0.72 pounds.

Learn more about cost here: https://brainly.com/question/1153322

#SPJ1

Answer:

All you have to do is turn x-2y=6 into y=mx+b form. That would mean you need to get y by itself. Subtract x from 6. Then you have -2y=6-x. Now you have to divide both sides of the equation by -2. So then you have -2y/-2 = 6-x/-2. That turns out to y=3-1/2x Which is easier read by: y=1/2x - 3

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

These ratios are different because they express the number of laps for two different numbers of hours.

To better understand how these ratios compare, let's simplify the second ratio:

192 laps/ 8 hours = 24, which means the ratio would be 24 laps per hour

This means that the ratios express the same number of laps per hour.

Basically, the two ratios tell us the number of laps but using different hours. In this way, the first ratio expresses the number of laps in only one hour, while the second ratio amplifies this ratio to eight hours.

Learn more about ratios in https://brainly.com/question/13419413

#SPJ1

Answer:

ASA

Step-by-step explanation:

Angle BAC and angle CDE are congruent ( indicated by a single dashed dashed line on the angle )

Side AC and side DC are congruent ( also indicated by a single  dashed line )

Angle DCE and angle BCA are congruent ( this is because they are vertical angles and vertical angles are congruent )

Hence, the two triangles are congruent because of the congruency statement ASA

( angle. side, angle )