Identify the equation of the line with the given slope and Y intercept,

This problem can be solved with integration. The first step is to integrate f '(t) dt. We use the integration formula for this purpose.The function f(t) has been found using the differential equation f'(t) = sec(t)(sec(t) tan(t))

f '(t) = sec(t)(sec(t) tan(t))

Integral calculus is used to find f(t) since it deals with derivatives.

Let's solve it.

f '(t) = sec(t)(sec(t) tan(t)) f(t) = ∫f '(t) dt

Using the integration formula,

f(t) = ∫ sec^2(t)dt = tan(t) + C [where C is the constant of integration]

f(t) = tan(t) + C

Now we have f(4) = -7. To find the value of C, we'll use

f(4) = -7=tan(4) + C7 = 1.1578 + C C = -7 - 1.1578 = -8.1578

Thus, the function

f(t) = tan(t) - 8.1578.

Therefore,The function f(t) has been found using the differential equation f'(t) = sec(t)(sec(t) tan(t))

In conclusion,f '(t) = sec(t)(sec(t) tan(t)) has been solved using integration. The value of the constant of integration, C, was found using the value of f(4) = -7. The function f(t) = tan(t) - 8.1578 is the solution to the differential equation.

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Answer:

a = 5120

b = 1.25

Step-by-step explanation:

Let the exponential function representing the given table is,

f(x) = \(a(b)^x\)

Here, f(x) = Number of views

x = Number of weeks

We choose two points from the given table and satisfy the equation of the function.

Let the points are (0, 5120) and (1, 6400)

For a point (0, 5120),

f(0) = a(b)⁰ = 5120

a = 5120

Now for the second point (1, 6400),

6400 = 5120(b)¹

b = \(\frac{6400}{5120}\)

b = 1.25

Therefore, a = 5120 and b = 1.25 are the values.

Answer:

f(x)=8(0.5)^x

Step-by-step explanation:

Two events that are disjoint are not independent. This is because that disjoint events do not overlap, which means that if one event occurs, the other cannot. So, the occurrence of one event provides information about the absence of the other, which violates the definition of independence.

Two events A and B are considered independent if the occurrence of A has no effect on the likelihood of B occurring, and vice versa.

In other words, the probability of both events happening at the same time is equal to the product of their individual probabilities:

\(P(A and B) = P(A) * P(B) (B).\)

This formula cannot be satisfied when two events are disjoint because if one event occurs, the other cannot occur. As a result, two disjoint events are not independent.

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Answer:

.

Step-by-step explanation:

Answer:

9222.23333 is the value good sir :)

Step-by-step explanation:

Answer:

x = 112

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 35 when x = 140, then

35 = 140k ( divide both sides by 140 )

0.25 = k

y = 0.25x ← equation of variation

When y = 28, then

28 = 0.25x ( divide both sides by 0.25 )

x = 112

Answer:

x= -14

Step-by-step explanation:

All the solutions are;

1) Circle

2) A point

3) An oval that becomes more elongated as the angle with the horizontal increases.

4) An isosceles triangle.

Since, A cross-section is a plane section that is a section of a three-dimensional object that is parallel to one of its planes of symmetry or perpendicular to one of its lines of symmetry.

Now, We can formulate;

1) Plane Parallel to the circular base, not passing through the tip of the cone:

⇒ Circle.

2) Plane Parallel to the circular base, passing through the tip of the cone:

⇒ A point.

3) Plane not parallel to the base, not passing through the base, and making an angle with the horizontal that is less than that made by the slant height of the cone:

⇒ An oval that becomes more elongated as the angle with the horizontal increases.

4) Plane making an angle with the horizontal that is greater than that made by the slant height, passing through the tip of the cone :

⇒ An isosceles triangle.

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Answer:

\(y\ =\ \ \tan\theta\ +2\)

Step-by-step explanation:

Answer:

5/3*1/5= 1/3

Step-by-step explanation:

change the mixed fraction into improper fraction which is 1*3+2=5

then multiply

Answer:

-7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

The conversion time for a 12-bit ADC with a clock frequency of 1 MHz is 12 microseconds (μs).

The conversion time for a 12-bit ADC with a clock frequency of 1 MHz is 13 microseconds.

An Analog to Digital Converter (ADC) transforms an analog signal into a digital signal.

The conversion time for an ADC (Analog-to-Digital Converter) can be calculated using the formula:

Conversion Time = (Number of ADC Cycles x Clock Period)

For a 12-bit ADC with a clock frequency of 1 MHz, each conversion requires 12 cycles of the ADC clock. The clock period can be calculated as the inverse of the clock frequency:

Clock Period = 1 / 1,000,000 = 1 μs

Therefore, the conversion time can be calculated as:

Conversion Time = (12 x 1 μs) = 12 μs

So the conversion time for a 12-bit ADC with a clock frequency of 1 MHz is 12 microseconds (μs).

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Answer: 3 pieces of pie

Step-by-step explanation:

You gave Joe two pieces at first, then you gave joe another piece of pie

2 + 1 = 3 pieces of pie

Answer:

You will be able to spend your money for a total of 16 days.

Step-by-step explanation:

Total money won: $48

Since you are starting off with $48, divide the amount of money you will be using each day. 48 divided by 3 is equal to 16.

From the given curve we found that

T(1) = 2i + 2j

N(1) = (1/sqrt(2))i + (1/sqrt(2))j

An(1) = i + j

To find the tangent vector T(t), normal vector N(t), acceleration vector At, and normal acceleration vector An at the given time t for the curve r(t) = t^2i + 2tj, we need to compute the derivatives of the position vector r(t) with respect to time.

The tangent vector is the derivative of the position vector with respect to time:

T(t) = r'(t) = d(r(t))/dt

Differentiating each component of r(t):

T(t) = (d(t^2)/dt)i + (d(2t)/dt)j

= 2ti + 2j

At t = 1:

T(1) = 2(1)i + 2j

= 2i + 2j

The normal vector is obtained by normalizing the tangent vector:

N(t) = T(t) / ||T(t)||

Finding the magnitude of T(t):

||T(t)|| = sqrt((2t)^2 + 2^2)

= sqrt(4t^2 + 4)

= 2sqrt(t^2 + 1)

Normalizing the tangent vector:

N(t) = (2i + 2j) / (2sqrt(t^2 + 1))

= (i + j) / sqrt(t^2 + 1)

At t = 1:

N(1) = (i + j) / sqrt(1^2 + 1)

= (i + j) / sqrt(2)

= (1/sqrt(2))i + (1/sqrt(2))j

The acceleration vector is the derivative of the velocity vector with respect to time:

At(t) = d(T(t))/dt

Differentiating each component of T(t):

At(t) = (d(2t)/dt)i + 0j

= 2i

At t = 1:

At(1) = 2i

Normal acceleration vector An:

The normal acceleration vector is obtained by projecting the acceleration vector onto the normal vector:

An(t) = (At(t) · N(t)) * N(t)

Calculating the dot product of At(t) and N(t):

At(t) · N(t) = (2i) · ((1/sqrt(2))i + (1/sqrt(2))j)

= (2/sqrt(2)) + (0/sqrt(2))

= sqrt(2)

Projecting the acceleration vector onto the normal vector:

An(t) = (sqrt(2)) * ((1/sqrt(2))i + (1/sqrt(2))j)

= i + j

At t = 1:

An(1) = i + j

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5 ori 5 fac 25 și cu 25 egal 14 și cu 14 egal 100 și cu 100 egal 12

Step-by-step explanation:

sper ca team ajutat

Answer:

∠ 6 = 45°

Step-by-step explanation:

∠ 6 and 45° are vertically opposite angles and are congruent , so

∠ 6 = 45°

Answer:

9

Step-by-step explanation:

1/5 of 30 is 6 or 30/5. 1/2 of 30 is 15 or 30/2. 6+15=21. 30-21=9

(a)The range of the given set of measurements is 4.

(b)The sample mean of the given set of measurements is approximately 5.625.

(c)The sample variance of the given set of measurements is approximately 2.337768, and the sample standard deviation is approximately 1.529.

(a) The range is the difference between the largest and smallest values in the set of measurements. In this case, the largest value is 8 and the smallest value is 4, so the range is 8 - 4 = 4.

To calculate the range, we subtract the smallest value from the largest value. In this case, the largest value is 8 and the smallest value is 4.

Range = Largest value - Smallest value

Range = 8 - 4

Range = 4

The range provides a simple measure of the spread or dispersion of the data. In this case, the range tells us that the values range from the smallest value of 4 to the largest value of 8, with a difference of 4 between them.

(b) The sample mean, denoted as x, is the sum of all the measurements divided by the total number of measurements.

To calculate the sample mean, we add up all the measurements and then divide by the total number of measurements. In this case, we have 8 measurements.

Sum of measurements = 4 + 4 + 7 + 6 + 4 + 6 + 6 + 8 = 45

Sample mean = Sum of measurements / Total number of measurements

Sample mean = 45 / 8

Sample mean ≈ 5.625

The sample mean represents the average value of the measurements and provides a measure of central tendency.

(c) The sample variance, denoted as s^2, measures the variability or dispersion of the data points around the sample mean. It is calculated as the average of the squared differences between each measurement and the sample mean.

To calculate the sample variance, we first calculate the squared difference between each measurement and the sample mean. Then, we average those squared differences.

Squared difference for each measurement:

(4 - 5.625)^2 = 2.890625

(4 - 5.625)^2 = 2.890625

(7 - 5.625)^2 = 1.890625

(6 - 5.625)^2 = 0.140625

(4 - 5.625)^2 = 2.890625

(6 - 5.625)^2 = 0.140625

(6 - 5.625)^2 = 0.140625

(8 - 5.625)^2 = 5.390625

Sum of squared differences = 2.890625 + 2.890625 + 1.890625 + 0.140625 + 2.890625 + 0.140625 + 0.140625 + 5.390625 = 16.364375

Sample variance = Sum of squared differences / (Total number of measurements - 1)

Sample variance = 16.364375 / (8 - 1)

Sample variance ≈ 2.337768

The standard deviation, denoted as s, is the square root of the sample variance.

Sample standard deviation = √(Sample variance)

Sample standard deviation = √(2.337768)

Sample standard deviation ≈ 1.529

These measures provide information about the dispersion or spread of the data points around the sample mean. A higher variance or standard deviation indicates greater variability in the measurements.

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Answer:

The 1 represents a whole number, and 28/99= .28282828 (the repeating decimal wanted)

Therefore 1.28= 1 28/99

Step-by-step explanation:

Answer:

because we want to learn with there meaning. so first we want to study about what that picture is tell about and what is the shape, why it is use. so only they uses the properties. we not magup the maths. we want learn and write.

Step-by-step explanation:

please mark me as a brainlist..

Answer:

Total amount spent for meal = $16.65

Step-by-step explanation:

Given:

Amount spent on dinner = $20

Tip = 20%

Find:

Total amount spent for meal

Computation:

Total amount spent for meal = Amount spent on dinner / (1+tip)

Total amount spent for meal = 20 / 1.2

Total amount spent for meal = 16.666

Total amount spent for meal = $16.65

(i) The probability that 2 pears and 1 orange are eaten in any order is equal to \(\frac{14}{55}\)

(ii) The probability that the third fruit eaten is an orange is equal to \(\frac{7}{15}\)

(iii) The probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is equal to \(\frac{6}{11}\)

What is Probability?

What are Combinations?

Here, it is given that the box contains 4 pears and 7 oranges in the box.

So, the total number of fruits in the box = 4 + 7 = 11

Combination when 2 pears is chosen out of 4 pears from the box \(= {4 \choose 2} = \frac{4!}{2!(4-2)!} =6\)      

Combination when 1 orange is chosen out of 7 oranges from the box \(= {7 \choose 1} = \frac{7!}{1!(7-1)!} =7\)

Combination when 2 pears and 1 oranges are taken from the box containing a total of 11 fruits \(= {11 \choose 3} = \frac{11!}{3!(11-3)!} =165\)

So, the probability that 2 pears and 1 orange are eaten, in any order,

\(P(A) =\frac{ {4 \choose 2} \times {7 \choose 1} }{ {11 \choose 3} } \\\implies P(A) = \frac{6 \times 7}{165} \\\implies P(A) = \frac{14}{55}\)

Now, the probability that the third fruit eaten is an orange is given as,

\(P(B)= \frac{{1 \choose 4}{1 \choose 3}{1 \choose 7}+{11 \choose 4}{1 \choose 7}{1 \choose 6}+{1 \choose 7}{1 \choose 6}{1 \choose 5}}{A(11,3)} \\P(B)=\frac{460}{990} \\P(B)=\frac{7}{15}\)

Next, we can find the probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is a conditional probability problem where one event depends on another event.

The probability that the third fruit is orange P(A) is equal to 7/15

The probability that the first fruit eaten was a pear is calculated as,\(P(C)= \frac{{1 \choose 4}{1 \choose 3}{1 \choose 7}+{11 \choose 4}{1 \choose 7}{1 \choose 6}}{A(11,3)} \\P(C)=\frac{252}{990} \\P(C)=\frac{14}{55}\)

So, according to conditional probability,

Probability of C given A,

\(P(C/A)=\frac{P(C \cap A)}{P(A)} \\\implies P(C/A)=\frac{\frac{14}{55} }{\frac{7}{15} } \\\implies P(C/A)=\frac{6}{11}\)

There, the (i) probability that 2 pears and 1 orange are eaten in any order is equal to \(\frac{14}{55}\)

(ii) probability that the third fruit eaten is an orange is equal to \(\frac{7}{15}\)

(iii) probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is equal to \(\frac{6}{11}\)

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Answer:

P(t) = 10t - 400

Step-by-step explanation:

Selling price of each ticket = $10

Cost of setting up the dance= $400

Profit = Revenue - cost

Revenue = price × quantity

Revenue that will maximize profit = 10t

where t= quantity of tickets that maximises profits

Cost = $400

Profit(t) = Revenue - cost

P(t)= 10t - 400

We want to find the equation that represents the school's profit. We will get:

P(x) = $10*x - $400

We know that the tickets to the school dance are sold for $10 each, then the revenue, if they sell x tickets, is just:

r(x) = $10*x

And we know that they spent a total of $400.

Remember that profit is defined as the difference between revenue and costs, so the profit equation is just:

P(x) = $10*x - $400

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Answer:

150m^2

Step-by-step explanation:

Given data

a=8m

b=17m

h=12m

We know that the expression for the area of a trapezoid is given as

Area= (a+b/2)*h

substitute

Area= (8+17/2)*12

Area= 25/2 *12

Area= 12.5*12

Area= 150 m^2

Hence the area is 150m^2

Answer:

y=6

RS= 47

ST= 22

RT= 69

Step-by-step explanation:

Average rate of change ... of what?

Given some continuous function \(f(x)\) and some interval \([a,b]\), its average rate of change over the interval is

\(\dfrac{f(b)-f(a)}{b-a}\)

Without knowing what your function is exactly, I can only give a symbolic answer,

\(\dfrac{f(18)-f(0)}{18}\)

Answer: -5/18

Step-by-step explanation: edg

Answer:

solution,

given,

10 + 8 × 90 ÷ 9 - 4

=10 + 8 ×10 - 4

=10 + 80 - 4

=90 - 4

=86

Step-by-step explanation:

it is simplify . In simplification, we solve it by following rules bracket,divide, multiply, add and subtract. please remind it

i think it was helpful for all of you.

Answer:

im not exactly sure but i think it would be y=1x-2