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The rate of the plane in still air is 1130 km/hr and the rate of the wind is: 140 km/hr

Let the speed of plane in still air be p km/hr and wind speed be w km/hr.

The speed of plane with air is (p + w) km/hr and speed of plane against air is (p − w) km/hr

Flying with air: (p + w)⋅4 = 5080

or p + w = 1270  ----(1)

Flying against air: (p − w)⋅9 = 8910

or p − w = 990;(2)

Adding equations (1) & (2) we get,

(p + w) + (p − w) = 1270 + 990

or 2p = 2260

∴ p = 2260/2

= 1130 km/hr.

Putting p = 1130 in equation (1)

we get,

1130 + w = 1270

or

w = 1270 − 1130

w = 140  km/hr.

The speed of plane in still air is 1130 km/hr and wind speed is  140 km/hr.

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The nth term of the sequence 1, 7, 13, 19 is given by the formula: nth term = 1 + (n - 1) * 6 = 19

To discover the nth time period of the sequence 1, 7, 13, 19, we want to become aware of the sample or rule that governs the sequence.

In this case, we look at that every time period will increase by way of 6 in contrast to the preceding term.

We can categorical this sample in the following equation:

nth time period = 1 + (n - 1) * 6

Let's follow this equation to discover the nth term:

For n = 1:

nth time period = 1 + (1 - 1) * 6

= 1 + zero * 6

= 1

For n = 2:

nth time period = 1 + (2 - 1) * 6

= 1 + 1 * 6

= 1 + 6

= 7

For n = 3:

nth time period = 1 + (3 - 1) * 6

= 1 + two * 6

= 1 + 12

= 13

For n = 4:

nth time period = 1 + (4 - 1) * 6

= 1 + 3 * 6

= 1 + 18

= 19

As we can see, the equation efficiently generates the given phrases of the sequence.

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The relationship between the quantities shown in the table is +10. The values in column 2 (y) are obtained by adding 10 to the corresponding values in column 1 (x).

In the given table, the values in column 1 (labeled "x") are 1, 2, 3, and 4. The values in column 2 (labeled "y") are 11, 22, 33, and 44.

To determine the relationship between the quantities in the table, we can compare the values in column 2 (y) with the corresponding values in column 1 (x).

If we subtract each value in column 1 from the corresponding value in column 2, we find that:

11 - 1 = 10

22 - 2 = 20

33 - 3 = 30

44 - 4 = 40

By observing these results, we can see that the difference between each value in column 2 and its corresponding value in column 1 is always 10.

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Rounding to the nearest hundredth, the area of the sector is approximately 49.06 cm².

To find the area of the sector of a circle, you can use the formula:

Area = (θ/360) * π * r²,

where θ is the central angle in degrees, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.

In this case, the central angle is 225° and the radius is 5 cm. Plugging these values into the formula, we get:

Area = (225/360) * 3.14 * (5 cm)²

Area = (0.625) * 3.14 * 25 cm²

Area ≈ 49.0625 cm²

Rounding to the nearest hundredth, the area of the sector is approximately 49.06 cm².

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Answer:

[tex]\mathrm{5m}[/tex]

Step-by-step explanation:

[tex]\mathrm{sin30^o=\frac{p}{h}}\\\\\mathrm{or,\ \frac{1}{2}=\frac{Y}{10}}\\\\\mathrm{or,\ Y=5m}[/tex]

Answer: -20.4 pounds

Step-by-step explanation:

To find the total weight Judy lost, you would multiply the amount she lost each week (1.7 pounds) by the number of weeks she has been dieting (12 weeks).

1.7 pounds/week * 12 weeks = 20.4 pounds

Since the weight loss is to be expressed as a negative number, Judy's total weight loss is -20.4 pounds.

Para determinar la distancia recorrida por el balón, podemos usar el teorema de Pitágoras para calcular la distancia horizontal y vertical por separado y luego sumarlas.

La distancia horizontal entre Ana y el edificio es de 30 metros, mientras que la altura del edificio es de 10 metros. Dado que el balón alcanza el techo del edificio, la distancia vertical recorrida es igual a la altura del edificio, es decir, 10 metros.

Utilizando el teorema de Pitágoras, podemos calcular la distancia recorrida por el balón:

Distancia recorrida = √(Distancia horizontal^2 + Distancia vertical^2)

= √(30^2 + 10^2)

= √(900 + 100)

= √1000

≈ 31.62 metros

Por lo tanto, la distancia recorrida por el balón es aproximadamente 31.62 metros.

The implicit general solution is 0.5y² = -0.5x² + 0.5x + C, here C should pass through the origin of the circle. The family of curves (T)  represents the integral curve. The graph (T) is represented below.

a. To find the implicit general solution of the given differential equation, we can integrate both sides with respect to x. Let's start by rewriting the equation:

yy' = -x + 1/2

Integrating both sides:

∫ yy' dx = ∫ (-x + 1/2) dx

Using integration by parts on the left side, let u = y and dv = y' dx:

[tex]\int u dv = uv - \int v du\\\\y\int dy = \int (-x + 1/2) dx\\\\1/2 y^2 = -1/2 x^2 + 1/2 x + C\\\\0.5y^2 = -0.5x^2+0.5x+C[/tex]

Where C is the constant of integration. This is the implicit general solution of the given differential equation.

b. The family of curves (T) that represents the general solution in an orthonormal system is known as the integral curves of the differential equation.

c. To find the graph (T) that passes through the origin O(0, 0), we substitute the point (x, y) = (0, 0) into the implicit general solution and solve for C:

[tex]1/2(0)^2 = -1/2(0)^2 + 1/2(0) + C\\\\0 = 0 + 0 + C\\\\\C = 0[/tex]

So the graph (T) that passes through the origin is given by:

[tex]1/2 y^2 = -1/2 x^2 + 1/2 x[/tex]

This equation represents the specific curve that satisfies both the differential equation and the condition of passing through the origin.

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Answer:

  20579.53 m³

Step-by-step explanation:

You want the volume of a sphere 34 m in diameter.

The formula for the volume of a sphere is ...

  V = (4/3)πr³ . . . . . where r is half the diameter

In terms of diameter, this is ...

  V = (4/3)π(d/2)³ = (π/6)d³

  V = (π/6)(34 m)³ ≈ 20,579.53 m³

The volume of the sphere is about 20,579.53 cubic meters.

<95141404393>

hello

the answer to the question is:

[tex]p = 2\pi \: r \\ 36 = 2 \times 3.14 \times r \\ r = 5.7 \: m \\ \\ v = \frac{4}{3} \pi {r}^{3} \\ v = \frac{4}{3} \times 3.14 \times {5.7}^{3} \\ = 775.3 \: {m}^{3} [/tex]

Answer:

The two lines are parallel to each other.

Step-by-step explanation:

We see that the two lines are both in slope-intercept form, whose general equation is y = mx + b, where

When two lines have the same slope, they are parallel to each other.

Answer:To make the equality 1+23+45=65 true by inserting parentheses, you can group the numbers and operations in the following way:

(1+2)*(3+4)*5 = 65

This can be calculated as:

3 * 7 * 5 = 65

So, by adding parentheses as (1+2)(3+4)5, the equality 1+23+45=65 becomes true.

Answer:

Step-by-step explanation:

Area= height * base

therefore:

Area= 6*5

       = 30

Answer:

2f+15

Step-by-step explanation:

f toy cars

toy dolls : 2f+15

option number 4

The answers to the questions are as follows: 1: FD = 1.1. 2: 25%. 3: There is a weak, negative linear association. 4: scatter plot with points plotted at 1,9, 3,7, 4,5, 4,6, 5,3, 6,4, 7,4, 8,4, 9,2, and 10,1, with a line drawn through 7,4 and 9,2.

Question 5: 90° clockwise rotation. 6: y = one-half times x minus 3. 7: Reflection across the x-axis and 8: option B. is the answer.

Going through each question step by step:

1. (Similar Triangles):

Triangle ABC is similar to triangle DEF. We are given the measurements of sides AB, CA, BC, and DE. However, more information to determine the measurement of side FD. Without additional information or ratios between corresponding sides, calculate the length of FD. The correct answer is: FD=1.1.

2. (Experimental Probability):

To find the probability of no heads, we need to find the frequency of outcomes where no heads occur. Looking at the table, we see that "Tails, Tails" occurs 50 times. The total number of trials is 200. Therefore, the probability of no heads is 50/200 = 25%. The correct answer is: 25%.

3. (Scatter Plots):

The scatter plot displays the relationship between the number of cupcakes and the cost per cupcake. By examining the plotted points, we can see that as the number of cupcakes increases, the cost per cupcake generally decreases. This indicates a negative association. However, the association is not very strong since the points do not form a perfect straight line. The correct answer is: There is a weak, negative linear association.

4. (Line of Fit):

The scatter plot shows a set of points. To determine which graph represents a line that fits the data, we need to examine the plotted points. Looking at the options, the scatter plot with a line drawn through the points (7,4) and (9,2) seems to follow the general trend of the data points. The correct answer is: scatter plot with points plotted at 1,9, 3,7, 4,5, 4,6, 5,3, 6,4, 7,4, 8,4, 9,2, and 10,1, with a line drawn through 7,4 and 9,2.

5. (Identifying Transformations):

The graph shows the original polygon ABCD in quadrant 1 and the transformed polygon A'B'C'D' in quadrant 4. By comparing the coordinates of corresponding points, we can observe a clockwise rotation of 270°. The correct answer is: 270° clockwise rotation.

6. (Linear Relationships):

A proportional relationship between two variables means that they are directly proportional, or in other words, they have a constant ratio. Looking at the given options, "y = one-half times x" represents a proportional relationship since the coefficient of x is the constant ratio. The correct answer is: y = one-half times x.

7. (Reflections):

The graph displays two polygons, ABCDE and A'B'C'D'E'. By comparing the coordinates of corresponding points, we can observe that the transformation results in a reflection across the x-axis. The correct answer is: Reflection across the x-axis.

8. (Graphing Linear Equations):

The painter pays $60 for supplies, which is a fixed cost, and charges $20 per room painted, which is a variable cost. This relationship can be represented by a linear equation. To graph it, we can plot the fixed cost of $60 as the y-intercept (0, 60) and use the slope of $20 per room to find additional points. The correct answer is: a coordinate grid with the x-axis labeled "rooms painted" and the y-axis labeled "amount of money earned" and a line going from the point (0, 60) through the point (3, 120).

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Answer:

Step-by-step explanation: the answer is opstion 3

The equation of the circle with center (0,0) that passes through the point (-6,-6) is  x^2 +y^2 = 72. So, the correct option is A.

To find the equation of a circle, we need to know the center coordinates and the radius. In this case, the center of the circle is given as (0,0), which means the x-coordinate and y-coordinate of the center are both 0.

The radius can be determined by calculating the distance between the center and the given point on the circle, (-6,-6). We can use the distance formula, which is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Plugging in the coordinates of the center (0,0) and the given point (-6,-6), we get:

d = √((-6 - 0)² + (-6 - 0)²)

= √((-6)² + (-6)²)

= √(36 + 36)

= √72

= 6√2

The radius of the circle is 6√2.

Now we can use the standard form equation of a circle, which is:

(x - h)² + (y - k)² = r²

Where (h, k) represents the center coordinates and r represents the radius. Substituting the values, we have:

(x - 0)² + (y - 0)² = (6√2)²

x² + y² = 72

So, the equation of the circle with center (0,0) that passes through the point (-6,-6) is: x^2 +y^2 = 72

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The Function is increasing (-∞, 0), decreasing (2, ∞), and constant [0, 2].

The intervals on which the function is increasing, decreasing, or constant, we need to analyze the behavior of the function in each interval.

1. Interval t < 0:

In this interval, the function is given by f(t) = t + 2. Since the coefficient of t is positive (1), the function is increasing. Therefore, the interval t < 0 is an interval of increasing values.

2. Interval 0 ≤ t ≤ 2:

In this interval, the function is constant and given by f(t) = 2. The value of the function remains constant at 2 for all values of t in this interval.

3. Interval t > 2:

In this interval, the function is given by f(t) = -t + 4. Since the coefficient of t is negative (-1), the function is decreasing. Therefore, the interval t > 2 is an interval of decreasing values.

To summarize:

Increasing interval: t < 0

Decreasing interval: t > 2

Constant interval: 0 ≤ t ≤ 2

Using interval notation, we can express the intervals as follows:

Increasing interval: (-∞, 0)

Decreasing interval: (2, ∞)

Constant interval: [0, 2]

In interval notation, (a, b) denotes an open interval, which means it includes all values between a and b, but excludes the endpoints. [c, d] denotes a closed interval, which includes both endpoints c and d.

Therefore, the function is increasing on the interval (-∞, 0), decreasing on the interval (2, ∞), and constant on the interval [0, 2].

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Answer:

[tex]f(x)=8\sin(2\pi x)[/tex]

Step-by-step explanation:

The explanation is attached below.

Answer: f(x)=8sin(2πx)

Step-by-step explanation

Hope this explanation helps.  Please see the attachment.

Answer:

To solve the equation 3x²2 - 2x + 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 3, b = -2, and c = 4. Substituting these values into the quadratic formula, we have:

x = (-(-2) ± √((-2)² - 4(3)(4))) / (2(3))

x = (2 ± √(4 - 48)) / 6

x = (2 ± √(-44)) / 6

Since the discriminant (-44) is negative, the solutions involve imaginary numbers. Therefore, the answer is:

1 ± i√11

3

Hence, the correct answer is 1 ± i√√11/3.

Answer: $1652.17

Step-by-step explanation:

First, let's calculate the hire purchase cost of the video game set.

The hire purchase cost is the initial deposit plus the total cost of the monthly installments.

The total cost of the monthly installments is $171 * 12 = $2052.

So, the total hire purchase cost is $190 (deposit) + $2052 (total monthly payments) = $2242.

Now, let's calculate the selling price of the video game set if no sales tax is included.

If the marked price of $1900 includes a 15% sales tax, we can calculate the pre-tax price (the selling price without the tax) by dividing the marked price by 1 plus the tax rate.

The tax rate in decimal form is 15% = 0.15.

So, the selling price without the tax would be $1900 / (1 + 0.15) = $1900 / 1.15 = approximately $1652.17.

The model for S(t) is given as:

S(t) = (-0.03t^2 + 1.6t - 13.65)^(-1)

This model predicts the searching period length in days. It is an inverse function of the quadratic equation (-0.03t^2 + 1.6t - 13.65). As the temperature increases, the searching period decreases, indicating that the larvae are more efficient at finding the host tree at higher temperatures.

To calculate S(25), we substitute t = 25 into the equation:

S(25) = (-0.03(25)^2 + 1.6(25) - 13.65)^(-1)

= (-0.03(625) + 40 - 13.65)^(-1)

= (-18.75 + 26.35)^(-1)

= 7.6^(-1)

= 0.1316 days

Therefore, when the air temperature is 25 degrees Celsius, the predicted length of the searching period is approximately 0.1316 days.

The model for N(t) is given as:

N(t) = -0.85t^2 + 45.4t - 547

This model predicts the percentage of larvae surviving the searching period. It is a quadratic function (-0.85t^2 + 45.4t - 547). As the temperature increases, the percentage of larvae surviving the searching period may increase or decrease depending on the behavior of the quadratic function.

To calculate N(25), we substitute t = 25 into the equation:

N(25) = -0.85(25)^2 + 45.4(25) - 547

= -0.85(625) + 1135 - 547

= -531.25 + 1135 - 547

= 56.75%

Therefore, when the air temperature is 25 degrees Celsius, the predicted percentage of larvae surviving the searching period is 56.75%.

2. The rate of change of the searching period S(t) with respect to temperature t can be found by taking the derivative of the function S(t) with respect to t, which is denoted as ds/dt.

ds/dt = d/dt [(-0.03t^2 + 1.6t - 13.65)^(-1)]

To find when ds/dt = 0, we set the derivative equal to zero and solve for t:

ds/dt = 0

However, without the specific equation of S(t) in its original form, it is not possible to provide an exact value of t when ds/dt equals zero.

Regarding the behavior when t = 0, we cannot determine this without further information or the specific form of the function S(t). The behavior at t = 0 depends on the equation itself and how it is defined.

3. The rate of change of the percentage of larvae surviving the searching period N(t) with respect to the length of the searching period S(t) can be found by taking the derivative of the function N(t) with respect to S(t), denoted as dN/dS.

dN/dS = d/dS [(-0.85t^2 + 45.4t - 547)]

This rate of change provides information about how the percentage of larvae surviving the searching period changes with respect to the length of the searching period. It gives insight into the sensitivity

1)

When input is 5 output will be 15 and when input is 6 output will be 16.

Given,

input = 3 ; output = 13

input = 4 ; output = 14

Now,

Rule = Add 10 to the input supplied.

Input = 5 ; Output = 15.

Input = 6 ; Output = 16.

Hence,

when input supplied is 5 , output will be 15.

when input supplied is 6 , output will be 16.

2)

When input is 7 output will be 4 and when input is 8 output will be 15.

Given,

Input = 5 ; Output = 2

Input = 6 ; Output = 3

Now,

Rule = Subtract 3 to the input supplied.

Input = 7 ; Output = 4.

Input = 8 ; Output = 5.

Hence,

when input supplied is 7 , output will be 4.

when input supplied is 8 , output will be 5.

3)

When input is 3 output will be 15.

Given,

Input = 0 ; Output = 3

Input = 1 ; Output = 7

Input = 2 ; Output = 9

Now,

Rule = Add 3, 6, 9, 12 which are having common difference as 3 between them.

Input = 3 ; Output = 15.

Hence,

when input supplied is 3 , output will be 15.

4)

When input is 13 output will be 25.

Given,

Input = 10 ; Output = 19

Input = 11 ; Output = 21

Input = 12 ; Output = 23

Now,

Rule = Add 9, 10, 11, 12 which are having common difference as 1 between them.

Input = 13 ; Output = 25.

Hence,

when input supplied is 13 , output will be 25.

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Answer:

The Correct answer is 1.53m=153cm

Step-by-step explanation:

1m=100cm

1.53m=x

[tex]x = 100 \times 1.53m[/tex]

x=153m

The final payment that paid off the loan was , R235,891.64.

Now, We can use the formula,

FV = P  [(1 + r/n)^(nt) - 1] / (r/n)

where FV is the future value, P is the periodic payment, r is the interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years.

Let's first calculate the interest rate per month:

r = 8% / 12 = 0.0066667

Next,  the future value of the loan after 6 months:

n = 12 (compounding monthly)

t = 6/12 = 0.5 years

P = 0 (no payment made)

Hence,

FV1 = 530000 [(1 + 0.0066667/12)^(120.5) - 1] / (0.0066667/12)

FV1 ≈ 545,978.61

After 6 months, the loan balance is, R545,978.61.

Next, the future value of the loan after 18 months;

n = 12 (compounding monthly)

t = 1.5 years

P = 120000

Hence, FV2 = (530000 - 120000) [(1 + 0.0066667/12)^(121.5) - 1] / (0.0066667/12)

FV2 ≈ 307,329.33

After 18 months, the loan balance is ,R307,329.33.

Finally, we need to calculate the future value of the loan after 2 years:

n = 12 (compounding monthly)

t = 2 years

P = 27000

Hence, FV3 = (530000 - 120000 - 27000) [(1 + 0.0066667/12)^(122) - 1] / (0.0066667/12)

FV3 ≈ 235,891.64

Therefore, the final payment that paid off the loan was approximately R235,891.64.

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The missing values are

<UTQ = 41 degree

x= 1

<UQT = 47 degree

We have a parallelogram QRST.

We know that the opposite sides of the parallelogram is equal and parallel then

QR || ST

QT || SR

Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)

<UTQ = 41

Similarly, <UQT = <SRQ = 47

Now, RU = UT

2x + 1= 3

2x = 2

x= 1

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The results are:

i. Range: Le 635,000

ii. Mean: Le 445,666.67

iii. Median: Le 420,000

iv. Mode: None

We have,

To compute the range, mean, median, and mode of the given data set, let's first arrange the rent amounts in ascending order:

Le 00,000, Le 335,000, Le 373,000, Le 385,000, Le 410,000, Le 410,000, Le 430,000, Le 462,000, Le 515,000, Le 535,000, Le 578,000, Le 635,000

i. Range:

The range is calculated by subtracting the minimum value from the maximum value in the data set:

Range = Maximum value - Minimum value

Range = Le 635,000 - Le 00,000

Range = Le 635,000

ii. Mean:

The mean is the average of the rent amounts. We sum up all the values and divide by the number of values in the data set:

Mean = (Sum of all rent amounts) / (Number of rent amounts)

Mean = (Le 00,000 + Le 335,000 + Le 373,000 + Le 385,000 + Le 410,000 + Le 410,000 + Le 430,000 + Le 462,000 + Le 515,000 + Le 535,000 + Le 578,000 + Le 635,000) / 12

Mean = Le 5,348,000 / 12

Mean = Le 445,666.67

iii. Median:

The median is the middle value in the sorted data set. In this case, since we have 12 rent amounts, the median will be the average of the 6th and 7th values:

Median = (Le 410,000 + Le 430,000) / 2

Median = Le 420,000

iv. Mode:

The mode is the value that appears most frequently in the data set. In this case, there is no rent amount that appears more than once, so there is no mode.

Therefore,

The results are:

i. Range: Le 635,000

ii. Mean: Le 445,666.67

iii. Median: Le 420,000

iv. Mode: None

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The values of the identity are;

a. tan Z  = 3/4

b. sin C = 4/10

c. tan Z = 20/21

d.  cos A =  5/13

e. tan Z = 9/12

To determine the value, we need to know the different trigonometric identities, we have;

From the information given, we have that;

a. tan Z = opposite/adjacent

substitute the values

tan Z = 24/32 = 3/4

b. sin theta = opposite/hypotenuse

sin C = 24/40 = 4/10

c. tan Z = opposite/adjacent

tan Z = 20/21

d. cos theta = adjacent/hypotenuse

cos X = 20/15 = 4/3

e. cos A = 15/39 = 5/13

d. tan Z = 27/36

tan Z = 9/12

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Answer:

Angle-Side-Angle

Second option

Step-by-step explanation:

We are given two triangles where two of the corresponding angles are equal and side of one triangle is equal to the corresponding side of the other triangle

The postulate to prove the two triangles are congruent is Angle-Side-Angle or ASA which states that two triangles are said to be congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle

Answer:

The deck will cover 153.86 square feet of Nicole's yard

Step-by-step explanation:

We want to find the area of the deck as the area is "the total space taken up by a flat (2-D) surface".  Furthermore, the mention of square feet also indicates that we want to find area since the area is always in square units.

The formula for the area of a circle is given by:

A = πr^2, where

Thus, we can plug in 3.14 for π and 7 for r, allowing us to solve for A, the area of the circular deck in square feet:

A = 3.14(7)^2

A = 3.14(49)

A = 153.86

Thus, the deck will cover 153.86 square feet of Nicole's yard.

An expression that is equivalent to 10√5 include the following: A. √500.

In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).

In this scenario and exercise, the non-simplified form of the given expression 10√5​ can be determined or calculated by taking the square of both numerical value as follows;

Expression² = (10√5)²

Expression² = 10² × (√5)²

Expression² = 100 × 5

Expression² = 500

Expression = √500

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Complete Question:

Which expression is equivalent to 10√5?

A. √500

B. √105

C. √50

D. √15