Gwen, Tristan, and Keith like to work out at the gym. They each have an app on their phone that estimates the calories they burn. By the time Tristan and Keith started exercising, Gwen had already burned 100 calories. Gwen burns 10 calories every minute, Tristan burns 125 every 10 minutes, and Keith burns 300 calories every 30 minutes. Let x represent the number of minutes since Tristan and Keith started exercising and y represent the number of app-estimated calories burned.

Answer:

Step-by-step explanation:

You want two unit vectors that make an angle of 60° with v(6, 8).

After we normalize v to a unit vector, we can find the two desired vectors by adding or subtracting 60° from its angle. The normalized vector v is ...

  v = (6, 8)/√(6² +8²) = (3/5, 4/5)

This can be rotated 60° CCW by the transformation ...

  (x, y) ⇒ (x·cos(60°)-y·sin(60°), x·sin(60°)+y·cos(60°)) = (x-y√3, x√3+y)/2

  (3/5, 4/5) ⇒ ((3-4√3)/10, (3√3+4)/10) . . . . 60° CCW from v

It can be rotated 60° CW by the transformation ...

  (x, y) ⇒ (x·cos(60°)+y·sin(60°), -x·sin(60°)+y·cos(60°)) = ((x+y√3, -x√3+y)/2

  (3/5, 4/5) ⇒ ((3+4√3)/10, (4-3√3)/10)

__

Additional comment

When the vector is written as a complex number, it can be rotated by multiplying by 1∠±60° = (cos(60°)±i·sin(60°). That is what the calculator did.

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The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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The Agnews' annual expenses are $12,205 less than their disposable income.

The amount of money a person or family has available to spend or save after paying taxes and other necessary costs like rent or mortgage payments, utilities, and insurance premiums is known as disposable income.

It stands for the money that is left over after taxes for discretionary expenses, such as savings or hobbies or amusement.

The Agnews' annual expenses are $39,826, and their disposable income is $52,031. To find out how much less their annual expenses are than their disposable income, we can subtract their annual expenses from their disposable income:

$52,031 - $39,826 = $12,205

Therefore, the Agnews' annual expenses are $12,205 less than their disposable income.

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The road with alternating white and black stripes and each 50 cm wide is 7.5 m wide.

The road consists of alternating white and black stripes

No. of white stripes = 8

As the first and last stripe is white so in between the black stripes will be 7

No. of black stripes = 7

Total no. of stripes = 15

Width of black stripe = 50 cm

Width of white stripe = 50 cm

Width of whole road = total no. of stripes × width of each stripe

Width of whole road = 15 × 50

Width of whole road = 750 cm

To convert m into cm

Now, 1 m = 100 cm

1 cm = 1/100 m

750 cm = 750/100 m

750 cm = 7.5 m

Hence the width of the road is 7.5 m

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Answer:

they are both 0 since they would not appear on a graph

Step-by-step explanation:

The measure of length DE if DF = 61 and EF = 18 is 43

From the question, we are given the following measurement:

DF = 61

EF = 18

Required:

DE

Using the expression to find the measure of DE

DE + EF = DF

Substitute the given values

DE + 18 = 61

Subtract 18 from both sides

DE + 18 - 18 = 61 - 18

DE = 43

Hence the measure of DE is 43

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If Sₙ denotes the sum of the reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive , then the smallest positive integer n for which Sₙ is an integer is 63 .

The "Sₙ" be the sum of reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive ;

We Let \(K= \sum_{i=1} ^{9} \frac{1}{i}\) ,

On further examination , we get that , \(S_{1} =K+1\) ;

Since each digit "n" appears once and the number 1 appears for an extra time.

Now , we write  S₂ .

So ,Each term of K will appear 10 times in the units place and 10 times in the tens place ,

So , we get \(S_{2} = (n10^{n-1})K+1\) ; and there are total "n" places ;

The denominator of K is written as \(D=2^{3} .3^{2} .5.7\) .

For Sₙ to be an integer, \(n10^{n-1}\) must be divisible by D , we must select "n" to be divisible by \(3^{2} .7\)   .

And since need to find the smallest integer "n" , So , the n is \(3^{2} .7 = 63\) .

Therefore , For Sₙ to be an integer , the smallest positive integer n is 63 .

The given question is incomplete , the complete question is

Let Sₙ be the sum of the reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive. find the smallest positive integer n for which Sₙ is an integer .

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In general, higher confidence levels provide wider confidence intervals.

What is the concept of confidence level and confidence interval?

Confidence level:

The confidence level refers to the long term success rate of the method , that is , how often this type of interval will capture the parameter of interest.

Confidence interval:

A specific confidence interval gives a range of plausible values for the parameter of interest.

As the confidence level increases, the width of confidence interval also increases.

A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means the interval is larger.

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Answer:

Step-by-step explanation:

The inscribed angle intersects an arc that is half the measure of the of the arc intersected by the central angle. The inscribed angle's arc measures 36%, and the central angle's arc measure 72%

Answer:

75

%Step-by-step explanation:

The inscribed angle intersects an arc that is half the measure of the of the arc intersected by the central angle.

(a) The time (in h) will the plane take to reach the city is 7.09 hours or 7.1 hours.

(b) The plane flies through a constant tailwind blowing at 53.5 km/h, the time (in h) will it take to reach the city is 3.58 hours or 3.6 hours.

(c) The plane flies through a constant crosswind blowing east at 53.5 km/h, the time (in h) will it take to reach the city is infinite.

(a) To find the time it will take for the plane to reach the city with a headwind, we need to first find the plane's ground speed. The ground speed is the speed of the plane relative to the ground. We can find the ground speed by subtracting the speed of the headwind from the plane's airspeed.

Ground speed = Airspeed - Headwind speed

Ground speed = 163 km/h - 53.5 km/h

Ground speed = 109.5 km/h

Now that we know the ground speed, we can use the formula:

Time = Distance ÷ Speed

Time = 776 km ÷ 109.5 km/h

Time = 7.09 hours or 7.1 hours

(b) To find the time it will take for the plane to reach the city with a tailwind, we need to first find the plane's ground speed. The ground speed is the speed of the plane relative to the ground. We can find the ground speed by adding the speed of the tailwind to the plane's airspeed.

Ground speed = Airspeed + Tailwind speed

Ground speed = 163 km/h + 53.5 km/h

Ground speed = 216.5 km/h

Now that we know the ground speed, we can use the formula:

Time = Distance ÷ Speed

Time = 776 km ÷ 216.5 km/h

Time = 3.58 hours or 3.6 hours

(c) To find the time it will take for the plane to reach the city with a crosswind, we need to first find the component of the crosswind that is perpendicular to the plane's direction of travel. This component will not affect how long it takes for the plane to reach its destination.

Component of crosswind = Crosswind speed × sin(angle between direction of travel and crosswind)

Component of crosswind = 53.5 km/h × sin(90°)

Component of crosswind = 53.5 km/h

Now we can find the ground speed of the plane relative to its direction of travel:

Ground speed = Airspeed × cos(angle between direction of travel and crosswind)

Ground speed = 163 km/h × cos(90°)

Ground speed = 0 km/h

Since the ground speed is 0 km/h, the plane will not make any progress towards its destination. Therefore, it will take an infinite amount of time to reach the city with a crosswind.

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The most appropriate statement to describe the comparison of spreads between Town A and Town B is that the IQR for Town A, 20°, is greater than the IQR for Town B, 10°. This suggests that Town A experiences a wider range of temperature fluctuations within the middle 50% of the data compared to Town B.

Based on the provided box plots, the most appropriate comparison of the spreads between Town A and Town B is that the interquartile range (IQR) for Town A, 20°, is greater than the IQR for Town B, 10°. The IQR is a measure of the spread of the middle 50% of the data.

In Town A, the box extends from approximately 15°F to 35°F, indicating that the middle 50% of the data falls within this range. The whiskers extend from the box to the minimum and maximum values, which are approximately 0°F and 45°F, respectively.

The IQR is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1), which in this case is 35°F - 15°F = 20°F.

On the other hand, in Town B, the box ranges from approximately 15°F to 30°F, representing the middle 50% of the data. The whiskers extend from the box to the minimum and maximum values, which are approximately 5°F and 58°F, respectively. The IQR for Town B is calculated as 30°F - 20°F = 10°F.

Comparing the IQRs, we observe that the IQR for Town A (20°F) is greater than the IQR for Town B (10°F). This indicates that there is more variability in the daily low temperatures in Town A compared to Town B within the middle 50% of the data.

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Answer:

8+11 would be 19

Step-by-step explanation:

Answer:

40

Hope this helped :P

Answer: Yes

Step-by-step explanation:

To test, we can see if 5^2 + 12^2 = 13^2.

As this holds true, this is a right triangle.

Answer:No

Step-by-step explanation: 5 squared x 12 squared does not equal 13 squared.

Answer:

Step-by-step explanation:

Answer:Problems based on special right triangles were given the code G-SRT.5 or ... The least possible sum of digits on a 12-hour digital clock is 1. ... The largest sphere that will fit inside this cube has a diameter equal to the length of the ... Using the Pythagorean Theorem, we can find the length d of the hypotenuse, which is the ...

Answer:

A is the answer because it is right

Attributes shared by rhombuses and rectangles:

Both are quadrilaterals.

Both have their opposing sides equal and parallel.

If a rhombus and a rectangle have the same length and width,

The perimeter of the rhombus equals the sum of the diagonals of the rectangle.

The sum of the diagonals of the rhombus equals the semiperimeter of the rectangle.

The angles of the rhombus equal the angles formed by the diagonals of the rectangle.

The angles formed by the diagonals of the rhombus are all right angles, as are the angles of the rectangle.

The area of the rhombus is one half of the area of the rectangle.

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To reverse the order of integration, we need to rewrite the given double integral as an iterated integral with the order of integration reversed. We can do this as follows:

i = ∫0^6 ∫0^(x/2) z^3 f(x, y) dy dx

Now, we can reverse the order of integration by integrating with respect to x first and then with respect to z:

i = ∫0^3 ∫2y^2^6 z^3 f(x, y) dx dz

Therefore, the reversed order of integration is:

∫2y^2^6 ∫0^3 z^3 f(x, y) dz dx

Note that this is just the iterated integral with the original limits of integration but with the order of integration reversed. We can evaluate this integral using these limits of integration, but we cannot determine the actual value of the integral without knowing the function f(x, y).

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To find the variance of xx, we need to calculate the squared difference between each possible value and the expectation, multiply it by the corresponding probability, and sum them up.

(a) The sample space of the experiment consists of all possible pairs of integers that can be chosen from the set \{1, 3, 5\} without replacement.

The sample space is:
\{(1, 3), (1, 5), (3, 1), (3, 5), (5, 1), (5, 3)\}

(b) The possible values of xx, the maximum of the two chosen integers, are: 3, 5.

(c) To find the probability mass function (PMF) for all possible values of xx, we need to determine the probability of each value occurring.

P(xx = 3) = 2/6 = 1/3 (since there are 2 pairs with 3 as the maximum out of 6 total pairs)
P(xx = 5) = 4/6 = 2/3 (since there are 4 pairs with 5 as the maximum out of 6 total pairs)

Therefore, the PMF for xx is:
P(xx = 3) = 1/3
P(xx = 5) = 2/3

(d) To find the expectation of xx, we multiply each possible value by its probability and sum them up.

E(xx) = (3 * 1/3) + (5 * 2/3) = 1 + 10/3 = 13/3 = 4.33 (approximately)

To find the variance of xx, we need to calculate the squared difference between each possible value and the expectation, multiply it by the corresponding probability, and sum them up.

Var(xx) = [(3 - 13/3)^2 * 1/3] + [(5 - 13/3)^2 * 2/3]
       = [(-4/3)^2 * 1/3] + [(4/3)^2 * 2/3]
       = (16/9 * 1/3) + (16/9 * 2/3)
       = 16/27 + 32/27
       = 48/27
       = 16/9

Therefore, the variance of xx is 16/9.

In summary:
(a) Sample space: \{(1, 3), (1, 5), (3, 1), (3, 5), (5, 1), (5, 3)\}
(b) Possible values of xx: 3, 5
(c) PMF for xx: P(xx = 3) = 1/3, P(xx = 5) = 2/3
(d) Expectation of xx: 4.33 (approximately)
(d) Variance of xx: 16/9

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The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

Step-by-step explanation:

First, start with a diagram so you can 'see' the situation....I'll us a compass rose coordinate system ( see image below)

Vertical component of point C  ( which is the resultant displacement from A)

   900 sin(35) + 600 sin (130) = 975.845 km

Horizontal component  900 cos (35) + 600 cos (130) = 351.56 km

Using Pyhtagorean theorem   d = sqrt ( 975.845^2 + 351.56^2)  = 1037 km

    distance from A to C = 1037 km

Bearing of C from A = arctan ( 975.845/351.56) = 70 degrees

solving the equation given to us first:

-5x/2 = 5/1 ( ignore the ≤ symbol for now and replace with =) and cross multiply

you will get

-5x = 10

x = -10/5 ( minus doesn't stay in denominator so so we take up to numerator )

x = -2

so x ≤ -2

NOTE: if we have ≤ we shade the dot but if we have just < or we don't shade the dot.

soooo

x ≤ -2 will be going backwards

so the answer is option (C).

Hope this helps.

Good luck.

Answer:

7/3 and 1/3

Step-by-step explanation:

Answer:

1/3 and 7/3

Step-by-step explanation:

Reciprocal of 3: 1/3

Reciprocal of 7/3: 3/7

\(\frac{-3}{5} > -2\) indicates that -3/5 is located on the right of -2 on the number line.

What is number line?

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

consider, \(\frac{-3}{5} > -2\)

Here, -3/5 = -0.6

-0.6 > -2

-0.6 is the number greater than -2.

So, -3/5 is located on the right side of -2.

Hence, -3/5  is located on the right of -2 on the number line.

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To solve the initial value problem y'' - 2y' - 3y = 0, with y(0) = 1 and y'(0) = 2, we can use the method of Laplace transforms.

First, we take the Laplace transform of the given differential equation to obtain an algebraic equation in terms of the Laplace transform of the unknown function y(t). Then, we solve the algebraic equation for the Laplace transform of y(t) using standard algebraic techniques. Finally, we take the inverse Laplace transform to obtain the solution y(t) in the time domain.

Applying the Laplace transform to the given differential equation, we have s²Y(s) - sy(0) - y'(0) - 2(sY(s) - y(0)) - 3Y(s) = 0, where Y(s) represents the Laplace transform of y(t). Simplifying this equation, we get (s² - 2s - 3)Y(s) - (s - 2) = s²Y(s) - 3s - 4. Rearranging the equation, we have Y(s) = (s - 2) / (s² - 2s - 3).

To solve this equation for Y(s), we can decompose the expression into partial fractions, which yields Y(s) = 1 / (s - 3) - 1 / (s + 1). Taking the inverse Laplace transform of Y(s), we obtain y(t) = e^(3t) - e^(-t), which is the solution to the initial value problem.

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Answer: (-4,16)

Step-by-step explanation:

The other endpoint of the given line segment is (29, -9).

If O(x, y) is the midpoint between the line segment AB with end points A(x₁, y₁) and B(x₂, y₂). The coordinate of the midpoint is:

x = (x₁ + x₂)/2; y = (y₁ + y₂)/2

Let A(x, y) be the other end point. Since one end point is (-9, 9) and Midpoint (10,0), hence:

10 = (x + (-9))/2

20 = x - 9

x = 29

0 = (y + 9)/2

0 = y + 9

y = -9

Therefore the other endpoint of the given line segment is (29, -9).

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The previous balance method will have a finance charge of $2.55 greater than the daily balance method.

Here, we have

Given:

Between the previous balance method and the daily balance method, the previous balance method will have a finance charge of $2.55 greater than the daily balance method.

The difference between the two methods lies in the way in which interest is calculated. In the previous balance method, finance charges are based on the beginning balance of the month; on the other hand, in the daily balance method, interest is based on the average daily balance of the month.

The formula used to calculate the daily balance method is:

Average Daily Balance (ADB) = (Total of all balances during billing period ÷ Number of days in billing period)

So, the first step is to compute David's average daily balance using the formula mentioned above:

ADB = ((1,998.11 x 30) + (43.86 x 21) + (225 x 7) + (61.21 x 2)) ÷ 30 = $1,153.03

The finance charge using the daily balance method would be:($1,153.03 x 13.59% ÷ 365) x 30 = $5.41

The previous balance method charges interest based on the initial amount. As a result, the finance charge is equal to the balance at the end of the billing period multiplied by the APR divided by 12.

The finance charge using the previous balance method would be:($152.65 x 13.59% ÷ 12) = $1.71

Therefore, the previous balance method will have a finance charge of $2.55 greater than the daily balance method.

The previous balance method will have a finance charge of $2.55 greater than the daily balance method.

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The matrix A of the rotation about the y-axis through an angle of π/2 clockwise as viewed from the positive y-axis is \(A=\left[\begin{array}{ccc}0 & 0 & -1 \\0 & 1 & 0 \\1 & 0 & 0\end{array}\right]\).

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

To find the matrix A of the rotation about the y-axis through an angle of π/2 (90 degrees) clockwise as viewed from the positive y-axis, we can use the following rotation matrix:

\(A=\left[\begin{array}{ccc}\cos (\theta) & 0 & -\sin (\theta) \\0 & 1 & 0 \\\sin (\theta) & 0 & \cos (\theta)\end{array}\right]\)

Substitute θ with π/2, which is the angle of rotation.

\(A=\left[\begin{array}{ccc}\cos \left(\frac{\pi}{2}\right) & 0 & -\sin \left(\frac{\pi}{2}\right) \\0 & 1 & 0 \\\sin \left(\frac{\pi}{2}\right) & 0 & \cos \left(\frac{\pi}{2}\right)\end{array}\right]\)

Compute the trigonometric values for cos( π/2) and sin( π/2).

cos( π/2) = 0
sin( π/2) = 1

Substitute the computed values back into the matrix.

\(A=\left[\begin{array}{ccc}0 & 0 & -1 \\0 & 1 & 0 \\1 & 0 & 0\end{array}\right]\)

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