Please help me......

When two variables vary directly they follow the next:

k is a constant.

Use the given data: when x=48, y=36 o find the value of k:

Then, x and y vary directly following the next equation:

Use the equation above to find x when y=18:

Answer:

∠a= 65°, ∠b= 115°, ∠c= 25°

Step-by-step explanation:

The sum of the angles in a triangle is 180°. This is abbreviated to '∠ sum of ∆'.

∠c +55° +60° +40°= 180° (∠ sum of ∆PQR)

∠c +155°= 180°

∠c= 180° -155°

∠c= 25°

∠a +60° +55°= 180° (∠ sum of ∆PQS)

∠a +115°= 180°

∠a= 180° -115°

∠a= 65°

The sum of the angles on a straight line is 180°. It's abbreviation is 'adj. ∠s on a str. line'.

∠b +∠a= 180° (adj. ∠s on a str. line)

∠b +65°= 180°

∠b= 180° -65°

∠b= 115°

The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.

Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:

Volume = Length * Width * Height

Using the given measurements:

Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches

To simplify the calculation, we can convert the mixed numbers to improper fractions:

Volume = (21/2) inches * (61/2) inches * (129/4) inches

Next, we multiply the fractions:

Volume = (21/2) * (61/2) * (129/4) = 17289/8

The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:

Volume = 2161 1/8 in³.

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Answer: The first three odd prime numbers are 3, 5, and 7. A number is a multiple of two but not three of these prime numbers if it is divisible by two of them, but not the third.

To find the number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers, we can count the number of multiples of each pair of prime numbers and subtract the number of multiples of all three prime numbers.

There are 200 multiples of 3 and 5 between 1000 and 2000 (200 numbers for each, for a total of 200 * 2 = 400). There are 133 multiples of 3 and 7 between 1000 and 2000 (133 numbers for each, for a total of 133 * 2 = 266). There are 80 multiples of 5 and 7 between 1000 and 2000 (80 numbers for each, for a total of 80 * 2 = 160). There are no multiples of all three prime numbers between 1000 and 2000.

Thus, the total number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers is 400 + 266 + 160 = 826.

Step-by-step explanation:

The vector makes an angle of approximately -84.29 degrees with the positive x-axis.

To find the angle that a vector from the origin to the point (1, -10) makes with the positive x-axis, we can use trigonometry.

First, we need to determine the values of the coordinates (x, y). In this case, x = 1 and y = -10.

The angle θ between the vector and the positive x-axis can be found using the Arctan function:

θ = arctan(y / x)

Substituting the values, we have:

θ = arctan((-10) / 1)

Evaluating the arctan function, we find:

θ ≈ -84.29 degrees

Therefore, the vector makes an angle of approximately -84.29 degrees with the positive x-axis.

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The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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The measures of the corresponding inscribed angles, and then add those angles together to find the measure of angle L. Therefore, the measure of angle L is 64 degrees.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. In other words, if we have an angle whose vertex is on the circumference of a circle, and whose sides intersect two points on the circumference, then the measure of the angle is half the measure of the arc between those two points.

In this problem, we are given the measures of two arcs, DR and SV, and we want to find the measure of angle L. We can start by using the Inscribed Angle Theorem to find the measures of the corresponding inscribed angles. Let's call these angles A and B, where A is the inscribed angle that intercepts arc DR, and B is the inscribed angle that intercepts arc SV.

Using the Inscribed Angle Theorem, we can find that m∠A=12m⌢DR=12(34∘)=17∘m∠B=12m⌢SV=12(94∘)=47∘

To find the measure of angle L, we simply add angles A and B together: m∠L=m∠A+m∠B=17∘+47∘=64∘

Therefore, the measure of angle L is 64 degrees.

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Answer:

Step-by-step explanation:

Five fish equals two bread, and two bread equals two bananas (plus however many oranges), therefore he can get two bananas.

The lengths of the legs of the trip are:

Shortest leg: 20 miles

Middle leg: 21 miles

Longest leg: 27 miles

According to the given information:

1) The middle leg is 11 miles greater than one-half the length of the shortest leg:

y = (1/2)x + 11

2) The longest leg is 12 miles greater than three-fourths of the shortest leg:

z = (3/4)x + 12

We also know that the length of the entire trip is about 68 miles, so the sum of the lengths of the three legs is equal to 68:

x + y + z = 68

Now we can solve this system of equations to find the values of x, y, and z.

Substituting the value of y from equation 1 into equation 3:

x + ((1/2)x + 11) + z = 68

Simplifying the equation:

(3/2)x + z = 57    (Equation 4)

Substituting the value of z from equation 2 into equation 4:

(3/2)x + ((3/4)x + 12) = 57

Simplifying the equation:

(3/2)x + (3/4)x = 57 - 12

(6/4)x + (3/4)x = 45

(9/4)x = 45

Multiplying both sides by (4/9):

x = 45 x (4/9)

x = 20

Now we can substitute the value of x back into equation 1 to find y:

y = (1/2)x + 11

y = (1/2)20 + 11

y = 10 + 11

y = 21

Finally, substituting the value of x into equation 2 to find z:

z = (3/4)x + 12

z = (3/4)20 + 12

z = 15 + 12

z = 27

Therefore, the lengths of the legs of the trip are:

Shortest leg: 20 miles

Middle leg: 21 miles

Longest leg: 27 miles

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Answer:

D

Step-by-step explanation:

Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica

Answer:

2,000 steps.

Step-by-step explanation:

Answer:

\(\frac{dc}{dt}\approx13.8146\text{ km/min}\)

Step-by-step explanation:

We know that the plane travels at a constant speed of 14 km/min.

It passes over a radar station at a altitude of 11 km and climbs at an angle of 25°.

We want to find the rate at which the distance from the plane to the radar station is increasing 4 minutes later. In other words, if you will please refer to the figure, we want to find dc/dt.

First, let's find c, the distance. We can use the law of cosines:

\(c^2=a^2+b^2-2ab\cos(C)\)

We know that the plane travels at a constant rate of 14 km/min. So, after 4 minutes, the plane would've traveled 14(4) or 56 km So, a is 56, b is a constant 11. C is 90+20 or 115°. Substitute:

\(c^2=(56)^2+(11)^2-2(56)(11)\cos(115)\)

Evaluate:

\(c^2=3257-1232\cos(115)\)

Take the square root of both sides:

\(c=\sqrt{3257-1232\cos(115)}\)

Now, let's return to our law of cosines. We have:

\(c^2=a^2+b^2-2ab\cos(C)\)

We want to find dc/dt. So, let's take the derivative of both sides with respect to t:

\(\frac{d}{dt}[c^2]=\frac{d}{dt}[a^2+b^2-2ab\cos(C)]\)

Since our b is constant at 11 km, we can substitute this in:

\(\frac{d}{dt}[c^2]=\frac{d}{dt}[a^2-(11)^2-2a(11)\cos(C)]\)

Evaluate:

\(\frac{d}{dt}[c^2]=\frac{d}{dt}[a^2-121-22a\cos(C)]\)

Implicitly differentiate:

\(2c\frac{dc}{dt}=2a\frac{da}{dt}-22\cos(115)\frac{da}{dt}\)

Divide both sides by 2c:

\(\frac{dc}{dt}=\frac{2a\frac{da}{dt}-22\cos(115)\frac{da}{dt}}{2c}\)

Solve for dc/dt. We already know that da/dt is 14 km/min. a is 56. We also know c. Substitute in these values:

\(\frac{dc}{dt}=\frac{2(56)(14)-22\cos(115)(14)}{2\sqrt{3257-1232\cos(115)}}\)

Simplify:

\(\frac{dc}{dt}=\frac{1568-308\cos(115)}{2\sqrt{3257-1232\cos(115)}}\)

Use a calculator. So:

\(\frac{dc}{dt}\approx13.8146\text{ km/min}\)

And we're done!

The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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Performing discrete trials is a teaching technique used in behavior analysis to teach new skills or behaviors.

It involves breaking down a complex task or behavior into smaller, more manageable steps and teaching each step through repeated trials. Each trial consists of a discriminative stimulus, a response by the learner, and a consequence (either positive reinforcement or correction) based on the accuracy of the response.

To demonstrate performing discrete trials on an initial competency assessment, the assessor would typically design a task or behavior to be learned and break it down into smaller steps. They would then present the first discriminative stimulus and prompt the learner to respond. Based on the accuracy of the response, the assessor would provide either positive reinforcement or correction.

The assessor would then repeat the process with the next discriminative stimulus and continue until all steps of the task or behavior have been completed. The number of trials required for the learner to achieve competency would depend on the complexity of the task or behavior and the learner's individual learning pace.

By demonstrating performing discrete trials on an initial competency assessment, the assessor can assess the learner's ability to learn new skills or behaviors using this technique and determine if additional training or support is needed. It also provides a standardized and objective way to measure learning outcomes and track progress over time.

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Answer:

Step-by-step explanation:

A+B+C+D=360 degree(sum of all sides of a parallelogram)

60+4x+60+4x=360

120+8x=360

8x=360-120

x=240/8

x=30

Answer:

23

Step-by-step explanation:

20 - 3(-1)

20 - (-3)

20 + 3 =

23

Kimberly sent approximately 34 cylindrical boxes that contained soap

Let's assume Kimberly sent a total of 100 gift boxes. Since half of the boxes were cylindrical, that means she sent 50 cylindrical boxes.

If a third of the rectangular boxes contained soap, then 1/3 * (100 - 50) = 1/3 * 50 = 50/3 ≈ 16.7 rectangular boxes contained soap. Since we cannot have a fraction of a box, let's round it down to 16 rectangular boxes containing soap.

Now, since each box contains exactly one gift, the remaining cylindrical boxes must contain the pack of spicy roasted almonds. Therefore, out of the 50 cylindrical boxes, 50 - 16 = 34 cylindrical boxes contain soap.

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.

The original number from the given decimal number is  0.02.

For the given question;

Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.

This results in:

10000x = 4.(1/x)

Simplifying.

x² = 4/10000

x > 0.

Taking square root of the number.

x = 2/100

x = 0.02

Thus, the original number from the given decimal number is  0.02.

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The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016, when  open ground in a year has mean 6 and standard deviation 2.4.

It imply a quantity that falls somewhere between the values of the extreme members of a set in mathematics. There are different types of means, and how they are calculated relies on the relationship that is known about or is regarded as governing the other members.

Given,

Mean = 6

Standard deviation = 2.4

The value that has been reduced by the population mean and divided by the standard deviation is called the z-value.

z = x - mean/ standard deviation/√n

z = 5 - 6/2.4/√50

z = - 2.95

Using table A, calculate the corresponding probability;

= P(x <5)

= P( z < -2.95)

= 0.0016

The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016.

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Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer:

2 1/5

2 X 5 + 1 = 11/5

11/5 X 2/1 = 22/5

1 3/4

1 X 4 + 3 = 7/4

7/4 X 2/1 = 14/4

22/5 + 14/4

5 X 4 = 20

4 X 22 = 88

5 X 14 = 70

88/20 + 70/20 = 158/20

20 goes into 158 7 times with 18 left over

7 18/20 simplified = 7 9/10

The indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

The integral of cos(x) is sin(x) + C, where C is the constant of integration.

The notation for the integral of cos(x) is ∫cos(x) dx, where the symbol ∫ represents the integral sign, cos(x) is the function being integrated, and dx represents the variable of integration, which in this case is x.

The antiderivative of cos(x) is sin(x), meaning that if we take the derivative of sin(x), we get cos(x). The constant of integration, C, is added because the derivative of a constant is always zero.

Therefore, the indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

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∂z/∂s = 3cos(t)/y, ∂z/∂t = 3s*cos(t)/y - sin(s)/x (using the chain rule to differentiate each term and substituting the given expressions for x and y)

To find ∂z/∂s and ∂z/∂t using the chain rule, we start by finding the partial derivatives of z with respect to x and y, and then apply the chain rule.

First, let's find ∂z/∂x and ∂z/∂y.

∂z/∂x = ∂/∂x [ln(5x^3y)]

= (1/5x^3y)  ∂/∂x [5x^3y]

= (1/5x^3y) 15x^2y

= 3/y

∂z/∂y = ∂/∂y [ln(5x^3y)]

= (1/5x^3y) ∂/∂y [5x^3y]

= (1/5x^3y)  5x^3

= 1/x

Now, using the chain rule, we can find ∂z/∂s and ∂z/∂t.

∂z/∂s = (∂z/∂x)  (∂x/∂s) + (∂z/∂y)  (∂y/∂s)

= (3/y)  (cos(t)) + (1/x)  (0)

= 3cos(t)/y

∂z/∂t = (∂z/∂x)  (∂x/∂t) + (∂z/∂y)  (∂y/∂t)

= (3/y) * (scos(t)) + (1/x)  (-sin(s))

= 3scos(t)/y - sin(s)/x

Therefore, ∂z/∂s = 3cos(t)/y and ∂z/∂t = 3s*cos(t)/y - sin(s)/x.

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Answer:

4 km -> 400,000 mm

put a decimal point at the end of 4 and move it to the left 6 times because we know that 1 km is equal to 100,000 and it has zeros.

hence, it is proven that 4 km is equal to 4000,000.

Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

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Step-by-step explanation:

h(x) is positive when h(x) is greater than 0.

When h(x) = 0, 2x + 10 = 0, x = -5

Since this is a straight line graph and the gradient is positive, the interval is (-5,∞).

The interval is: \(\left(-5,\infty\right)\).

If h(x) is positive then h(x)>0.

\(2x+10>0\\2x>-10\\x>-5\)

So the interval is: \(\left(-5,\infty\right)\).

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Answer:

(2,-3)

Step-by-step explanation:

I thought you'd actually have to calculate it but I guess they just wanted to give you guys a graph lol

1. The straight-line solutions are of the form y = kx + c, where k and c are constants.

2. The general solution is f(x) = kx + c, where k and c can be any real numbers.

3. The behavior of solutions depends on the value of k: if k > 0, the solutions increase as x increases; if k < 0, the solutions decrease as x increases; and if k = 0, the solutions are horizontal lines. The equilibrium point at (0, 0) is classified as a stable equilibrium point.

a) To identify the straight-line solutions, we need to find the points on the graph where the slope is constant. This means the derivative of the function with respect to x is a constant. Let's assume our function is f(x).

So, we have f'(x) = k, where k is a constant.

By integrating both sides, we get f(x) = kx + c, where c is an arbitrary constant.

Therefore, the straight-line solutions are of the form y = kx + c, where k and c are constants.

b) The general solution can be written as f(x) = kx + c, where k and c can be any real numbers.

c) The behavior of solutions depends on the value of k.
- If k > 0, the solutions will be increasing lines as x increases.
- If k < 0, the solutions will be decreasing lines as x increases.
- If k = 0, the solutions will be horizontal lines.

The equilibrium point at (0, 0) is classified as a stable equilibrium point because any small disturbance will bring the system back to the equilibrium point.

In summary, the straight-line solutions are of the form y = kx + c, where k and c are constants. The behavior of solutions depends on the value of k, and the equilibrium point at (0, 0) is a stable equilibrium point.

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Answer:

C. $89.21

Step-by-step explanation:

First...Eliminate

$10.26 and $20

They are under the bill total which is $78.95

Then 13% is actually 0.13

13/100 = .13

take 0.13 ×$78.95= 10.2635. ( I used a calculator)

$ 10.2635 of 13%

Take 10.2635 + $78.95(the bill)= Total cost

10.2635 don't forget to line up the demicals

+ 78.95 Or use a calculator

89.2135

$89.21 is your total