Joan needs $80 for a class trip. She has $32. She can earn $8 an hour baby-sitting. If the equation below shows this relationship, how many hours must Joan work to have the money she needs?

The area of triangle JHK is 4.18 units²

A triangle is a polygon with three sides having three vertices. There are different types of triangle, we have;

The right triangle, the isosceles , equilateral triangle e.t.c.

The area of a figure is the number of unit squares that cover the surface of a closed figure.

The area of a triangle is expressed as;

A = 1/2bh

where b is the base and h is the height.

The base = 2.2

height = 3.8

A = 1/2 × 3.8 × 2.2

A = 8.36/2

A = 4.18 units²

Therefore the area of triangle JHK is 4.18 units²

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To find the center and radius of the circle r = 5 sin(θ) in rectangular coordinates, we can rewrite the equation using the trigonometric identity sin(θ) = y/r. This gives us the equation y = 5 sin(θ), which represents a vertical line passing through the origin. Therefore, the center of the circle is the origin (0, 0), and the radius is 5 units.

To find the intersection points between the two curves, we can set the equations equal to each other and solve for θ. By substituting the expressions for r, we get 5 sin(θ) = 3 - sin(θ). Solving this equation will give us the values of θ at the intersection points.

To set up the integral for finding the area of the region inside the circle r = 5 sin(θ) and outside the polar curve r = 3 - sin(θ), we need to determine the limits of integration. This can be done by finding the points of intersection obtained in part (b). The integral can then be set up using the formula for the area between two polar curves, which is given by A = (1/2)∫[θ1,θ2] [(r1)^2 - (r2)^2] dθ, where r1 and r2 are the equations of the curves and θ1 and θ2 are the limits of integration.

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Answer:

2.9 x 10∧-7

Step-by-step explanation:

Answer:

2.9 × 10^-7

Hope this helps

The solution of the inequality is, x ∈ (- ∞, 5) ∪ (10, ∞)

Where, x represent the number of totts.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

My friend Raw has either no more than 5 toots and more than 10 toots.

Now, Let number of toots = x

Hence, We get;

⇒ x < 5

And, x > 10

Thus, The solution of the inequality is,

⇒ x ∈ (- ∞, 5) ∪ (10, ∞)

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Answer:

1: the number of years since 2008 2. t is greater than or equal to 0 3. negative values 4. continuous

Step-by-step explanation:

1. t usually represents time

2. t must be greater than 0 as you can not go backward in time

3. the range must be positive as you can not have negative bobcats

4. its continuous because its a quadratic equation

1. no. of bobcats since 2008

2. greater than equal to 0

3 negative values

4. discrete because no. of bobcats cannot be broken into fraction.

The probability of drawing 2 green balls simultaneously from a bag containing 2 yellow and 4 green balls can be determined using the following method:

First, calculate the total number of balls in the bag. There are 2 yellow balls and 4 green balls, so the total is 6 balls.

Now, let's find the probability of drawing 2 green balls. To do this, consider the number of green balls (4) and the total number of balls (6). When drawing the first green ball, there are 4 green balls out of 6 total balls. Therefore, the probability of drawing one green ball is 4/6.

Since the balls are drawn simultaneously, there's no change in the number of balls for the second draw. So, the probability of drawing a second green ball remains 4/6.

Now, we can calculate the probability of both events occurring simultaneously by multiplying the probabilities:

(4/6) * (4/6) = 16/36

To simplify the fraction, divide both numerator and denominator by their greatest common divisor (4):

16/36 = 4/9

So, the probability of drawing 2 green balls simultaneously is 4/9.

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Answer:

Smaller factor/larger figure = 3/6 = ½

Step-by-step explanation:

Scale factor of similar figures is usually the ratio of one to the other.

In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.

Length of smaller figure = 3

Corresponding length of larger figure = 6

Scale factor = smaller figure/larger figure = 3/6

Simplify

Scale factor = ½

The coordinates of point D 0.25 x-axis for the points A(2, 6), B(0, 0), C(-5, 8), and D(-2, 10) are (-2, -2.5) when point D is reflected across the x-axis. This is obtained by negating the y-coordinate of point D and keeping the x-coordinate the same.

To find the coordinates of point D 0.25 x-axis, we need to reflect point D across the x-axis. This will result in the y-coordinate of point D being negated while the x-coordinate remains the same.

The coordinates of point D are (-2, 10), so when we reflect it across the x-axis, we get the new coordinates:

D 0.25 x-axis = (-2, -10/4) = (-2, -2.5)

Therefore, the coordinates of point D0.25∘rx-axis for the given points A, B, C, and D are (-2, -2.5).

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Step-by-step explanation:

Typical speed of Bernard= x km/hr

Bernard's speed while sick= 41.5 km/hr

the difference in the speed=13.5 km/hr

the equation representing the difference will be:

x-41.5=13.5 km/hr

Answer:

Patterns

Step-by-step explanation:

Deductive reasoning is used to prove conjectures to be true

Answer:

patterns

Step-by-step explanation:

Deductive reasoning is a simple form of arriving at a conclusion by joining two or more pieces of information. Deductive reasoning is used to prove conjectures to be true.

For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.

Probability is a measure of the likelihood that an event will occur.

The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.

Let, X be the random variable denoting the number of shoppers on a random day.

Then, X follows normal with mean 505 and standard deviation of 115.

Then, we can say that,

Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.

We have to find

P (250 <X< 450)

= P {(250-505)/155} < Z < {(450-505)/155}

= P (-1.64 <Z< -0.03)

Where, Z is the standard normal variate.

ρ = -1.64 <ρ< -0.03

Where, ρ is the distribution function of the standard normal variate.

From the standard normal table, this becomes

=0.00585

For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.

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Answer:

C, Almost fifty percent

Step-by-step explanation: I just got it right.

Answer:

...…...................c = 50

Answer:

-22 , -21 , -20

Step-by-step explanation:

Answer:

thrid one

Step-by-step explanation:

Answer:

If im correct

EG and FH

Answer:

See below

Step-by-step explanation:

An actual popsicle stick has THREE lines of symmetry

   the figure shown has TWO lines of symmetry

The integral converges for values of p > 1. This can be determined by using the integral test for convergence. The integral test states that if a series ∑ a_n converges, then the integral of the function f(x) = a_x from 1 to infinity also converges. In this case, the function is f(x) = 1/x^p.

To determine if the integral converges, we can take the integral of the function:

∫(1/x^p) dx = (x^(-p+1))/(-p+1) + C

As x approaches infinity, the integral will converge if the exponent of x is less than -1. This means that -p+1 < -1, or p > 1. Therefore, the integral converges for values of p > 1.

In inequality form, the answer is:

p > 1

This means that the integral converges for values of p greater than 1.

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The expression for the length of the sail is x = 7( tan 50° ).

According to the given question.

The sail of a boat is in the shape of a right triangle.

And, the sail of a boat is a right triangle with an acute angle at the tip equal to 50 degrees and the side of the sail which is the hypotenuse to the right triangle is 7 meters long.

Now, the side that measures 7 meters would be the adjacent because its right next to the angle and its not the hypotenuse because its not the largest side

And, the side which we do not know the length to will be the opposite side because it is opposite from where the angle is.  

So, we have the the measure of the adjacent side and the angle of the tip. And we have to find the expression for the length of the sail.

Let the length of the sail be x meters.

Now, in the given right angled triangle

We can say that

tan A = Opposite side/Adjacent side

⇒ tan 50° = x/7

⇒ x = 7( tan 50° )

Hence, the expression for the length of the sail is x = 7( tan 50° ).

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Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

look at the png

An inverse relationship can not direct.

We know that an inverse proportion represents inverse or indirect relation between two quantities.

In inverse relationship, one value increases while the other value decreases, and vice versa.

But in case of direct relationship, if one quantity increases , the other quantity also increases, and  if one quantity decreases , the other quantity also decreases.

When two quantities 'm' and 'n' are inversely proportional to each other, it means when the value of m increases while the value of quantity  'n' decreases, and vice versa.

Also, an inverse relationship always has a negative slope.

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Answer:

2.4 × 101

Step-by-step explanation:

that is 24 in scientific notation

Answer:

24 * 10^1

Step-by-step explanation:

Hope this helps. :)

Answer:

L = 5cm

Step-by-step explanation:

Subtract 6 from both sides.

L = 11-6 cm

L = 5cm

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The skier's displacement from his starting point is 127.179 m and makes an angle of 33.78°.

The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.

Given A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º

base distance = 100 m

We will utilize the cosine rule to determine the magnitude of displacement because the triangle formed by the starting point, where he begins to ascend, and the ending point does not have a 90-degree angle. Cosine law requires a triangle with two sides and an angle between them, both of which are present.

a² = b² + c² - 2.b.ccos(α)

here a is the length of the third side,

b = base = 100m

c = 35 m

and α = 180 - 35 = 135°

so a² = b² + c² - 2.b.ccos(α)

a² = 100² + 35² - 2(100)(35)cos(135)

a² = 10000 + 1225 + 4949.74

a² = 16174.74

a = 127.179 m

and the angle between sides 100m and 127.179 m is given by

cosβ = (a² + c² - b²)/2a.c

cosβ = (127.179² + 35² - 100²)/2(127.179)(35)

cosβ = 0.831

β = cos⁻¹(0.831)

β = 33.78°

Hence displacement from the starting point is 127.179 m and forms an angle of 33.78°.

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There are three possible partitions on the set {1, 2, 3}: Partition 1: { {1}, {2}, {3} } This partition corresponds to the equivalence relation R1 from the previous problem. Partition 2: { {1, 2}, {3} } This partition corresponds to the equivalence relation R2 from the previous problem. Partition 3: { {1, 3}, {2} } This partition corresponds to the equivalence relation R3 from the previous problem.
A partition of a set is a collection of disjoint subsets of the set that together cover the entire set. In other words, each element of the set belongs to exactly one of the subsets. For the set {1, 2, 3}, there are five partitions:
- P1 = {{1}, {2}, {3}}
- P2 = {{1, 2}, {3}}
- P3 = {{1, 3}, {2}}
- P4 = {{2, 3}, {1}}
- P5 = {{1, 2, 3}}
Each of these partitions corresponds to a different equivalence relation on the set {1, 2, 3}.

For example, the partition P1 corresponds to the equivalence relation R1 = {(1, 1), (2, 2), (3, 3)}, which is the identity relation. The partition P2 corresponds to the equivalence relation R2 = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}, which relates 1 and 2 to each other but not to 3. The partition P3 corresponds to the equivalence relation R3 = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}, which relates 1 and 3 to each other but not to 2. The partition P4 corresponds to the equivalence relation R4 = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}, which relates 2 and 3 to each other but not to 1.

Finally, the partition P5 corresponds to the equivalence relation R5 = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1, 3), (3, 1), (2, 3), (3, 2)}, which relates all of the elements to each other.

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To find the distance from the ranger's station to the forest fire, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of depression to the forest fire, the height of the ranger's station above the ground, and the distance from the ranger's station to the forest fire to form a right triangle.

We can then use the tangent function to find the distance from the ranger's station to the forest fire as follows:

tan(35°) = opposite/adjacent

opposite = tan(35°) * adjacent

opposite = tan(35°) * 100 feet

opposite = 0.7392 * 100 feet

opposite = 73.92 feet

Therefore, the distance from the ranger's station to the forest fire is approximately 74 feet. To the nearest tenth of a foot, this is 73.9 feet.

Answer:

161

Step-by-step explanation:

When the spinner is divided evenly into eight parts with three colored blue, one colored orange, two colored purple, and two colored yellow, the likelihood that the spinner is spun once and the color is not blue is 62.5%.

Here,

number of possibility=8

number of sample case=5

Probability that spinner is spun once and color is not blue,

=5/8

=0.625

=62.5%

The probability that spinner is spun once and color is not blue is 62.5% when spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow.

Hence the correct option is B.

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