what is the graphed line of the equation 2x + 3y = -6

The given trigonometric expression sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.

As we know that sin⁻¹(x) = -cos⁻¹(x) + π/2, which is the angle in the fourth quadrant whose cosine is 3sqrt(2)/2.

We have:

cos²θ + sin²θ = 1

Since sine is negative and cosine is positive, we know that:

sinθ = -sqrt(1 - cos²θ)

Substituting cosθ = 3√(2)/2, we get:

sinθ = -√(1 - (3√(2)/2)²) = -√(1 - 9/8) = -√(1/8) = -√(2)/2

Therefore, sin^(-1)(-3sqrt(2)/2) = -cos^(-1)(3sqrt(2)/2) + π/2.

Since cosine is positive in the fourth quadrant, we have:

cos⁻¹(3√(2)/2) = π/4

Substituting this value, we get:

sin⁻¹(-3√(2)/2) = -π/4 + π/2 = π/4

Therefore, sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.

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Answer:

translation

hope this helps:) !!

Answer:

100

Step-by-step explanation:

The number has the same digit in its hundreds place and its hundredths place. The digit in the hundreds place is 100 times greater than the digit in the hundredths place (https://ccssmathanswers.com/hundredth-place-in-decimals). Therefore, the value of the digit in the hundreds place is 100 times greater than the value of the digit in the hundredths place.

Therefore, the answer is 100.

If lines m and n are parallel, then the value of x must be 4.

If lines m and n are parallel, then the measures of the angles in the correspondent quadrants must be the same ones.

Here we can see that the two angles are in the third quadrant, thus, these angles have the same measure. Then we can write this as:

6x² = 96

Now we can solve this for x, we will get:

x² = 96/6

x² = 16

x = √16

x = 4

That is the value of 4.

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the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent.

A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge. T

he line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.

A circle is a fundamental 2D form whose radius is quantified. The interior and exterior parts of the aircraft are separated by the circles.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, π (pi) is a constant approximately equal to 3.14, and r is the radius.

The difference in the mean circumferences of the Earth and the Moon can be found by subtracting the circumference of the Moon from the circumference of the Earth.

The circumference of the Earth is:

C earth = 2π * 6371.0 km = 40075.04 km (rounded to two decimal places)

The circumference of the Moon is:

C moon = 2π * 1737.5 km = 10921.16 km (rounded to two decimal places)

The difference in the mean circumferences of the Earth and the Moon is:

C earth - C moon = 40075.04 km - 10921.16 km ≈ 29153.88 km

Therefore, the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.

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Answer:

Step-by-step explanation:

There are 6 possible outcomes when rolling a single cube (1, 2, 3, 4, 5, or 6). When rolling two cubes, the possible sums range from 2 (1+1) to 12 (6+6). Using the chart provided, we can see that the sum of two cubes being equal to 5 only occurs once in the 36 possible combinations: when one cube shows a 1 and the other cube shows a 4.

To find the expected number of times this sum will occur if Tamara rolls the cubes 180 times, we need to multiply the probability of this event occurring on any given roll by the number of rolls. The probability of rolling a sum of 5 is 1/36, since there is only one way to get a sum of 5 out of the 36 possible combinations. Therefore, the expected number of times this sum will occur in 180 rolls is:

(1/36) x 180 = 5

So Tamara should expect to roll a sum of 5 about 5 times in 180 rolls of two cubes.

The left-handed students in the music program are option A 15 students.

A table that shows the frequencies of two category variables is known as a two-way frequency table. It is a method for succinctly and clearly organising and displaying data for two variables. One variable is represented by the table's rows, while the other variable is represented by the table's columns. The frequency of each combination of categories is displayed in the table's cells. To examine the relationship between the two variables and to spot patterns and trends in the data, a two-way frequency table can be employed. To summarise and analyse data, it is frequently used in statistics, the social sciences, and other disciplines.

From the given table the number of students that are in music program and left handed is given by the intersection of the row and column of the two.

Thus, he left-handed students in the music program are 15.

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we know that

discriminant of quadratic is [tex]b^{2}[/tex]-4ac

putting values we get

81-32

= 49

hence the discriminant is 49

Therefore, the probability of spinning a 2 or 3 on the spinner and drawing a blue tile is 1/6.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur. Probability theory is an important branch of mathematics used in many fields, including statistics, economics, engineering, and science, to help make predictions and informed decisions based on data and uncertain events.

Here,

Based on the given tree diagram, the probability of spinning a 2 or 3 on the spinner is 1/2 since there are two possible outcomes (2 or 3) out of four equally likely outcomes (1, 2, 3, or 4).

The probability of drawing a blue tile after spinning a 2 or 3 is 1/3 since there is only one blue tile out of three possible outcomes (blue, green, or red) for each spin result of 2 or 3.

To calculate the probability of both events happening together (spinning a 2 or 3 and drawing a blue tile), we need to multiply the two probabilities:

P(2 or 3 and blue) = P(2 or 3) x P(blue | 2 or 3)

= (1/2) x (1/3)

= 1/6

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The value of x in the circle is 4.2

From the question, we have the following parameters that can be used in our computation:

The circle

Using the intersecting chords equation, we have

(5x - 8) * 4 = (x + 1) * 10

When solved for x, we have

x = 4.2

Hence. the value of x is 4.2

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The fraction expression 2 1/2 - 4 1/4 when evaluated is -1 3/4

To solve 2 1/2 - 4 1/4, we need to convert the mixed numbers into improper fractions, then find a common denominator and subtract the two fractions.

First, we convert 2 1/2 and 4 1/4 into improper fractions:

2 1/2 = 5/2

4 1/4 = 17/4

Next, we find a common denominator. In this case, the smallest common denominator is 4:

5/2 = 10/4

17/4 = 17/4

Now we can subtract the fractions:

10/4 - 17/4 = -7/4

Finally, we can convert the resulting improper fraction back into a mixed number:

-7/4 = -1 3/4

Therefore, 2 1/2 - 4 1/4 = -1 3/4.

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If John pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

In order to arrive at a solution, it is necessary to commence by reducing the fraction 1/1.5 into a more basic form.

Thus, we do this below:

1 ÷ 1.5 = 1 ÷ (3/2) = 1 × (2/3) = 2/3

So, John has 29 full buckets and another bucket that is 2/3 full.

If he pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

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John has 29 full buckets of water and another bucket that is 1/1.5 full. How many full buckets of water would he have if he pours the partially filled bucket into an empty one?

Answer:

$52.50

Step-by-step explanation:

1500 * 3.5% = 52.50

Answer:

$52.5 for the first year

Step-by-step explanation:

You can derive a decimal from a percentage by dividing by 100.

For example, 1% is 0.01

3.5% is 0.035

You can also move the decimal point back 2 places, but that's cringy.

So the problem says how much interest she will have to pay after one year, when the interest rate is 3.5%.

Therfore, we must multiply:

1500 by 3.5%

We stated that 3.5% is 0.035, so we can replace that

1500 * 0.035

Plug that into a caluclator and we get.....

$52.5 for the first year

ANSWER CHOICE 1

Phew! That was a long problem! May I please have Brainliest?

Is this compound interest or simple interest? I'll just do it by the simple interest method. The answer is 9 months!

We can set up the equation :

0.9x = 110 ,

where x is the unknown number. To solve for x, we can divide both sides by 0.9 :

x = 110 ÷ 0.9

x = 122.22 (rounded to two decimal places)

So the unknown number is approximately 122.22.

To find 9% of that number, we can multiply 122.22 by 0.09 :

0.09 × 122.22 = 11.00 (rounded to two decimal places)

Therefore, 9% of the number is approximately 11.

Answer:

Step-by-step explanation:

To write the standard equation of a circle with its center in the fourth quadrant tangent to x=7, y=-4 and x=17, we can first find the center of the circle.

Since the center is in the fourth quadrant and tangent to x=7, y=-4 and x=17, the center must lie on the line x=12 (the midpoint between 7 and 17) and y=-4 (the point of tangency).

So the center of the circle is (12, -4).

Next, we need to find the radius of the circle. Since the circle is tangent to x=7 and x=17, the radius is the distance from the center to either x=7 or x=17.

The radius is thus 12 (the difference between 12 and 7) or 5 (the difference between 12 and 17).

So the standard equation of the circle is:

(x - 12)^2 + (y + 4)^2 = 25

Answer: each package weighs 3.25lb 

Step-by-step explanation:

looking at the weight of each package (3lb 4oz), we can convert the 4oz to pounds by dividing by 16oz/lb; 4/16 = 0.25lb 

For the drug used to treat asthma in a clinical trial:

Part 1:

The test is right-tailed because the alternative hypothesis is that less than 9% of treated subjects experienced headaches.

Part 2:

The test statistic is z = 0.64, rounded to two decimal places (given in the calculator display).

Part 3:

The P-value is 0.7401, rounded to four decimal places (also given in the calculator display).

Part 4:

The null hypothesis is Upper H₀: p ≥ 0.09. We conclude that there is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

Part 5:

We fail to reject the null hypothesis because the P-value is greater than the significance level, α=0.01.

Part 6:

The final conclusion is: D, There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

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The maximum voltage produced by the system is 12 volts.

The function given is:

[tex]v_{inst}(t) = 12 * sin(360 * 60 * 6.3 + 79)[/tex]

To find the maximum voltage produced by the system, we need to determine the maximum value of the sine function within the given range.

Let's focus on the argument of the sine function: 360 * 60 * 6.3 + 79.

First, calculate the value of the argument:

360 * 60 * 6.3 + 79 = 136080 + 79 = 136159

Now, substitute this value back into the sine function:

sin(136159)

The sine function has a periodicity of 360 degrees or [tex]2\pi[/tex] radians. Therefore, we can subtract multiples of 360 degrees from the argument without changing the value of the sine function. Let's find the nearest multiple of 360 degrees to 136159:

136159 ÷ 360 [tex]^\sim_\sim[/tex] 378.22

Since the quotient is not an integer, we can conclude that subtracting multiples of 360 degrees will not bring us closer to a maximum or minimum value of the sine function.

Therefore, to find the maximum voltage, we need to evaluate sin(136159) directly. However, calculating the sine function of such a large number is not practical or necessary. The sine function oscillates between -1 and 1, and the maximum value it can reach is 1.

So, regardless of the specific value of sin(136159), the maximum voltage produced by the system will be:

Maximum voltage = 12 * 1 = 12 volts.

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Answer:

m<H = 62.7°

Step-by-step explanation:

If we use an inverse sin, then that would be sin^-1(8/9) Because Sin equals opposite over adjacent.

Answer:

H = 62.7 degrees

Step-by-step explanation:

Because this is a right triangle, we can use one of the trigonometric functions to find angle H:

Notice that sides HJ and IJ are given. If we are trying to find angle H, then HJ is the hypotenuse (longest side) and IJ is the opposite (side opposite to the angle we are trying to find). Since the opposite and hypotenuse are both given, we can use a sine function to find the angle of H (keep in mind that sin(<) = opp/hyp):

sin(H) = 8/9

We have to use the inverse of sine (sin^-1 or arcsin) to find angle H and use a calculator to solve:

arcsin(8/9) = H = 62.7 degrees

Answer:

x ≥ -5

Step-by-step explanation:

Since we see the dot is filled in, we know the sign is either ≤ or ≥. Then, we can see that x is greater than -5 as the arrow is pointing in the positive direction (to the right). Therefore, it would be x ≥ -5

Answer:

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

As per given, the distance from the center to both of the chords is same, therefore both chords have same length:

The length of each chord is:

Use Pythagorean theorem to find the radius, the distance from the center to one end of the chord:

The correct options are rectangular prism, square pyramid.

When a shape has a rectangular cross-section, it means that if the shape is cut perpendicular to its base, the resulting cut will be a rectangle. So, the only shapes that will have a rectangular cross section are those whose base is a rectangle or a shape that can be inscribed within a rectangle.

The shapes that have rectangular cross sections when they are cut perpendicular to the base are:

Rectangular prism

Square pyramid

Therefore, the correct options are rectangular prism, square pyramid.

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Complete question:

The result of the row 1 multiplication by 1/4 is determined as  [¹/₂  0 ].

The resultant of the row multiplication in the surd is calculated by applying the following method;

row 1 in the given surds = [2 0]

To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;

[2 0] x 1/4 = 1/4(2 0)

= [¹/₂  0 ]

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that 2, and 0 by 1/4.

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The quadratic equation is solved and intersect at the points (4, 1) and (-1, 16)

Given data ,

To find the intersection points of the two functions, we can set them equal to each other and solve for x:

x² - 6x + 9 = -x² + 17

Bringing all the terms to one side:

2x² - 6x - 8 = 0

Dividing by 2:

x² - 3x - 4 = 0

We can factor this quadratic equation as:

(x - 4)(x + 1) = 0

So the solutions are:

x = 4 or x = -1

To find the corresponding values of y, we can substitute each value of x into either of the original equations

y = x² - 6x + 9

When x = 4:

y = 4² - 6(4) + 9 = 1

So one intersection point is (4, 1).

When x = -1:

y = (-1)² - 6(-1) + 9 = 16

So the other intersection point is (-1, 16).

Hence , the two functions intersect at the points (4, 1) and (-1, 16)

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Let the number of twin births in 2000 be x.

According to the problem, the number of twin births in 2015 increased by 14%, which means the number of twin births in 2015 is:

x + 0.14x = 1.14x

We also know that the number of twin births in 2015 is approximately 133,950, so we can set up the following equation:

1.14x = 133,950

Solving for x, we get:

x = 117,500

Therefore, there were approximately 117,500 twin births in 2000.

The length of wire used for the square is 0.25 meters and the length of wire used for the circle is 1 meter. To maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.

To minimize the total area of both figures and minimize the length of wire used, the wire should be cut in half, giving each piece a length of 1 meter.

For the square frame, we know that each side of the square is equal to the length of wire used to make it, so we can divide the 1 meter of wire in half to get 0.5 meters for each side of the square.

The perimeter of the circle is the length of wire used to make it, so we can use the remaining 1 meter of wire to find the radius of the circle:

2πr = 1

r = 1/(2π)

Using this radius, we can find the circumference of the circle and the length of wire used:

C = 2πr = 1 meter

Therefore, the length of wire used for the square is 0.5 meters and the length of wire used for the circle is 1 meter.

To maximize the total area, we need to cut the wire into two equal pieces, each with a length of 1 meter.

For the square frame, each side will have a length of 0.25 meters, which will give us a total area of 0.0625 square meters.

For the circle, the radius will be 1/(4π) meters, which will give us a circumference of 1/(2π) meters and a total area of π/(16) square meters.

Therefore, to maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.

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the value of the test statistic is approximately 5.19.we can get the answer by using formula .

what is statistic  ?

A statistic is a numerical value or measure that is calculated from a sample of data, and is used to describe or make inferences about a population. Statistics are used in various fields, including business, economics, social sciences, and natural sciences, to analyze data

In the given question,

To test the claim that the percentage of residents who favor construction is more than 49%, we can use a one-sample z-test. The test statistic can be calculated as:

z = (p - P) / √(P * (1 - P) / n)

where:

p = the sample proportion (0.53)

P = the hypothesized population proportion under the null hypothesis (0.49)

n = the sample size (800)

Substituting the given values into the formula, we get:

z = (0.53 - 0.49) / √(0.49 * 0.51 / 800) ≈ 5.19

Rounding the test statistic to two decimal places, we get:

z ≈ 5.19

Therefore, the value of the test statistic is approximately 5.19.

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