evaluate : 20-[5+(9-6]​

(a) A vector v parallel to the line of intersection L is v = <1, 1, -2>. (b) The cartesian equation of the plane is -7x + 10y - 3z = -1

(a) To find a vector v parallel to the line of intersection L, we need to take the cross product of the normal vectors to the two given planes. The normal vectors are the coefficients of x, y, and z in the equations of the planes.

In this case, the equations of the planes are:

x + y - 2z = 1

4x + y + 3z = 4

The normal vectors to these planes are <1, 1, -2> and <4, 1, 3>, respectively. Since the line of intersection is parallel to both planes, a vector parallel to the line must be perpendicular to both normal vectors.

We can find such a vector by taking the cross product of the two normal vectors, which gives us: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>

Therefore, a vector v = <1, 1, -2>.

(b) To find the equation of the plane through the point (2, -1, 3) and perpendicular to L, we need to find a normal vector to the plane that is also parallel to L.

We can find such a vector by taking the cross product of the normal vectors to the two given planes. The normal vectors are <1, 1, -2> and <4, 1, 3>, so the cross product is: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>

This vector is parallel to L, so it can serve as the normal vector to the desired plane. The equation of the plane can be written in point-normal form as: -7(x - 2) + 10(y + 1) - 3(z - 3) = 0

Simplifying, we get:

-7x + 10y - 3z = -1

Therefore, the cartesian equation of the plane is -7x + 10y - 3z = -1, and it passes through the point (2, -1, 3) and is perpendicular to the line of intersection between the given planes.

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[tex]\textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{5}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 13^2 - 5^2}\implies h=\sqrt{ 169 - 25 } \implies h=\sqrt{ 144 }\implies h=12 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{10\times 10}{100}\\ h=12 \end{cases}\implies V=\cfrac{(100)(12)}{3}\implies V=400~in^3[/tex]

The translation used is of 4 units to the right and 4 units upwards.

To find it, we just need to look at one of the vertices of the figures.

We can see that the vertex U starts at:

U = (0, -1)

And the second vertex U' is at (4, 3)

Taking the difference we will get:

(4, 3) - (0, -1) = (4, 4)

So we have a translation of 4 units to the right and 4 units upwards.

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Answer:

Its B because you find the number in the middle, if theres two numbers in the middle, you add them up and divide by 2

the answer is B

the answer is B because 21 and 23 both seem to be in the middle. when two numbers are in the middle, you add them, then divide by two as a result, you would get 22.

The result of the regression analysis will provide you with the best-fitting model and its R² value.

To find the model that best fits the data, we will perform a regression analysis using the given data. The dependent variable is the number of insect species, and the independent variable is the year coded as 1, 2, 3, and so on. The table can be rewritten as:

Year (X): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Species (Y): 53, 38, 49, 35, 42, 47, 60, 67, 82

A linear regression can be performed to determine the model that best fits the data. After analyzing the data, we will identify the corresponding R² value, which represents the proportion of the variance in the dependent variable (insect species) that is predictable from the independent variable (year).

The result of the regression analysis will provide you with the best-fitting model and its R² value. Keep in mind that higher R² values (closer to 1) indicate a better fit of the model to the data.

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The correct answer is F.

To apply the Ratio Test, we need to compute:

L = lim(n → ∞) |a(n+1)/a(n)| = lim(n → ∞) |(8(2n+3) + 4)/(8(2n+1) + 4)|

Dividing numerator and denominator by 8(2n+3), we get:

L = lim(n → ∞) |(1 + 1/(2n+3))/(1 + 1/(2n+1))|

As n → ∞, both fractions approach 1, so the limit simplifies to:

L = lim(n → ∞) 1 = 1

Since L = 1, the Ratio Test is inconclusive. We cannot say anything about the convergence or divergence of the series from this test alone.

Therefore, the correct answer is F. The Ratio Test is inconclusive, but the series may converge conditionally by another test or tests.

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Answer: 6

Step-by-step explanation: Area = 1/2 (a+b) x h, divide both side by 1/2(a+b), we have Area : (1/2 (a+b)) = h. Now, replace A = 24, a=5.8, b= 2.2. We got h = 6.

Answer:

Subtract the smaller amount of [tex]x[/tex] → [tex]2x+6 > 15[/tex]

Then subtract 6 from 15 as it is a plus you do the opposite → [tex]2x > 9[/tex]

Now divide 9 by 2 to isolate [tex]x[/tex] → [tex]x > 4.5[/tex]

The data sets represent the answers of twenty students in Class A and twenty students in Class B regarding the number of hours they took to prepare for an exam. These data sets are important because they help us understand the study habits and time allocation of the students in each class.

To analyze the data sets, first, collect the data from each student in both classes. Record the number of hours they took to prepare for the exam, ensuring you have 20 responses from Class A and 20 from Class B. Then, you can compute the average, or mean, time spent for each class by summing up the hours reported by all students in each class and dividing by 20.

Next, compare the averages for Class A and Class B to determine if there is a significant difference in the time spent preparing for the exam. Additionally, you can calculate other statistical measures such as median and mode to gain further insight into the data sets.

Furthermore, analyzing the distribution of the data, such as the range, will provide information on the variability of the time spent studying in each class. This can help identify any trends or patterns in the students' preparation time.

In conclusion, the data sets representing the number of hours spent by students in Class A and Class B to prepare for an exam can provide valuable insights into their study habits, the effectiveness of their preparation, and any possible correlations between time spent studying and exam performance.

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The number of yellow marbles Stefan received is 4.

To find out how many yellow marbles Stefan received, we need to calculate 10% of the total number of marbles, which is 40.

Percentage calculations involve finding a part of a whole, and in this case, we are looking for the part that represents the yellow marbles. To find 10% of 40 marbles, you simply multiply the total number of marbles (40) by the percentage value (10%) as a decimal. To convert 10% to a decimal, you divide by 100, giving you 0.1.

Now, multiply the total marbles by the decimal value:

40 marbles * 0.1 = 4 marbles

So, Stefan received 4 yellow marbles in the bag he bought from the craft store.

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The component form of u + v is approximately (2.9886, 2.6077).

We have,

To find the component form of u + v, we need the lengths of u and v and the angles they make with the positive x-axis.

Given:

||u|| = 3

θu = 5° (angle with the positive x-axis)

||v|| = 1

θv = 120° (angle with the positive x-axis)

We can express the vectors u and v in component form using their magnitudes and the trigonometric functions:

u = ||u|| x cos(θu) x i + ||u|| x sin(θu) x j

v = ||v|| x cos(θv) x i + ||v|| x sin(θv) x j

Now, let's calculate the components of u and v:

For u:

u = 3 x cos(5°) x i + 3 x sin(5°) x j

For v:

v = 1 x cos(120°) x i + 1 x sin(120°) x j

To find u + v, we can add the corresponding components:

u + v = (3 x cos(5°) + 1 x cos(120°)) x i + (3 x sin(5°) + 1 x sin(120°)) x j

Now, we can simplify the expressions for the x and y components:

u + v = (3 x 0.996194698 + 1 x (-0.5)) x i + (3 x 0.087155743 + 1 x 0.866025404) x j

= 2.988584094 x i + 2.607735164 x j

Therefore,

The component form of u + v is approximately (2.9886, 2.6077).

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To find the cube of a semimajor axis length (A), we need to raise the value to the third power, which is simply multiplying it by itself three times. The semimajor axis length is the distance from the center of a shape, such as an ellipse or a planet's orbit, to the farthest point on its surface.

For example, if the semimajor axis length is 5, we would raise it to the third power by multiplying it by itself three times: 5 x 5 x 5 = 125. So the cube of a semimajor axis length of 5 is 125.

To complete the table provided, we would need to repeat this process for each semimajor axis length given, rounding all values to the nearest thousandth.

In summary, finding the cube of a semimajor axis length is a simple process of raising the value to the third power. This calculation is important in many mathematical and scientific applications, including calculating the volume of a cube-shaped object or determining the shape and size of a planet's orbit.

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This is the correct answer. I hope this helps!

Grass Seed Area = L - 20 1/8

To help Warren determine the area of his lawn where grass seed is needed, we first need to know the total area of his lawn.

Unfortunately, you have not provided the dimensions of the entire lawn. However, I can guide you through the process using the information given about the pool.

First, let's find the area of the pool. The dimensions are 5 3/4m by 3 1/2m. To find the area, multiply the length by the width:
Area = (5 3/4) * (3 1/2)
Convert the mixed numbers to improper fractions:
Area = (23/4) * (7/2)
Multiply the fractions:
Area = (23*7) / (4*2) = 161/8

Now convert the improper fraction back to a mixed number:
Area = 20 1/8 square meters
This is the area of the pool. To find the area where grass seed is needed, subtract the pool's area from the total area of the lawn. Assuming the total area of the lawn is "L" square meters, the area to be covered with grass seed would be:
Grass Seed Area = L - 20 1/8

Once you provide the dimensions of the entire lawn, you can follow these steps to find the area where grass seed is needed.

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[tex](x)(18)=(x+1)(16)\implies 18x=16x+16\implies 2x=16 \\\\\\ x=\cfrac{16}{2}\implies x=8=RW[/tex]

Caroline bought approximately 3.70 pounds of chicken breast.

Let's use algebra to solve the problem:

Let x be the number of pounds of chicken breast Caroline bought.

We know that 2.5 pounds of chicken breast cost $23.50, so we can set up the following proportion:

2.5 / $23.50 = x / $34.78

To solve for x, we can cross-multiply and simplify:

2.5 * $34.78 = x * $23.50

$86.95 = $23.50x

x = $86.95 / $23.50

x ≈ 3.70 pounds

Therefore, Caroline bought approximately 3.70 pounds of chicken breast.

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The height of the cone is approximately 12.15 millimeters (rounded to the nearest hundredth).

To find the height of the cone, we need to use the formula for the volume of a cone:

V = (1/3)πr²h

where V is the volume, r is the radius, h is the height, and π is approximately equal to 3.14.

We are given the volume of the cone as 2,279.64 cubic millimeters. We can plug this value into the formula and solve for h:

2,279.64 = (1/3)πr²h

Multiplying both sides by 3 and dividing by πr², we get:

h = (3 × 2,279.64) / (π × r²)

Now, we need to find the radius of the cone. Unfortunately, we are not given this information directly. However, we can use the fact that the volume of a cone is also given by:

V = (1/3)πr²h

If we rearrange this formula to solve for r², we get:

r² = 3V / (πh)

Now, we can substitute the given values for V and h and simplify:

r² = 3(2,279.64) / (π × h) ≈ 2,304.32 / h

Taking the square root of both sides, we get:

r ≈ √(2,304.32 / h)

Now, we can substitute this expression for r into our earlier formula for h:

h = (3 × 2,279.64) / (π × r²) ≈ (6,838.92 / π) / (2,304.32 / h)

Simplifying, we get:

h ≈ 2,279.64 × h / (2,304.32 / h)

h² ≈ 2,279.64 × h / (2,304.32 / h)

h³ ≈ 2,279.64

Taking the cube root of both sides, we get:

h ≈ 12.15

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The probability to select a male or someone in their 40's for a ceo position is company is equals to the 1/18. So, the option(c) is right answer for the problem.

We have a data of employees' information. It contains gender and age of employees in acme painting company. Randomly one employee is selected. We have to determine chance or probability that a ceo select a male or someone in their 40's. Sample size, n= 18

Probability is defined as chances of occurrence of an event. It is calculated by dividing the favourable response to the possible total outcomes.

Total possible outcomes= 18

number of male in her 40's age = 1

So, probability that select a male or someone in their 40's = 1/18

Hence, required probability is 1/18.

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Complete question:

the above figure completes the question.

the gender and age of acme painting company's employees are shown below. age gender 23 female 23 male 24 female 26 female 27 male 28 male 30 male 31 female 33 male 33 female 33 female 34 male 36 male 37 male 38 female 40 female 42 male 44 female if the ceo is selecting one employee at random, what is the chance he will select a male or someone in their 40s?

a)1/3

b)1/2

c) 1/18

d) 11/18

Answer:

Si hoy es martes en 300 días será lunes.

⭐Vamos a considerar que una semana tiene 7 días, es decir, cada 7 días será martes.

Pensamos una aproximación de semanas, al dividir 300 entre 7:

300 ÷ 7 = 42,85 ≈ 42 semanas completas

Cantidad de días que hay en 42 semanas:

7 × 41 = 294 días

Cantidad de días que faltan para completar 300:

300 - 294 = 6 días

El día 294 será martes

6 días después (para completar 300) será lunes ✔️

Step-by-step explanation:

Brainlist porfavor

Answer:

Si hoy es martes en 300 días será lunes.

The slope of the secant line connecting two points on a curve can be calculated using the formula: slope of secant line = (change in y) / (change in x).

For this problem, the two points are (-1, f(-1)) and (2, f(2)), and we need to find the slope of the secant line connecting them. To do this, we first need to find the y-coordinates of these points by plugging the given x-values into the function f(x) = 3x^2 + 4x - 5. Then we can use the formula for the slope of a secant line to find the slope of the line connecting these two points. The slope of the secant line is an important concept in calculus and is used to approximate the instantaneous rate of change of a function at a particular point.

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The vertical distance traveled by the rover is approximately 140.784 meters.

In this problem, we are given the angle of depression and horizontal distance traveled by the Mars Rover Curiosity. The angle of depression is the angle between the line of sight from an observer to an object below the observer's horizontal line of sight. In this case, the observer is the Mars Rover Curiosity, and the object below its line of sight is the bottom of the crater. The horizontal distance traveled by the rover is 110 meters.

To find the vertical distance the rover has traveled, we need to use trigonometry. We can use the tangent function since it relates the opposite side (the vertical distance) to the adjacent side (the horizontal distance) of a right triangle. Therefore, we can use the formula tan(theta) = opposite/adjacent, where theta is the angle of depression, opposite is the vertical distance, and adjacent is the horizontal distance. Rearranging this formula, we get opposite = adjacent * tan(theta).

Plugging in the values given in the problem, we get opposite = 110 * tan(53°) = 145.911 meters (rounded to the nearest thousandth). Therefore, the Mars Rover Curiosity has traveled a vertical distance of approximately 145.911 meters into the crater.

This would be:

Let h be the vertical distance traveled by the rover. Then we have:

tan(53°) = h/110

Solving for h, we get:

h = 110 * tan(53°) ≈ 140.784 meters

Therefore, the vertical distance traveled by the rover is approximately 140.784 meters.

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Distance time speed of different animals are:

Lion = 60 km/h  Sailfish = 130 km/h Peregrine Falcon  = 389 km/h Cheetah = 120 km/h  Springbok = 100 km/h Golden Eagle  = 320 km/h.

Here are the answers for each one:

1. Lion: The lion traveled a distance of 30 kilometers in a time of 30 minutes. To find the lion's speed, we can use the formula: speed = distance ÷ time. So, the lion's speed was 30 km ÷ 0.5 hours = 60 km/h.

2. Sailfish: The sailfish traveled a distance of 195 kilometers in a time of 1 hour and 30 minutes, which is the same as 1.5 hours. To find the sailfish's speed, we can again use the formula: speed = distance ÷ time. So, the sailfish's speed was 195 km ÷ 1.5 hours = 130 km/h.

3. Peregrine Falcon: The peregrine falcon traveled a distance of 778 kilometers in a time of 120 minutes, which is the same as 2 hours. To find the peregrine falcon's speed, we can once again use the formula: speed = distance ÷ time. So, the peregrine falcon's speed was 778 km ÷ 2 hours = 389 km/h.

4. Cheetah: The cheetah traveled a distance of 30 kilometers in a time of 15 minutes, which is the same as 0.25 hours. To find the cheetah's speed, we can use the formula: speed = distance ÷ time. So, the cheetah's speed was 30 km ÷ 0.25 hours = 120 km/h.

5. Springbok: The springbok traveled a distance of 10 kilometers in a time of 6 minutes, which is the same as 0.1 hours. To find the springbok's speed, we can use the formula: speed = distance ÷ time. So, the springbok's speed was 10 km ÷ 0.1 hours = 100 km/h.

6. Golden Eagle: The golden eagle traveled a distance of 240 kilometers in a time of 45 minutes, which is the same as 0.75 hours. To find the golden eagle's speed, we can use the formula: speed = distance ÷ time. So, the golden eagle's speed was 240 km ÷ 0.75 hours = 320 km/h.

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The value of Emma's deposit after 3 years, including simple interest, is $90 + $10.80 = $100.80.

Simple Interest = Principal x Rate x Time

In this case, the Principal is $90 (the initial deposit), the Rate is 4% (0.04 as a decimal), and the Time is 3 years.

Step 1: Calculate the simple interest.
Simple Interest = $90 x 0.04 x 3
Simple Interest = $10.80

Step 2: Add the simple interest to the initial deposit.
Total Value = Principal + Simple Interest
Total Value = $90 + $10.80
Total Value = $100.80

So, the value of Emma's deposit after 3 years is $100.80.

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Since f''(x) is always 0, f(x) is not concave upward on any interval.

On what interval is f concave upward?

The first derivative of f(x) is f'(x) = 6.
The second derivative of f(x) is f''(x) = 0.
The interval on which f(x) is increasing is when f'(x) > 0, which is when x is in the interval (-2,-5) U (1,60).
The interval on which f(x) is decreasing is when f'(x) < 0, which is when x is in the interval (-5,1).
The interval on which f(x) is concave downward is when f''(x) < 0, which is all values of x.
The interval on which f(x) is concave upward is when f''(x) > 0, which is no values of x.

To find the first derivative of f(x), we need to take the derivative of each term separately. The derivative of 3 is 0, the derivative of 6x is 6, and the derivative of -153 +3.2 is 0. Adding these up gives us f'(x) = 6.

To find the second derivative of f(x), we need to take the derivative of f'(x), which is a constant function. The derivative of a constant function is always 0, so f''(x) = 0.

To determine where f(x) is increasing, we need to find the values of x where f'(x) > 0. Since f'(x) is a constant function, it is always positive, so f(x) is increasing on the interval (-2,-5) U (1,60).

To determine where f(x) is decreasing, we need to find the values of x where f'(x) < 0. Since f'(x) is a constant function, it is always positive, so f(x) is decreasing on the interval (-5,1).

To determine where f(x) is concave downward, we need to find the values of x where f''(x) < 0. Since f''(x) is always 0, f(x) is concave downward on all values of x.

To determine where f(x) is concave upward, we need to find the values of x where f''(x) > 0. Since f''(x) is always 0, f(x) is not concave upward on any interval.

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As a general guideline, the research hypothesis should be stated as the alternative hypothesis, which is the statement that researchers are trying to support or prove.

The research hypothesis is a statement that describes the expected relationship between variables or the expected difference between groups in a research study. It should be based on a clear and specific research question, and it should be testable using appropriate statistical methods.

In other words, the research hypothesis should be a clear and concise statement that proposes a relationship or difference between variables that can be tested through data analysis. It should also be framed in a way that allows for the rejection or acceptance of the hypothesis based on the results of the study.

The null hypothesis, on the other hand, is the statement that there is no significant relationship or difference between variables. It serves as the default assumption until evidence is provided to support the alternative hypothesis.

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A research hypothesis should be stated as the predicted outcome of the study. It's often a declarative sentence that shows the relationship between variables in a study. The research hypothesis is often contrasted with a null hypothesis, which claims no significant relationship between the study's variables.

In general, a research hypothesis should be stated as the predicted outcome of the study. A research hypothesis is usually written in a declarative sentence format and states the relationship between variables in the study. For example, if your research is about studying the impact of amount of study time on test scores, your hypothesis could be: 'Students who spend more time studying will have higher test scores.'

The research hypothesis is often contrasted with a null hypothesis, which states there will be no significant relationship between the study's variables. In our example, the null hypothesis would be: 'The amount of study time will not impact the test scores significantly.' Remember, a research hypothesis should always be testable through research methods.

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Answer:

Step-by-step explanation:

We can start by converting the distance and time to the appropriate units.

1200000 meters = 1200 kilometers (since 1 kilometer = 1000 meters)

120 minutes = 2 hours (since 1 hour = 60 minutes)

Now we can use the formula:

speed = distance / time

speed = 1200 km / 2 hours

speed = 600 km/h

Therefore, the speed of the new plane is 600 km/h.

Answer: 600km/

First step:

1200000m=1200Km * 1m=0,001km

Second step:

120min=2h *1h=60min

Last step:

1200km÷2h= 600km/

SOLUTION

600km/

Step-by-step explanation:

Answer:

  124°

Step-by-step explanation:

You want the measure of the angle marked (4+10x) where chords cross. The chords intercept arcs marked (9x+20) and (10x).

The measure of the angle where chords cross is the average of the measures of the intercepted arcs.

  ((9x +20) +(10x))/2 = 4 +10x

  19x +20 = 20x +8 . . . . . . . . . multiply by 2

  12 = x . . . . . . . . . . . . . . subtract (19x+8)

The angle at E is ...

  4 +10(12) = 124

The measure of angle DEC is 124°.

__

Additional comment

Arc DC is 128°; arc BU is 120°.

$148.39 much money will he have to spend for his skateboard.

Levi will have to spend approximately $148.39 for his skateboard.

The original price can be defined as the cost price of an item or a service. The decrease in the original price of a product or service is called the discount offered to the buyer. Generally, this discount is expressed as a percentage.

Original Sale Price means the price at which the current Owner purchased the Property (not including commissions, loan origination fees, appraisals fees, title insurance premiums and other similar transaction costs).

To calculate this, we need to find 6% of the original price and add it to the original price:

6% of 139.99 = 0.06 x 139.99 = 8.3994

Adding this to the original price gives:

139.99 + 8.3994 = 148.3894

Rounding to the nearest cent gives $148.39.

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Given AB and AC are lines that are tangent to the circle with the measure of angle BAC = 40°, ∠BDC is 140°.

A tangent to a circle is a line that intersects the circle at a single point. The point at which the tangent intersects the circle is known as the point of tangency. The tangent is perpendicular to the circle's radius, with which it meets.

You've been handed two tangent lines. You will also be handed a four-sided figure. All four-sided figures have 360 degrees of rotation. At 90 degrees, a radius meets a tangent.

∠BDA = 90°

∠DCA = 90°

∠BCA = 40°

All the angles in total make 360°, so:

∠BDA + ∠DCA + ∠BCA + ∠BDC = 360

90 + 90 + 40 + ∠BDC = 360

220 + ∠BDC = 360

∠BDC = 360 - 220

= 140°

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Correct question:

Given AB and AC are lines that are tangent to the circle with the measure of angle BAC = 40°, what is the measure of angle BDC? Image is attached below.

The fraction is 1/6. Option D

First, we need to know the conversion factor the parameters.

Then, we have that';

1 liter = 1000 milliliter

10 milliliters (ml) = 1 centiliter (cl)

10 centiliters =  1 deciliter (dl) = 100 milliliters

1 liter =  1000 milliliters

1 milliliter =  1 cubic centimeter

1 liter =  1000 cubic centimeters

Then, we can say that;

If 1 liter = 1000ml

Then 2 4/8 = 400ml

2.4 liters is equal to 2.4 x 1000= 2400 milliliters.

400/2400

Simplify the fraction;

4/24

Divide the values, we get;

1/6

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