use the image and the information given to choose the correct answer on how line segments AC and BD are related.

To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Answer:

900 = 2 * 2 * 3 * 3 * 5 * 5 = 2^2 * 3^2 * 5^2

Step-by-step explanation:

900/2 = 450

450/2 = 225

225/3 = 75

75/3 = 25

25/5 = 5

5/5 = 1

900 = 2 * 2 * 3 * 3 * 5 * 5 = 2^2 * 3^2 * 5^2

Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}\)

Therefore, a sample size of at least 962 students should be taken to get a distribution of means of the samples with a standard deviation of 10.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much, on average, the individual data points deviate from the mean of the dataset. A smaller standard deviation indicates that the data points tend to be closer to the mean, while a larger standard deviation indicates that the data points are more spread out. The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences of each data point from the mean.

Here,

To calculate the sample size required to get a distribution of means with a standard deviation of 10, we can use the formula:

n = (z * σ / E)²

where:

n = sample size

z = z-score (corresponding to the desired level of confidence)

σ = population standard deviation

E = desired margin of error (which is the standard deviation of the distribution of sample means)

In this case, we want a distribution of means with a standard deviation of 10, so E = 10.

To determine the z-score, we need to choose a level of confidence. Let's say we want a 95% level of confidence, which corresponds to a z-score of 1.96.

Plugging in the numbers we have:

n = (1.96 * 70 / 10)²

n = 961.54

We can't have a fractional sample size, so we need to round up to the nearest whole number:

n = 962

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Answer:

y=2x+6

Step-by-step explanation:

1) The expression 2⁻ˣ⁺³ = 3 is matched with graph B.

2 The expression  3ˣ⁺¹=3 is matched with graph C.

3) The expression 4ˣ = 3 is matched with graph

4 ) The expression 1ˣ/4 = 3 is matched with graph

1) The graph of the expression 2⁻ˣ⁺³ = 3  represents an exponential function where the y-coordinate is 3 when the base 2 raised to the power of (-x+3).

2) The graph of the expression 3ˣ⁺¹=3represents an exponential function where the y-coordinate is 3 when the base 3 raised to the power of (x+1). This graph is a straight line with a slope of 1.

3)  The graph of the equation 4ˣ = 3 represents an exponential function where the base 4 raised to the power of x is equal to 3. This equation has a single solution, which can be determined using logarithms.

4) The graph of the expression 1ˣ/4 = 3 represents an exponential function where the base 1 raised to the power of (x/4) is equal to 3.

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Answer:

Step-by-step explanation can’t because he might pull out more than 10 dollars or less than 10 dollars.

Hey there! I'm happy to help!

A variable is a letter or symbol used to represent an unknown number.

We see two letters here: m and n. Therefore, those are the variables.

Have a wonderful day! :D

Answer:

It's A

Because it said that x-4 is bigger than 13 so anything bigger than 13 is the answer

Answer:

first term (a)=-2

common difference (d)=8

Now,

87th term=a+(n-1)d

=-2+(87-1)×8

=-2+86×8

=-2+688

=686

To earn an average score of 90, the score on the fourth test needs to be 98.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.

Given the score of the first three tests as:

91, 84, 87.

The average is given by the following formula:

Average = Sum of scores ÷ total number of tests

Let us suppose the score of fourth test as x.

Given that A = 90:

90 = (91 + 84 + 87 + x) ÷ 4

x = 98

Hence, the score on the fourth test must be equal to 98, to get an average score of 90.

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Answer:

Question unclear.

If the question was about the perimeter of the rectangle, it is calculated as:

= (Length * 2) + (Height * 2)

= (11 * 2) + (6 * 2)

= 22 + 12

= 34 cm

If the question was bout Area, the area is:

= Length * width

= 11 * 6

= 66 cm²

The magnitude of the vector is shown by the length of the vector and the angle it makes with the positive x-axis is shown by the direction of the vector.

The magnitude of vector v is 2 and the angle it makes with the positive x-axis is given as θ = 3.

The component form of vector v can be found by using the following formula:

V = ||V|| (cosθi + sinθj)

Therefore, the component form of vector v is given by:

V = 2 (cos3i + sin3j)

We can calculate the components by substituting the values for ||v|| and θ in the above formula.

Therefore, the x component of vector v is given by:

Vx = 2 cos3

Vx = 1.86

The y component of vector v is given by:

Vy = 2 sin3

Vy = 3.42

Therefore, the component form of vector v is given by:

V = 1.86 i + 3.42 j

This can be represented graphically as shown in the figure.

The magnitude of the vector is shown by the length of the vector and the angle it makes with the positive x-axis is shown by the direction of the vector.

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D 231 = 46w can be used to solve for w, the number of white eggs used last week.

The radioactive sponteanous decay of the parent nucleus gives rise to the daughter nucleus.

Radioactivity refers to the sponteanous decay of a substance. We have the formula;

N(t) = Noe^-kt

Where;

N(t) = amount of radioactive material left after time t

No = amount of radioactive material initially present

k = decay constant

t = time taken

Let us now solve the questions individually;

a)

No = 20 pounds

N(t) = ?

k = 0.0231

t = 10 years

N(t) = 20e^-(0.0231 * 10)

N(t) = 16 pounds

b)

No =  80 pounds

N(t) = ?

k = 0.0248

t =  75 years

N(t) =80e^-(0.0248 * 75)

N(t) = 12.45 pounds

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By using fraction, it can be calculated that

30 boards are required to cover a floor of width 205 inches wide

What is fraction?

Suppose there is a collection and a part of collection has to be taken.

The part which is taken is called fraction. In other words part of a whole is called fraction.

The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

This is a word problem on fraction

Width of each board = \(6\frac{5}{6}\) inches = \(\frac{41}{6}\) inches

Total width of floor = 205 inches

Number of boards required = \(205 \div \frac{41}{6}\) = \(205 \times \frac{6}{41}\) = 30

30 boards are required

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Answer:

The canister hold water = 14 litres

Step-by-step explanation:

Given - While 2/7 of a canister is full, it has 4 litre water in it.

To find - How many litres of water does the canister hold?

Proof -

Given that,

When is canister is \(\frac{2}{7}\) full , Total water = 4 litre

⇒If the canister is full , Total water = 4×\(\frac{7}{2}\) litre

                                                         = 2 × 7 = 14 litres

⇒The canister hold water = 14 litres

option (a) x = 9

Step-by-step explanation:

2/3x = 6

2x = 18

x = 18/2

x = 9.

The Definition of the Derivative correctly stated by

In mathematics, a derivative is the rate at which a function changes in relation to a variable. Calculus and differential equations issues must be solved using derivatives.

As, we know by definition of derivative

= \(\lim_{h \to 0}\) f(x+h)- f(x) / h

Also, the Derivative also shows the Slope of the secant line.

and, derivative is widely used to the rate of change then it also shows

Instantaneous rate of change.

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Answer:

(4 2/7) x (11 1/4) = 48 3/14

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Slope is defined as rise over run, so it is (26-11)/(5-2) = 15/3 = 5

Answer:

slope is 5

Step-by-step explanation:

slope formula says m= y2-y1/x2-x1

m=26-11/5-2

m=15/3

m=5

Answer: So, the sales tax on the item is $49.

Step-by-step explanation:

The sales tax rate is already given as 14%. It is stated that the item costs $350 before tax, and the sales tax rate is 14%. Therefore, the sales tax amount can be calculated by multiplying the cost of the item by the tax rate:

Sales tax amount = $350 * 14% = $350 * 0.14 = $49

So, the sales tax on the item is $49.

Answer:

163.67 ( I )

Step-by-step explanation:

Answer:

u=-1

Step-by-step explanation:

if you replace with a or b the answer on the left side is actually bigger since it is closer to 0 than -20. same with choice d

choice c makes -12-28 which is a smaller value than -20

The rate of interest is given by the equation R = 3.5 %

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the rate of interest be represented as R

Now , the simple interest I = $ 175

The principal amount invested P = $ 2,500

The time period T = 2 years

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )

Substituting the values in the equation , we get

Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )

Rate of Interest R = 17500 / 5000

Rate of Interest R = 3.5 %

Hence , the interest rate is 3.5 %

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Step-by-step explanation:

X = the angle between 28° and 49° (Directly opposite angles)

X + 28 + 49 = 180 (Sum of angles in a triangle)

X +77 = 180

X = 180 - 77

X = 103

The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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Answer:

The mean number of scores per game is 8

Step-by-step explanation:

Since we know we can find the mean by adding all the numbers and dividing them by many numbers there were. Once you add 8, 14, 4, 7, 6, 4, and 7, you will get 64. Since there were 8 numbers, you divide 64 by 8 to get 8.

If tan Ф = 15/8 then we have these trigonometric functions cosec Ф = 17/15, sec Ф = 17/8 and cot Ф = 8/15.

According to the question,

We have the following information:

Tan Ф = 15/8

We know that in this trigonometric function we have perpendicular divided by base.

Now, we can find the hypotenuse using the Pythagoras theorem:

Let's denote hypotenuse with h, perpendicular with p and base with b.

\(h^{2} =p^{2} +b^{2}\)

\(h^{2}\) = \((15)^{2} +(8)^{2}\)

\(h^{2} = 225+64\\h^{2} = 289\\h = \sqrt{289}\)

h = 17 units

Now, we have the following values:

Cosec Ф = 17/15 (Hypotenuse/perpendicular)

Sec Ф = 17/8 (h/b)

Cos Ф = 8/17 (b/h)

Cot Ф = 8/15 (b/p)

Hence, the correct options are A, B and D.

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