ACTIVITY 4: Solve the following inequalities.

Answer:

Step-by-step explanation:

In a circle, the measure of an inscribed angle is equal to half the measure of its intercepted arc. In this case, the inscribed angle is ∠WVX and its intercepted arc is ⌢WX.

Since the length of ⌢WX is (9/2)π, its measure in degrees is (9/2)π * (180/π) = 810/2 = 405 degrees.

Therefore, the measure of ∠WVX is half the measure of its intercepted arc, which is 405/2 = 202.5 degrees.

The ratio of 8 : 1/3 is equivalent to the simplified ratio of 24 : 1.

To analyze and describe the ratio 8 : 1/3, we need to convert the fraction to a ratio with a whole number. One way to do this is to express the fraction as a ratio with a denominator of 3:

1/3 = 1:3

Now we can rewrite the ratio 8 : 1/3 as:

8 : 1:3

We can simplify this ratio by multiplying both terms by 3 to get rid of the fractional term:

8 × 3 : 1:3 × 3

24 : 1

Therefore, the ratio 8 : 1/3 is equivalent to the simplified ratio 24 : 1. This means that for every unit in the second part of the ratio, there are 24 units in the first part of the ratio. In other words, the first part of the ratio is 24 times larger than the second part.

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The likelihood that a milkshake chosen at random will be a sloppy, thin, flavourless mess is 0.62.

The possibility or chance of an event occurring is measured by probability. It is a number between 0 and 1, where 0 denotes that the occurrence is impossible and 1 denotes that it is unavoidable. By dividing the number of favourable outcomes by the total number of potential outcomes, the probability of an occurrence is determined.

a. The milkshake will most likely turn out to be a watery, thin, flavourless mess (2, 4, 7).

The likelihood that a milkshake chosen at random would be a sloppy, thin, flavourless mess is equal to the final result of the milkshake will be a watery, thin, flavourless mess.

=2+4+7/21

=13/21

=0.62

b. No association can be removed from this table. We are unable to forecast the result of any event since the overall number of events is random.

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The given function, f(x) = x⁴ - 2x², is even function.

The nature of the function, whether it is even or odd can be determined by applying the following rules.

Even function, f(x) = f(-x)

Odd function; f(x) = -f(-x)

The given function, f(x) = x⁴ - 2x²

Test of for even function;

f(-x) = (-x)⁴ - 2(-x)²

f(-x) = x⁴ - 2x²

so f(x) = f(-x), the function is even.

Test for odd function;

-f(-x) = - [(-x)⁴ - 2(-x)²]

-f(-x) = -x⁴ + 2x²

so, f(x) ≠ -f(-x), the function is not odd.

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Area of the base of the pyramid is 16 square centimeters

Area of one lateral face of the pyramid  is  14 square centimeters

The lateral surface area of the pyramid is  56 square centimeters

The total surface area of the pyramid is 72  square centimeters

Area of the base of the pyramid = length x length

= 4 x 4

=16 square centimeters

Area of one lateral face of the pyramid = area of a triangle

=1/2×base×height

=1/2×4×7

=14 square centimeters

The lateral surface area of the pyramid =  4 x area of one lateral face

= 4 x 14

= 56square centimeters

The total surface area of the pyramid = lateral surface area of the pyramid +  area of the base

=56+16

=72 square centimeters

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Answer:

Step-by-step explanation:

sina=12/20=0.6

cosa=16/20=0.8

tana=0.6/0.8=0.75

Answer: e

Step-by-step explanation:

Answer:Valid

Step-by-step explanation:

The midpoint is M = 0.6 and the distance is D = 4.2

Given data ,

The distance between points D and E on the number line

D = 4.2

Now , the first point D = -1.8

And , the point E = 2.4

And , the distance D = 2.4 - 1.8 = 4.2 units

Thus, the midpoint between points D and E on the number line = 0.6

Hence, the distance and midpoint between points D and E on the number line 4.2 and 0.6

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The complete question is attached below :

What is the distance and midpoint between points D and E on the number line?

Answer:

sin(2A) = 2sin(A)cos(A)

To find cos(A), we can use the Pythagorean theorem:

sin^2(A) + cos^2(A) = 1

cos^2(A) = 1 - sin^2(A)

cos(A) = -√(1 - sin^2(A)) (since A is in QIII, cos(A) is negative)

cos(A) = -√(1 - (-24/25)^2) = -7/25

Now we can substitute into the double angle formula:

sin(2A) = 2sin(A)cos(A)

sin(2A) = 2(-24/25)(-7/25)

sin(2A) = 336/625

Therefore, sin(2A) = 336/625.

Hi! To determine if two lines are parallel given their equations, follow these steps:

1. Identify the slopes of the lines from their equations.

If the equations are in the slope-intercept form (y = mx + b), the slope is the coefficient of x (m). If the equations are in standard form (Ax + By = C), you can find the slope by rearranging the equation to the slope-intercept form.

2. Compare the slopes of both lines. If the slopes are equal, the lines are parallel.

In summary, given their math equations, you need to describe their slopes and check if they are equal to determine if the lines are parallel.

Hi to confirm that two lines are parallel lines given their equation you the gradient which is the value of x in the equation y=mx + c. Where m is the gradient

It should be noted that 3/10 kg to grams will be 300 grams.

To convert 3/10 kg to grams (g), we can use the following conversion factor:

1 kg = 1000 g

Therefore:

3/10 kg = (3/10) x 1000 g = 300 g

Hence, 3/10 kg is equal to 300 grams (g).

In conclusion, it should be noted that 3/10 kg to grams will be 300 grams.

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Using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem.

In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

A second-order equation of the form ax² + bx + c = 0 denotes a quadratic equation, where a, b, and c are real number coefficients and a 0.

So, we have the equation:

x²-3x+ 5 = 0

Now, solve it using the quadratic formula as follows:

x²-3x+ 5 = 0

a = 1

b = -3

c = 5

x = -(-3)±√(-3)² -4*1*5/2

Solve this further:

x = 3±√11/2

Therefore, using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.

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Correct question:

Solve x²-3x+ 5 = 0.

A.3+√-29 +VE/2 and 3- 2-29

B. 3+√29 and 3-√29

C. 3+√-11 and 3-√-11/2

D. 3+√11/2 and 3-√11/2

To check if the total number of beads used in each bracelet is even, we need to find out if the sum of the digits in the number 72 is even or odd.

If Ava made an even number of bracelets using the 72 beads, then the total number of beads used in each bracelet must be an even number.

One way to check if the total number of beads used in each bracelet is even is to find out if the sum of the digits in the number 72 is even or odd. If the sum of the digits is even, then it is possible that Ava made an even number of bracelets. If the sum of the digits is odd, then it is not possible that Ava made an even number of bracelets.

The sum of the digits in 72 is 7 + 2 = 9, which is an odd number. Therefore, it is not possible for Ava to have made an even number of bracelets using the 72 beads, without dividing the beads.

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Answer:

  x = ±1, ±√65

Step-by-step explanation:

You want the solution to (x² -1)³ = 64(x² -1)².

Subtracting the right side, we have ...

  (x² -1)³ -64(x² -1) = 0

  (x² -1)²(x² -1 -64) = 0

The solutions make the factors zero:

  x² -1 = 0   ⇒   x = ±1

  x² -65 = 0   ⇒   x = ±√65

Solutions are x = ±1 and x = ±√65.

__

Additional comment

The solutions ±1 are each multiplicity 2.

The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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Answer:

2x^2 = (2 x 2) x (2 x 2)

= 4 x 4

= 16

I hope this helps you

Answer: The square root of 1681 is 41.

Answer:

41

Step-by-step explanation:

It is 41

41 * 41 = 1681

41 ^ 2 = 1681

a) is Right angle Triangles both of them

b) The scale factor is 1:2.

Given AFD = 90 degrees, So CFD = 90 degrees.

So it a Right Angle Triangle.

Again ABC = 90 degrees, It's also a Right Angle Triangle.

Here see both the Triangle are opposite to each other so according to the theorem sum of all three angles of a triangle is 180 degrees

so if any angle is 90 deg then the other two sum is also 90 deg.

Given the scale Factor, 1/6 inch = 1 foot,

So it is a Reducing Scale so let 'x' be in inches

So the Scale Factor = 1:2

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water is being pumped into the tank at a rate of 23.7 cm³/min.we can take the derivative of the volume formula with respect to time and solve it

what is derivative  ?

In mathematics, a derivative is a measure of how much a function changes as its input value changes. More specifically, the derivative of a function is defined as the rate of change of the function at a particular point.

In the given question,

We can solve this problem using related rates, where we relate the rate of change of one variable to the rate of change of another variable.

Let's denote the height of the water in the tank by h, and the radius of the water surface by r. Then, we can use the formula for the volume of a cone to relate these variables:

V = (1/3)πr²h

We are given that the tank has height 9.0 m and diameter (and thus radius) 4.5 m at the top. We can use this information to find the relationship between h and r:

r = (1/2) × diameter = 2.25 m

h = 9.0 m - 2.0 m = 7.0 m

Now, we can take the derivative of the volume formula with respect to time:

dV/dt = (1/3)π(2r(dr/dt) + r²(dh/dt))

We want to find the rate at which water is being pumped into the tank, which is the rate of change of the volume with respect to time when the water level is rising at a rate of 21.0 cm/min. We are also given that water is leaking out of the tank at a rate of 11500.0 cm^3/min, so we can set these rates of change equal to each other:

dV/dt = (21.0 cm/min) × (1 m/100 cm)³ = 0.021 m³/min

11500.0 cm³/min = 11.5 × (1 m/100 cm)³ m³/min

Substituting these values and the values we found for r and h into the derivative formula, we get:

0.021 m³/min = (1/3)π(2(2.25 m)(dr/dt) + (2.25 m)²(11500.0 cm³/min)/(100 cm/m)³)

Simplifying and solving for dr/dt, we get:

dr/dt = [(0.021 m³/min) - (1/3)π(2(2.25 m)(11500.0 cm³/min)/(100 cm/m)³)] ÷ [(1/3)π(2(2.25 m))]

= 0.0237 m/min = 23.7 cm/min

Therefore, water is being pumped into the tank at a rate of 23.7 cm³/min.

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The matrix  that represents the solution to this system of equations is

1   0  0     2

0   1   0    -4

0   0   1      3

Therefore option B is correct.

A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

We solve a matrix by Arranging  the elements of equations in matrices and find the coefficient matrix, variable matrix, and constant matrix.

We then go ahead to write the equations in AX = B form.

we then take the inverse of A by finding the adjoint and determinant of A. Multiply the inverse of A to matrix B, thereby finding the value of variable matrix X.

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Here is a tree diagram to represent the sample space of Jill tossing a coin three times:

      H               T

    /   \           /   \

   H     T         H     T

 /  \   /  \     /  \   /  \

H   T  H   T    H   T  H   T

The concept of the sample space is fundamental to the calculation of probabilities because it defines the set of all possible outcomes that we are interested in measuring the likelihood of. By specifying the sample space, we can define events (subsets of the sample space) and assign probabilities to those events.

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The present value of $100 to be received after 3 years at 9% compounded quarterly is $73.67.

The formula for the present value of a future amount under quarterly compounding is:

PV = FV / (1 + r/4)⁴ⁿ

where PV is the present value,

FV is the future value, r is the interest rate per year, and n is the number of years.

In this case, FV = $100, r = 0.09 (9%), n = 3 years, and the interest is compounded quarterly

so the interest rate per quarter is r/4 = 0.0225.

Plugging these values into the formula, we get:

PV = $100 / (1 + 0.0225)¹² = $73.67

Therefore, the present value of $100 to be received after 3 years at 9% compounded quarterly is $73.67.

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The measure of angle x of the circle is x = 5.7

Given data ,

Let the center of the circle be represented as x

Now , the value of x is given by

The measure of angle ∠VWU = 43°

And , the measure of arc VU = ( 7x + 46 )°

Now , from the arc theorem of circle , we get

mVU = 2 ∠VWU

On simplifying , we get

2  ( 43 ) = ( 7x + 46 )

7x + 46 = 86

Subtracting 46 on both sides , we get

7x = 40

Divide by 7 on both sides , we get

x = 5.71

Hence , the measure of x of circle is x = 5.7

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Answer:

2 1/3

Step-by-step explanation:

add then multiplying to the nearest one.

The decimal used to figure the price of their clothing is 2.1

The improvement in Larry's test score written as a decimal is 1.52

Markup = 210%

= 210/100

= 21/10

= 2.1

Larry's increased test score percentage = 152%

= 152/100

= 1.52

In conclusion, the price of clothing and Larry's test score in decimals is 2.1 and 1.52 respectively.

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Answer:

[tex]x = \frac{(1 + \sqrt{11})( \sqrt{3 } - 1) }{2 } [/tex]

The midpoint of the line segment FG is the point (4, 12).

In geometry, the midpoint of a line segment is the point that is exactly halfway between the endpoints of the segment. It is the point that divides the segment into two congruent segments.

The formula for finding the midpoint of a line segment with end points (x₁, y₁) and (x₂, y₂) is:

Midpoint = [(x₁ + x₂)÷2, (y₁ + y₂)÷2]

So, the midpoint of the line segment with endpoints F(-10, 12) and G(18, 12) can be found as:

Midpoint = [(-10 + 18)÷2, (12 + 12)÷2]

= [8÷2, 24÷2]

= [4, 12]

Therefore, the midpoint of the line segment FG is the point (4, 12).

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The value of theta in the given trigonometry function is 45⁰.

The value of theta in the given trigonometry function is calculated as follows;

9 sin²θ tanθ  -  9 sin²θ = 0

Solve the equation as follows;

9 sin²θ tanθ  =  9 sin²θ

divide both sides by  9 sin²θ;

(9 sin²θ tanθ)/9 sin²θ = 9 sin²θ /9 sin²θ

tanθ = 1

Now, solve for θ as follows;

θ = tan⁻¹ (1)

θ = 45⁰

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