ACTIVITY 4: Solve the following inequalities.

The measure of angle U = 41.83 degree.

In the given right angle triangle

VW = 6

UV = 9

Since sinΘ  = (opposite side)/(hypotenuse)

Therefore,

sin U = VW/UV

        = 6/9

        = 0.667

Take inverse of sin both sides

     ∠U =  arcsin(0.667)

            = 41.83

Hence  ∠U = 41.83 degree

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The value of the constant term k in the exponential model of the bacteria population is k ≈ 0.0972

An exponential function is one in which the input variable is part of the exponent of the expression for the function.

The function for the population of the bacteria indicates;

[tex]P(t) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\cdot t)}}[/tex]

The population of the bacteria after t = 1 hour is P(1) = 10,532

Therefore;

[tex]P(1) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\times 1)}} = 10,532[/tex]

[tex]1 + 1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532}[/tex]

[tex]1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532} - 1[/tex]

[tex]e^{(-k\times 1)} = \frac{\frac{22,000}{10,532} - 1}{1.2}[/tex]

Taking the natural logarithm of both sides, we get;

[tex]\ln (e^{(-k\times 1)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]

[tex]\ln (e^{(-k)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]

[tex]\ln (e^{(-k)}) = -k = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex] ≈ -0.0972 (rounded to 4 decimal places)

-k ≈ -0.0972

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Answer:

The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 1, b = -1, and c = -1. So:

x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)

x = (1 ± sqrt(5)) / 2

Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.

Answer:

B.

Step-by-step explanation:

As the steps imply,

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 calculated value of the fraction that is greater than the fraction by the model is 1/2

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

Model fraction = 3/8

A fraction that is greater than the fraction by the model is represented as

Fraction > Model fraction

Substitute the known values in the above equation, so, we have the following representation

Fraction > 3/8

Add 1 to the numerator

So, we have

Fraction = 4/8

Simplify

Fraction = 1/2

Hence, the fraction that is greater than the fraction by the model is 1/2

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Answer:

x = -2/5

x = 3/4

Step-by-step explanation:

Factoring:

20x²-7x-6=0

20x²+8x - 15x - 6 = 0

4x * (5x + 2) - 3 * (5x + 2) = 0

(5x + 2) * (4x - 3) = 0

Cases:

5x + 2 = 0

4x - 3 = 0

x = -2/5

x = 3/4

Answer:

20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120

Step-by-step explanation:

now,

20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)

5x(4x-3) +2(4x-3)=0

(5x+2) (4x-3)=0

Either 5x=-2

X=-2/5

Or

4x=3

X=3/4

A measure of variability which the charity should use to accurately represent the data include the following: D. The range of 45 is the most accurate to use to show that they have plenty of money.

In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

Minimum (Min) = 10.

First quartile (Q₁) = 13.75.

Median (Med) = 20.

Third quartile (Q₃) = 26.25.

Maximum (Max) = 55.

For the IQR, we have:

IQR = Third quartile (Q₃) - First quartile (Q₁)

IQR = 26.25 - 13.75

IQR = 12.50

For the range, we have;

Range = maximum - minimum

Range = 55 - 10

Range = 45.

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To find the estimated amount John needs to save to buy the bike, we can subtract the amount he already has saved from the cost of the bike:

Estimated amount = Cost of bike - Amount already saved

Estimated amount = $337 - $103

Estimated amount = $234

Therefore, John needs to save an estimated $234 more to buy the bike.

Answer:

John needs to save about $234 more to buy the bike. Note that this is an estimate, as we do not know if John will need to pay any taxes or additional fees when purchasing the bike.

Step-by-step explanation:

To find out how much more John needs to save to buy the bike, we can subtract the amount he has already saved from the cost of the bike:

337 - 103 = 234

Therefore, John needs to save about $234 more to buy the bike. Note that this is an estimate, as we do not know if John will need to pay any taxes or additional fees when purchasing the bike.

If Justin mowed 45% of her garden in 18 minutes, then we can set up a proportion to find how long it would take him to mow 100% of the garden:

45/100 = 18/x

where "x" is the unknown number of minutes it would take to mow 100% of the garden.

To solve for "x," we can use cross-multiplication:

45x = 100 * 18

Simplifying the right-hand side:

45x = 1800

Dividing both sides by 45:

x = 40

Therefore, it would take Justin 40 minutes to mow all of his garden at the same rate of 45% in 18 minutes.

To explain this, we used the fact that the amount of work done (mowing a certain percentage of the garden) is directly proportional to the time it takes to do that work. This means that if Justin mowed 45% of the garden in 18 minutes, he would take proportionally longer to mow the entire garden. The proportion we set up allows us to find the unknown amount of time it would take to mow the entire garden. Solving the proportion, we found that it would take Justin 40 minutes to mow all of his garden at the same rate he mowed the 45%.

In a case whereby A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, the strength of the drug  can be expressed as 41%.

From the question, the total mass =400 g

The solvent mass = 236 g

Then the mass of the drug = 400-236

= 164

Then the mass percentage of the drug can be calculated as 164/400 * 100

= 41%

Therefore, the strenght of the drug can be expressed as  41%

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The solution to the prompt of multiple square roots is 5.

To obtain the sum of the multiple square roots, we need to first find the square of 30, sum it up in four places and find the square root of the last figure we obtained.

So this gives

√30 =5.47

5.47 + 5.47 + 5.47 + 5.47

= 21.88

=4.67 approximately 5

So. option 5 is the solution.

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The distance between the points (6,−10) and (6,−7) is 3 units

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

Points (6,−10) and (6,−7)

Because the points have the same x coordinate, the distance between the points (6,−10) and (6,−7) is the difference between the y coordinates

Using the above as a guide, we have the following:

Distance = -7 - -10

Evaluate

Distance = 3

Hence, the distance between the points (6,−10) and (6,−7) is 3 units

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Answer:

I dont know the answer I dont know  what it is I just needed points bye

Step-by-step explanation:

The number line on which point A represents the ant's position after crawling 2/8 yard would be a number line labeled in units of yards, with O representing 0 and A representing 1/4 yard to the right of O.

To decide the place of the insect subsequent to creeping 2/8 yard from the insect mount, we really want to address this distance on a number line.

Since 2/8 can be rearranged to 1/4, we can address the distance crept by the subterranean insect as 1/4 of a yard.

To develop a number line to address this distance, we can begin with the point addressing the subterranean insect mount (we should call it point O) and separate a distance of 1/4 of a yard to one side of O. This point, which we can name as point A, addresses the place of the insect subsequent to creeping 2/8 yard (or 1/4 yard) from the insect mount.

The number line would have units of yards, with the distance between every unit separated similarly. The point O would address 0 on the number line, and the point A would address 1/4 yard on the number line.

Thus, the number line on which point An addresses the insect's situation in the wake of creeping 2/8 yard would be a number line named in units of yards, with O addressing 0 and An addressing 1/4 yard to one side of O.

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The complete question is:

An ant crawled 2/8 yard from an ant mount. On which number line does point A represent the ants position after crawling 2/8 yard?

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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The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

A. x² + (y - 3)² = 36.

D. x² + (y + 8)² = 36.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.

Based on the information provided above, we have the following parameters:

Radius, r = diameter/2 = 12/2 = 6 units.

Center, (h, k) = (0, 3).

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 3)² = 6²

x² + (y - 3)² = 36.

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Answer:

60

Step-by-step explanation:

2$ times 30 luna bars at harmons is $60

Answer:

The equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

Step-by-step explanation:

To find the equation of a line that is parallel to 2y = x – 3, we need to determine the slope of the given line.

2y = x - 3 can be written in slope-intercept form y = (1/2)x - 3/2.

The slope of this line is 1/2.

Since we want a line parallel to this line, the slope of the new line will also be 1/2.

Next, we can use the point-slope form of a line to write the equation of the new line.

Point-slope form: y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Substituting the values, we get:

y - 3 = (1/2)(x - (-4))

Simplifying, we get:

y - 3 = (1/2)x + 2

Adding 3 to both sides, we get the final equation in slope-intercept form:

y = (1/2)x + 5

Therefore, the equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

The endpoints of the latus rectum of the parabola are (3, -2) and (3, -4)

Given data ,

Let the equation of the parabola be (y + 3)² = (x - 2)

Now , y² + 6y + 9 = x - 2

y² + 6y = x - 11

Now we can see that the vertex of the parabola is (2, -3), and the axis of symmetry is parallel to the y-axis. This means that the focus and directrix will also be parallel to the y-axis.

x = h - p

where (h, k) is the vertex and "p" is the distance between the vertex and the focus. In this case, (h, k) = (2, -3) and p = 1, so

x = 2 - 1

x = 1

Therefore, the equation of the directrix is x = 1

And , the axis of symmetry of the parabola is parallel to the y-axis, the latus rectum will be parallel to the directrix, and its endpoints will be equidistant from the focus and the directrix

The distance between the focus and the directrix is 1 unit, so the distance between the endpoints of the latus rectum will also be 1 unit

Therefore, the endpoints of the latus rectum will be at the points where the perpendiculars drawn from the focus to the directrix intersect the parabola

To find the points of intersection between this line and the parabola, we can substitute x = 3 into the equation of the parabola and solve for y

(y + 3)² = (x - 2)

(y + 3)² = (3 - 2)

(y + 3)² = 1

y + 3 = ±1

y = -2 or y = -4

Hence , the points of intersection between the perpendicular and the parabola are (3, -2) and (3, -4)

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Answer:

64.14

Step-by-step explanation:

Reading the passage I see that you have to multiply then divide

The surface area of the larger solid is,  171.7 mm²

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The volumes of two similar solids are 857.5 mm³ and 540 mm³.

And, The surface area of the smaller solid is 108 mm².l

Now, Let us assume that;

The surface area of the larger solid is, x

Hence, We get;

857.5 / x = 540 / 108

Solve for x as;

857.5 x 108 = 540 x

92,718 = 540x

x = 171.7 mm²

Thus, The surface area of the larger solid is,  171.7 mm²

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Using the sine ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6  units.

The sine ratio is part of the trigonometry ratios that can be applied to solve a right triangle, and it is written as:

sin ∅ = length of the opposite side / length of the hypotenuse of the right triangle

We are given the following information from the image above:

Reference angle (∅) = 75 degrees

length of the opposite side = x

length of the hypotenuse = 9

Plug in the values:

sin 75 = x/9

9 * sin 75 = x

x = 8.7 [to the nearest tenth]

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Jim must pay tax  $3.57.

The correct answer is (a) $3.57.

To calculate the sales tax that Jim must pay, we need to find 7% of the total cost of the shoes and laces.

The total cost of the shoes and laces is $50 (shoes) + $1 (laces) = $51.

To calculate the sales tax, we multiply the total cost by the tax rate:

Sales tax = 7% of $51

[tex]= 0.07 \times $51[/tex]

= $3.57.

Therefore, Jim must pay $3.57 in sales tax.

The correct answer is (a) $3.57.

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The resulting matrix will be in the form :

5 9 -4

0 -14 15

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.

To get a 1 in row 1, column 1, we perform the following elementary row operation:

R2 - 2R1 -> R2

This will subtract 2 times the first row from the second row and give us the result:

5 9 -4

0 -14 15

Matrices are useful for describing systems of linear or differential equations, as well as representing a linear application.

In conclusion,  in  a matrix function, the input and the output values are matrices.

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The quotient using a synthetic method of division is 8x² + 15x + 7/8 and the remainder is 71/64

The quotient expression is given as

(8x³ + 14x² - 2x + 1) divided by x - 1/8

Using a synthetic method of quotient, we have the following set up

1/8 |   8    14   -2   1

    |__________

Bring down the first coefficient, which is 8:

1/8 |   8    14   -2   1

    |__________

       8

Multiply 8 by 1/8 to get 1, and write it below the next coefficient and repeat the process

1/8 |   8    14   -2      1

    |_____1_15/8__7/64_

       8      15     7/8      71/64

So, the quotient is 8x² + 15x + 7/8 and the remainder is 71/64

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