precalculus problem need help

All values of n must be smaller than 11 in order to meet the inequality. The answer may be expressed as follows in interval notation: n (-∞, 10)

To solve the inequality 3n - 7 < 26, you can follow these steps:

Add 7 to both sides of the inequality to isolate the n variable on one side:

3n - 7 + 7 < 26 + 7

3n < 33

Divide both sides of the inequality by 3 to get n by itself:

3n/3 < 33/3

n < 11

Therefore, the values of n that satisfy the inequality are all values less than 11. In interval notation, you can write the solution as:

n ∈ (-∞, 10)

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Answer:

Step-by-step explanation:

4

It is the sum of rational numbers.

Any given number which can be expressed in form of fraction where its denominator is not zero, is said to be a rational number. Examples are: 2, 10, 3.14 etc.

While irrational numbers are numbers that can not be expressed as a fraction. Examples are: π, [tex]\sqrt{10}[/tex] etc.

To determine if the given number are rational or irrational numbers, then;

3.14 = 314/ 100

and

24 = 24/ 1

Therefore, both numbers are rational.

So that;

3.14 + 24 = 27.14

Then,

27.14 = 2714/ 100

Thus we can conclude that the sum is rational.

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The possible values for t for the points A and B with gradient 2 are t = -1 or t = 3/2.

Given the gradient 2 for the point A and B, we have that;

gradient = (y₂ - y₁)/(x₂ - x₁)

so;

2 = (2t² + 7 - t)/(7 - 2)

2 = (2t² + 7 - t)/5

10 = 2t² + 7 - t {cross multiplication}

2t² + 7 - t - 10 = 0

2t² - t - 3 = 0

2t² + 2t - 3t - 3 = 0 {we rewrite the middle term}

2t(t + 1) -3(t + 1) = 0

(2t - 3)(t + 1) = 0 {factorization}

2t - 3 = 0 or t + 1 = 0

t = 3/2 or t = -1

Therefore, the possible values for t for the points A and B with gradient 2 are t = -1 or t = 3/2.

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Answer: A, D

Step-by-step explanation:

We have sinx cosx = -1/4. This means that either sinx = -1/2 and cosx = 1/2 or sinx = 1/2 and cosx = -1/2. In the first case, we get x = 7pi/6 + 2npi or x = 11pi/6 + 2npi. In the second case, we get x = 7pi/12 + 2npi or x = 17pi/12 + 2npi. Therefore, the solutions are x = 7pi/12 + npi and x = 11pi/12 + npi. So, options A and D are correct. Options B and C are not solutions to the given equation.

The requried, 120 ft³ of water was needed to fill the pool during the summer.

The volume of the child's pool is given by multiplying its length, width, and height.

The volume of the pool = Length x Width x Height
                                       = 5 ft x 4 ft x 2 ft
                                       = 40 cubic feet

Since the pool was filled 3 times during the summer, the total amount of water needed is:

The total volume of water = Volume of pool x Number of times filled
                                           = 40 ft³ x 3
                                           = 120 ft³

Therefore, 120 ft³ of water was needed to fill the pool during the summer.

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The Average Daily Balance is 6106.77

The interest to be paid on 1st April April is 152.67

Balance Due on April 1 is 6412.67

Average Daily Balance = Total of (Number of days * Balance) / 31 days

= 189310 / 31

= 6106.77

(b.) The Interest to be paid on 1st April April = Average Daily Balance * 2.5%

= 6106.77 * 2.5%

= 152.67

(c.) Balance Due on April 1 = 6260 + Interest for April

= 6260 + 152.67

= 6412.67

(d.) In case of Minimum Due = 6412.64 / 36 = 178.13

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Answer:

So the smaller number is x = 1 and the larger number is y = 8.

Step-by-step explanation:

substitute y = 3x + 5 into the first equation and solve for x.

y = 2(x + 3) 3x + 5 = 2(x + 3) Expand the parentheses 3x + 5 = 2x + 6 Subtract 2x from both sides x + 5 = 6 Subtract 5 from both sides x = 1

Now we can plug x = 1 into either equation to find y.

y = 2(x + 3) y = 2(1 + 3) y = 2(4) y = 8

Answer:

$4.20 / 7 erasers = $0.60 per eraser

So each eraser in the package costs $0.60.

The radius of a sphere with a volume of 10000 cubic meters is 13.36 meters

We know that the formula for the volume of sphere is :

V = 4/3 × π × r³

where r is the radius of the sphere

Here, a volume of the sphere is 10000 cubic meters.

V =  10000 cubic meters

we need to find the radius 'r'

V = 4/3 × π × r³

10000 = 4/3 × π × r³

r³ = 10000 × 3/4 × 1/π

r³ = 30000/4π

r³  = 2387.32

taking cube root,

r = 13.36 meters

Therefore, the radius is 13.36 meters.

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The rectangle's circumference is 27+ (3/2) fee and one of its sides is a semicircle.

We can start by finding the perimeter of the rectangle, which is simply the sum of the lengths of all four sides:

Perimeter of rectangle = 2(length + width) = 2(12 + 3) = 30 feet

Next, we need to find the perimeter of the semicircle.

The diameter of the semicircle is equal to the width of the rectangle, which is 3 feet. The formula for the perimeter of a semicircle is:

Perimeter of semicircle = (π/2) x diameter + diameter

Plugging in the values, we get:

Perimeter of semicircle = (π/2) x 3 + 3 = (3/2)π + 3

Now, we can add the perimeter of the semicircle to the perimeter of the rectangle to get the total perimeter:

Total perimeter = Perimeter of rectangle + Perimeter of the semicircle- 2*diameter of the semicircle

= 30 + (3/2)π + 3 - 3*2

= 27+ (3/2)π

Therefore, the perimeter of the rectangle with a semicircle on one side is 27+ (3/2)π feet, or approximately 31.71 feet (rounded to two decimal places).

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The total surface area of the cylinder is 2260.8 cm².

The height of the cylinder is 18 centimetres and the diameter of the cylinder is 24 centimetres.

Therefore, the total surface area of the cylinder can be calculated as follows:

total surface area = 2πr(r + h)

where

Therefore,

r = 24 / 2 = 12 cm

h = 18 cm

total surface area = 2 × 3.14 × 12(12 + 18)

total surface area = 75.36(30)

total surface area = 2260.8 cm²

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Step-by-step explanation:

a probability is always the ratio

"desired" cases / totally possible cases

the totally possible cases here are 100.

now, the question focuses on non-defective units.

how many out of the 100 are non-defective ?

well, 100 - 12 = 88 units.

so, the probability to select a non-defective (= working) unit is

88/100 = 22/25 = 0.88

in other words, as a mean and expected value, in 88 of 100 attempts, or in 22 of 25 attempts you will select a non-defective unit.

There are 100 DVRs in the inventory, and 12 of them are defective. Therefore, the number of non-defective DVRs is:

100 - 12 = 88

The probability of selecting a non-defective DVR can be found by dividing the number of non-defective DVRs by the total number of DVRs:

P(non-defective DVR) = number of non-defective DVRs / total number of DVRs

                     = 88 / 100

                     = 0.88

Therefore, the probability of randomly selecting a DVR that is not defective is 0.88, or 88%.

The surface area of the triangular prism is  184 metres².

The surface area of the triangular base prism can be found as follows:

surface area of the prism = (s₁ + s₂ + s₃)l + bh

where

b =base

h = height

l = height of the prism

s₁, s₂ and s₃ are side length of the prism.

Therefore,

b = 6 units

h = 4 units

s₁ = 5 units

s₂ = 5 units

s₃ = 6 units

l = 10 units

Hence,

surface area of the prism = (5 + 5 + 6)10 + 6(4)

surface area of the prism = 160 + 24

Therefore,

surface area of the prism = 184 metres²

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The mean temperature of orange juice is 5 degrees greater than the mean temperature of water.

The mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in the dataset and then dividing by the total number of values.

According to the graph, the different temperatures of water and orange juice on different time can be taken into consideration.

Sum of Temperature of Water at different time

= 55 + 62 + 69 + 71 + 79 + 75

= 441 degrees

Mean Temperature of Water

= 441/6

= 68.5 degrees

Sum of Temperature of Orange juice at different time

= 59 + 65 + 72 + 79 + 85 + 81

= 441 degrees

Mean Temperature of Orang juice

= 441/6

= 73.5 degrees

Difference = 73.5 - 68.5 = 5 degrees

Hence, the mean temperature of orange juice is 5 degrees greater than the mean temperature of water.

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The value that would help Charlie find out how long it takes his basketball to reach the highest point is "x at the vertex". The correct option is A.

When the basketball reaches the highest point, its vertical velocity is zero. The time taken to reach this point can be found using the equation:

t = -b / (2a)

where a is the acceleration due to gravity (-9.8 m/s²) and b is the initial vertical velocity of the basketball.

The vertex of the parabolic path that the basketball follows is the point where the basketball reaches its maximum height. This point occurs at the halfway point of the ball's total flight time. The horizontal distance the basketball travels during this time is called "Ox at the vertex".

Therefore, by finding the "x at the vertex", Charlie can calculate the total flight time of the basketball, and then use the equation above to find the time it takes to reach the highest point.

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The sum of the first 9 terms of the arithmetic sequence is 81.

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term.

To calculate the sum of the first 9 terms of the arithmetic sequence, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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The value of the angle a is 38⁰

The value of the angle b is 52⁰

The value of the angle c is 104⁰

The value of the angle d is 90⁰

The value of the angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

a = ¹/₂ x arc 76⁰

a = 38⁰

Since the chord passed through the center, arc c is calculated as;

arc c = 180 - 76 (sum of angles of a semicircle)

arc c = 104⁰

b = ¹/₂ x 104⁰

b = 52⁰

d = 180 - (a + b) (sum of angles in a triangle)

d = 180 - (38 + 52)

d = 90⁰

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Answer:

Step-by-step explanation:

To differentiate y = 3x cos(x) + sin(x), we can use the product rule and the chain rule.

Let's start by differentiating the first term, 3x cos(x), using the product rule:

d/dx (3x cos(x)) = 3 cos(x) - 3x sin(x)

Next, we can differentiate the second term, sin(x), using the chain rule:

d/dx (sin(x)) = cos(x)

Putting it all together, we get:

dy/dx = 3 cos(x) - 3x sin(x) + cos(x)

Simplifying the expression, we get:

dy/dx = (4cos(x)) - (3xsin(x))

Therefore, the derivative of y = 3x cos(x) + sin(x) is dy/dx = 4cos(x) - 3xsin(x).

The coordinates that represents a point that is collinear with the given points: (4, -10) and (-2, 0) is (0, 10/3). So the correct answer is option C.

We must check to see if a point is on the straight line that connects two other points in order to determine if they are collinear.

Using the point-slope form of a line we can find the equation of the straight line passing through the points (4,-10) and (-2,0):

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

where (x1, y1) = (4, -10) and (x2, y2) = (-2, 0).

Substituting the values, we get:

(y + 10)/(x - 4) = (0 + 10)/(-2 - 4)

Simplifying, we get:

(y + 10)/(x - 4) = -5/3

Multiplying both sides by (x - 4), we get:

y + 10 = (-5/3)(x - 4)

Simplifying, we get:

y = (-5/3)x + (10 + 20/3)

y = (-5/3)x + (50/3)

So, any point that satisfies this equation is collinear with the given points.

Now checking all the three points whether they satisfy the equation:

(a) (2, -6)

Substituting the values in the equation, we get:

-6 = (-5/3)(2) + (50/3)

-6 = -10/3 + 50/3

-6 = 40/3, which is not true.

Therefore, the point (2, -6) is not collinear with the given points.

(b) (3, -3)

Substituting the values in the equation, we get:

-3 = (-5/3)(3) + (50/3)

-3 = -15/3 + 50/3

-3 = 35/3, which is not true.

Therefore, the point (3, -3) is not collinear with the given points.

(c) (0, 10/3)

Substituting the values in the equation, we get:

10/3 = (-5/3)(0) + (50/3)

10/3 = 50/3, which is true.

Therefore, the point (0, 10/3) is collinear with the given points.

Hence, the answer is (c) (0, 10/3).

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Correct Question

Which of the following coordinates represents a point that is collinear with the given points.

(4, -10) and (-2, 0)
(a) (2, -6)

(b) (3, -3)

(c) (0, 10/3)

The lateral surface area of the cylinder is 376.8 sq ft

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

Radius, r = 10 ft

Height, h = 6 ft

The lateral surface area of the cylinder is calculated as

Lateral area = 2 * 3.14 * rh

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

Lateral area = 2 * 3.14 * 6 * 10

Evaluate the products

So, we have

Lateral area = 376.8

Rounding the answer to the nearest tenth, we have

Lateral area = 376.8

Hence, the Lateral area is 376.8 sq ft

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The simplified form of the fraction is A = -1 / (x - 2)

Given data ,

Let the fraction be represented as A

Now , the value of A is

A = (6 - x) / (x² - 8x + 12)

On factorizing the denominator , we get

(x² - 8x + 12) = ( x - 6 ) ( x - 2 )

So , the new fraction is

A = ( 6 - x ) / ( x - 6 ) ( x - 2 )

A = - ( x - 6 ) / ( x - 6 ) ( x - 2 )

Taking the common factor out , we get

A = -1/ ( x - 2 )

Hence , the fraction is A = -1/ ( x - 2 )

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Comparing all the numbers, we can see that (d) 21/2500 is not equal to the other numbers, since it is a fraction and all the other numbers are decimals. Therefore, (d) is the answer.

To determine which of the numbers is not equal to the other, we can convert all the numbers to the same form and compare them.

a) 0.84% can be written as 0.0084 in decimal form.

b) (0.21)(0.04) equals 0.0084.

c) 8.4 x 10⁻² can be written as 0.084 in decimal form.

d) 21/2500 can be simplified by dividing both the numerator and denominator by 21 to give 1/119.

e) 21/2500 x 10⁻² can be simplified by dividing both the numerator and denominator by 21 and multiplying by 100 to give 0.084.

In conclusion, to determine which number is not equal to the other, we need to convert all the numbers to the same form and compare them. In this case, we converted all the numbers to decimal form except for (d), which is a fraction. By comparing the numbers, we found that (d) is not equal to the other numbers.

Therefore, (d) is the answer.

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Answer:

(2,0)

Step-by-step explanation:

Vertex is the top or bottom of the graph, depending on if the graph is upside down or not.

In this case, the graph is upside down, so the vertex will be at the top. We see that the vertex is located at (2,0) in this graph. So, the vertex is (2,0).

Step-by-step explanation:

so, the 1 yard is split into 6 equal parts.

each small square has therefore an area of 1/6 × 1/6 yard² = 1/36 yard²

the shaded area is 4×3 = 12 small squares large.

is area is therefore

12 × 1/36 = 1/3 yard²

since 1 yard = 3 ft, 1 × 1 = 1 yard² = 3 × 3 ft² = 9 ft².

and 1/3 yard² = 1/3 × 9 ft² = 3 ft²

so, whatever dimension you need.

the area is

1/3 yard² = 3 ft²

Note that the estimated time it will take to cause hearing loss at 106 decibels is 0.0625 hours or 3 minutes, 75 seconds.

The formula used is:


Exposure Time = 8/ 2^((dBA-85)/3)

Since the decibel (dBA) given is 106


Exposure Time = 8/ 2^((106-85)/3)

= 8/2^1
= 8/ 128

= 0.0625 hours or 3 minutes, 75 seconds.

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The distance will be in the decimal form is :41.34

Consider the triangle :

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

[tex]Hypotenuse^2 = Perpendicular^2 + Base^2[/tex]

[tex]c^2 = a^2 + b^2[/tex]

We have the points are:

15,-17 and -20, -5

To find the distance between them.

The distance of x- axis is:

15 - (-20)

= 15 + 20

= 35

The distance of y- axis is:

|17 - 5| = |-22| = 22

We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle:

[tex]x^2+y^2=(distance)^2[/tex]

[tex]35^2+22^2=distance^2[/tex]

[tex]1709= distance^2\\Distance = \sqrt{1709}[/tex]

In decimal form the distance would be around 41.34.

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