Consider Z=x^3-8
A) Find the real root of Z.

B) Write Z as a product of linear terms.

solution: [tex]x > -175[/tex]

interval notation:  (-175, ∞)

explanation:

[tex]-\frac{1}{5}x + 4 < 39\\[/tex]

Subtract 4 from both sides

[tex]-\frac{1}{5}x +4-4 < 39-4\\[/tex]

Simplify

[tex]-\frac{1}{5}x < 35[/tex]

Multiply both sides by -1 (reverse the inequality)

[tex](-\frac{1}{5}x )(-1) > 35(-1)[/tex]

Simplify

[tex]\frac{1}{5}x > -35\\[/tex]

Multiply both sides by 5

[tex]5[/tex] ·[tex]\frac{1}{5}x > 5(-35)[/tex]

Simplify

[tex]x > -175[/tex]

Jan earns more than Rachel. The range of what Jan earns is  360 dollars to 480 dollars per week. The range of what Rachel earns is  220 dollars to 330 dollars per week.

Jan's pay function is given as /(t) = 12 dollars this is the same as 12 dollars in one hour

the time that she has to work is given a 30 hours to 40 hours.

Hence the domain would be written as

domain : 30 ≤ t ≤ 40

we have to make use of the values of t

f(t) = 12 * 30 = 360

f(t) = 12 * 40 = 480

The range of Jan is going to be

range : 360 ≤ t ≤ 480

b. For Rachel, t is going to vary between 20 ≤ t ≤ 30

domain : 20 ≤ t ≤ 30

r*t = 11t

= 11 x 20 = 220

= 11 x 30 = 330

The range is given as

range: 220 ≤ t ≤ 330

Jan earns more per hour than Rachel

The amount earned is, Jan earns from 360 dollars to 480 dollars per week.

Rachel earns from 220 dollars to 330 dollars per week.

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Yes, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The function is given in the represented graph

According to the given graph, we can see the value of the domain of the given function f(x) when the function includes all possible variables of x values of a function.

Here the domain of the given function is  0 < x < 6

Therefore, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.

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Answer:

20 miles

Step-by-step explanation:

1.6km is equivalent to 1 mile

so 30km / 1.6 = 18.75 miles

therefore 20 miles is the closest to 30km

a) Daily dose for a man who weighs 195 pounds is 30 mg.

b)Here 422.5 mg is less than 600mg. Then, He doesn't receive proper dosage.

What is proportional ?

  Any relationship that always has the same ratio is referred to be proportionality. For instance, the average number of apples per tree determines the proportionality between the quantity of apples in a crop and the number of trees in the orchard.

Here , The adult daily dosage for a certain medicine is 260 mg

=> [tex]\frac{40}{260} = \frac{195}{x}[/tex]

=>  x = [tex]\frac{260*195}{40}[/tex]

=> x =1267.5  mg.

a) Daily dose for a man who weighs 195 pounds is 30 mg.

b) Here for 24 hours = 1267.5 then,

=>  8 hours = x

=> x = [tex]\frac{1267.5*8}{24}[/tex]

=> x = 422.5 mg.

Here 422.5 mg is less than 600mg. Then, He does'nt receive proper dosage.

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Answer:

Step-by-step explanation:

You want the measures of supplementary angles x° and (x-58)°.

Consecutive interior angles where a transversal crosses parallel lines are supplementary.

  x° +(x -58)° = 180°

  2x = 238

  x = 119

  x -58 = 61

The two angles are ...

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The probability that the proportion of Labradors in a sample of 694 pet dogs would differ from the population proportion by less than 3% is 0.9964

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 8% = 0.08

sample size, n = 694

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.08(1 - 0.08)) / 694}

= √{(0.08 * 0.98) / 694}

= 0.0103

The probability

differ from the population proportion by less than 3%

|X - 0.08| < 0.03

X < 0.11 OR X > 0.05

0.05 < X < 0.11

P(z < 0.11) - P(z < 0.05 )

z score for z < 0.05

z = (0.05 - 0.08) / 0.0103

= -2.9126

p value for z < -2.9126 = 0.001792

z score for z < 0.12

z = (0.12 - 0.09) / 0.0102

=  2.9412

p value for z < 2.9412 = 0.9982

The probability required = 0.9982 - 0.0016 = 0.9964 or 99.64%

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It should expect 4881 customers to have 10 months from now.

Function is a type of relation, or rule, that maps one input to specific single output.

Given that T-shirts, the number of customers has been Falling 10% per month

There are 14,000 customers this month

Now Creating the function :

Let y be the remaining customers and x be the number of months from now

y = (14,000)(1 - 0.1)ˣ

y = (14,000)(0.9)ˣ

Solving :

y = (14,000)(0.9)¹⁰

y = (14,000)(0.34867844)

y = 4881 customers

(nearest whole person)

Hence, it should expect 4881 customers to have 10 months from now.

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Answer:

It should expect 4881 customers to have 10 months from now.

Answer:

A. [tex]\log_9{3}=x[/tex]

Step-by-step explanation:

[tex]y=e^x\rightarrow\log_e{y}=x[/tex]

Therefore,

[tex]3=9^x\rightarrow\log_9{3}=x[/tex]

Answer:

It will take 7.5 days to complete the job.

Step-by-step explanation:

First, find how many total hours the ten men worked to complete the job

10 x 6 = 60 hours a day

12 x 60 = 720 hours total

Now compare that with the 8 men's hours

8 x 12 = 96 hours a day

720 / 96 = 7.5 days

The statement that proves the claim about the angle is incorrect is that;

c) Incorrect because arctan(-3/4) = -36.87

The 6 main trigonometric ratios of a right angle triangle are;

Sine θ = length of the opposite leg / length of the hypotenuse

Cosine θ = length of the adjacent leg / length of the hypotenuse

Tangent θ = sine θ/cosine θ = opposite leg / adjacent leg.

cosecant θ = 1 / sine θ = hypotenuse / opposite leg

secant θ = 1 / cosine θ = hypotenuse / adjacent leg

cotangent θ= 1 tangent θ = adjacent leg / opposite leg.

Now, we are told that the angle formed is 53.13°. Since the options are either arctan or arccos, we will use them to verify the angles;

cos 53.13° = 0.6

tan 53.13° = 1.33

They are both positive and it means both x and y values are positive since we are told that it involves the positive x-axis.

Thus, y/x cannot be negative or -3/4 as given.

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Answer: 231 thousand

Step-by-step explanation:

given,

total number of undergraduate students enrolled = 414000

let us take number of total number of male students as, X

then, total number of female students will be X + 48000

now we get,

total number of male students + total number of female students = total number of students enrolled.

X + (X + 48000) = 414000

X + X + 48000 = 414000

2X = 414000 - 48000

X = 366000/2

X = 183000

total number of male students is 183000

total number of female students is

X + 48000

183000 + 48000 = 231000

Answer:

$2.20

Step-by-step explanation:

6.6/3=2.2

Answer:

The cost would be $99 with each artist if the job took Eva 1 hour

Step-by-step explanation:

99=10x+89

subtract 89 from both sides

10=10x

1=x

Answer:

I'm assuming it's just a conversion of mm into cm?? in that case it will be 2.4 cm

If  a multipack of crisps contains 10 packets. the least and the greatest weights of the multipack is 315, 325.

Range = 31.5≤  x < 32.5

Range = 31.5≤  10 < 32.5

Hence,

Lowest and greatest possible for 32 grams

Lowest possible = 31.5 grams

Greatest possible =32.4 grams

Since multipack of crisps contain is 10 packets hence.

Least weight = 31.5 grams × 10

Least weight =315

Greatest weight = 32.5 grams × 10

Greatest weight = 325

Therefore 315 and 325 are the weight.

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The turning point is at x = 5, and this means that the substance changes from liquid to gas when x = 5.

Here we have the temperature function:

T(x) = (x - 5)^3 + 9

The turning point is the point where the curvature of the function changes,  by differentiating the function two times and finding the zero, we can get the turning points.

T'(x) = 3*(x - 5)^2

T''(x) = 3*2*(x - 5) = 6*(x - 5)

This is zero when x = 5, then:

T''(5) = 6*(5 - 5) = 0

So the turning point is there.

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For the given functions f(x) = 3x and g(x) = 1/x then domain of

(gof)(x) =1/3x is all the real numbers excluding zero.

As given in the question,

Given functions are as follow:

f(x) = 3x

g(x) = 1/x

Now ,

(gof)(x)

= g(f(x))

Substitute f(x) = 3x in the above function we have,

=g(3x)

Replace the value of x by 3x in the given function g(x) we get,

= 1/ 3x

For x = 0 (gof)(x) =1/3x is undefined.

Domain include all the real numbers except zero.

Therefore, for the given functions f(x) = 3x and g(x) = 1/x then domain of (gof)(x) =1/3x is all the real numbers excluding zero.

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From the given proof below, we have been able to show that quadrilateral ABCD is a Trapezoid.

A trapezoid is also called a trapezium and it is characterized by four straight sides and one set of parallel sides. The parallel sides are referred to as the base, while the non-parallel sides are referred to as the legs.

We are told that;

O is the point of intersection for the diagonals of quadrilateral ABCD;

where;

AO/BO = CO/DO

This can also be expressed as;

AO/CO = BO/DO

Thus, if we create line OE to be parallel to DC which is OE || DC. Then it means that point E lies on BC.

Using the Basic Proportionality Theory, in ΔBDC, we can say that;

BO/OD = BE/EC ............................1

We are also given that:

AO/CO = BO/DO   ..........................2

Thus, from Equations 1 and 2, we have;

AO/CO = BE/EC

Using the converse form of the Basic Proportionality Theorem, we have;

OE || AB

Therefore, AB || OE || DC.

Therefore we can conclude that ABCD is a Trapezoid.

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The present value of $2525 per year, at a discount rate of 10 percent, if the first payment is received 9 years from now and the last payment is received 24 years from now is; $9215.77

An annuity is defined as a fixed amount of cash that is received or paid periodically over a certain period of time. This would mean that the amount in each cash flow of the annuity would be equal and occur for a specific period of time.

The formula for present value is;

PV = P[1 - (1 + r)⁻ⁿ)/r]

where;

PV is present value

P is periodic cash flow

r is interest rate

n is time

We are given the following;

Periodic cash flow (P) = $2525 /Year

Interest rate (r) = 10% /Year = 0.1

Time (n) = 16 Year (from 9 years to 24 years)

Thus;

PV = 2525[1 - (1 + 0.1)⁻¹⁶)/0.1]

PV = $19754.86

This is the present value in 9 years

Thus, the present value in 24 years which is now will be expressed by the formula;

PV = FV/(1 + i)^(t)

where;

PV is present value

FV is future value

i is interest rate

t is time

Thus;

PV = 19754.86/(1 + 0.1)^(8)

PV = $9215.77

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An ordered pair which is a solution to the given system of linear equations is: (1, 4).

In order to determine which ordered pairs are valid and true solutions based on the given system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;

For ordered pair (0, -4), we have:

-3x + 2y = 5

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

0 - 8 = 5

-8 = 5 (No)

For ordered pair (-3, 5), we have:

-3x + 2y = 5

-3(-3) + 2(5) = 5

9 + 10 = 5

19 = 5 (No)

For ordered pair (1, 4), we have:

-3x + 2y = 5

-3(1) + 2(4) = 5

-3 + 8 = 5

5 = 5 (Yes)

For ordered pair (1, 4), we have:

y = 8x - 4

4 = 8(1) - 4

4 = 4 (Yes).

For ordered pair (-7, -8), we have:

-3x + 2y = 5

-3(-7) + 2(-8) = 5

21 - 16 = 5

5 = 5 (Yes)

For ordered pair (-7, -8), we have:

y = 8x - 4

-8 = 8(-7) - 4

-8 = -58 (No).

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The segment XY is a tangent to circle Z.

What is tangent to a circle?

Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent at a point to circle. Point of tangency is the point at which tangent meets the circle.

To check the segment YX is tangent to circle z, first we have to check that the triangle formed XYZ is right angle triangle or not.

If the triangle XYZ is a right triangle, then we have

XY² +XZ² = YZ²

3.6² +2.7² = (1.8 +2.7)²

 12.96 +7.29 = 20.25            it's true.

Therefore, the segment XY is a tangent to circle Z.

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The average power exerted on the flag of mass 2 kg by the student is 58.8 Watt.

Power can defined as the rate at which work is done.

To calculate the average power exerted on the flag, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the average power exerted is 58.8 Watt.

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The height of a person is 5.2ft in centimeter: 158.49cm

So, the conversion of measurement from the unit feet to centimeters is provided by the feet-to-centimeter calculator.

Approximately 30.48 cm makes up one foot.

1 ft = 30.48 cm

Therefore, 5.2 feet equals 5.2 x 30.48 centimeters.

5.2 feet is therefore equal to 158.49 cm in centimeters.

Hence, the height of a person who is 5.2 feet tall to centimeters is 158.49cm.

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The given polynomial solved as same as RHS is x^3/3(x^2- 1/x^2)

Polynomial is defined as the sum of variable terms in the form of k×x^n, where k is constant and x variable and n is an integer.

we have given a polynomial,

(x-1/x)(x^4/3+x^2/3) = (x^3/3)(x²-1/x²)

Take LHS

⇒  (x-1/x)(x^4/3+x^2/3)

⇒  (x^2-1/x)×(x^4 + x^2/3)

⇒  (x^2-1/x) x^2(x^2+1/3)

⇒  x^2/3x (x^2-1)(x^2+1)

⇒​x^2/3x(x^4-1)                                  ∴(a^2-b^2 = (a+b)(a-b))

multiply numerator and denominator by x

⇒x^3/3 (x^4-1/x^2)

⇒x^3/3(x^2- 1/x^2) = RHS

Hence, given problem has solved.

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The number of square cm of cheese layers that Anna needs to put on the pizza is  30.25π square cm.

What is the area of a circle?

In geometry, the area of a circle is the space occupied by the circle.

To find the area of a circle having radius "r", we can use the formula.

               Area of a circle = π×r².

In the given question, the diameter of the pizza is 11 cm.

so the radius will be = 11/2 = 5.5 cm.

                Area of the pizza = π×r²

                                              = π×(5.5)²

                                              = 30.25π square cm.

Hence, the number of square cm of cheese layers that need to be put on the pizza is  30.25π square cm.

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The number of months Amy can take the Gymnastic = 2 months.

Amy wants to start taking gymnastics.

The fee structure of the gymnastics is divided into two parts.

There is a one time fee payment of 35$ and there is a monthly payment that costs 85$ per month.

So the first month fee of the gymnastics = 35 + 85 = 120$

Savings of Amy = 225$

If Amy pays the 1st month fee ,

then the she will be left with the savings  = 225$ - 120$ = 105 $

It means Amy can join the gymnastics for one more month .

Hence the number of months Amy can take the Gymnastic = 2 months .

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The probability of taking math or science or both is 123/152

The total number of students = 152 students

Number of students who take math = 100 students

Number of student who take science = 77 students

Number of students who take both math and science = 55 students

The probability = Number of favorable outcomes /  Total number of outcomes

We have to find each term

The number of favorable outcomes =55+45+23

= 123

Total number of outcomes = 152

Substitute the values in the equation

​Probability of taking math or science or​ both = 123/152

Hence, the probability of taking math or science or both is 123/152

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