Assume that John Smith is a salesperson employed by McCrackin Company. Smith's regular rate of pay is $36 per hour, and any hours worked in excess of 40 hours per week are paid at 1½ times the regular rate. Smith worked 42 hours for the week ended October 27. What are his total earnings for the week?

Answer:

8. [tex]\displaystyle \frac{9[x + 5]}{x - 14}[/tex]

7. [tex]\displaystyle -\frac{2x - 1}{2[3x - 5]}[/tex]

6. [tex]\displaystyle \frac{2[x - 4]}{5[x + 3]}[/tex]

5. [tex]\displaystyle \frac{2x + 7}{x + 3}[/tex]

4. [tex]\displaystyle 3x^{-1}[/tex]

Step-by-step explanation:

All work is shown above from 8 − 4.

I am joyous to assist you anytime.

Solving [tex]-\frac{1}{2}x<-12[/tex] we get [tex]x>24[/tex]

Step-by-step explanation:

We need to solve the given inequality to find value of x.

[tex]-\frac{1}{2}x<-12[/tex]

Solving:

[tex]-\frac{1}{2}x<-12[/tex]

Multiply both sides by 2

[tex]-\frac{1}{2}x*2<-12*2[/tex]

[tex]-x<-24[/tex]

Multiply both sides by (-1) and reverse the inequality sign i.e < is changed to >

[tex]x>24[/tex]

So, solving [tex]-\frac{1}{2}x<-12[/tex] we get [tex]x>24[/tex]

Keywords: Solving inequalities

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Answer:

Jay's bread size is 220% of the original size.

Step-by-step explanation:

The question is incomplete.

The complete question is as follows.

Jay is letting her bread rise. After 3 hours,her bread is at 11/5 of its original size. What percent of its original size is jays bread dough?

Solution:

Let the original bread size be = [tex]100[/tex] units

After 3 hours the bread rises = [tex]\frac{11}{5}[/tex] of the original size

New size of bread =  [tex]\frac{11}{5}\times 100=220[/tex] units

Percent of original size the new bread is

⇒ [tex]\frac{New\ bread\ size}{Original\ bread\ size}\times 100[/tex]

⇒ [tex]\frac{220}{100}\times100[/tex]

⇒ [tex]220\%[/tex]

Answer:

  7/11

Step-by-step explanation:

Let d represent the original denominator. Then the original numerator is ...

  2d-15

The new numerator is ...

  (2d-15) +5

and the new denominator is ...

  d+7

The ratio of these is 2/3, so we have ...

  [tex]\dfrac{2d-15+5}{d+7}=\dfrac{2}{3}\\\\3(2d-10)=2(d+7) \quad\text{cross multiply}\\\\4d=44 \quad\text{add 30-2d}\\\\d=11\\\\2d-15=2(11)-15=7[/tex]

The original fraction is 7/11.

Answer:.

Step-by-step explanation:

.

Answer:

[tex]-\frac{ln(662)-2}{4}[/tex]

{-1.12}

Step-by-step explanation:

[tex]e^{2 - 4x} = 662[/tex]

Solve this exponential equation using natural log

Take natural log ln on both sides

[tex]ln(e^{2 - 4x}) = ln(662)[/tex]

As per the property of natural log , move the exponent before log

[tex]2-4x(ln e) = ln(662)[/tex]

we know that ln e = 1

[tex]2-4x= ln(662)[/tex]

Now subtract 2 from both sides

[tex]-4x= ln(662)-2[/tex]

Divide both sides by -4

[tex]x=-\frac{ln(662)-2}{4}[/tex]

Solution set is {[tex]x=-\frac{ln(662)-2}{4}[/tex]}

USe calculator to find decimal approximation

x=-1.12381x=-1.12

- In terms of natural logarithms: [tex]\( \{ \ln(2) \} \)[/tex]

- In decimal approximation: [tex]\( \{ 0.69 \} \)[/tex] (rounded to two decimal places)

To solve the exponential equation [tex]\( e^2 - 4x = 662 \),[/tex] we can follow these steps:

Step 1: Isolate the exponential term by subtracting 2 from both sides:

[tex]\[ e^2 - 2 = 662 \][/tex]

Step 2: Divide both sides by -4 to isolate ( x ):

[tex]\[ -4x = 660 \][/tex]

Step 3: Divide both sides by -4 to solve for ( x ):

[tex]\[ x = -\frac{660}{4} \][/tex]

[tex]\[ x = -165 \][/tex]

Now, let's express the solution in terms of natural logarithms:

[tex]\[ x = -165 \][/tex]

To obtain a decimal approximation for the solution, we can use a calculator. Substituting [tex]\( x = -165 \)[/tex] back into the original equation:

[tex]\[ e^2 - 4(-165) = 662 \][/tex]

[tex]\[ e^2 + 660 = 662 \][/tex]

[tex]\[ e^2 = 2 \][/tex]

Now, take the natural logarithm of both sides:

[tex]\[ \ln(e^2) = \ln(2) \][/tex]

[tex]\[ 2\ln(e) = \ln(2) \][/tex]

[tex]\[ 2 = \ln(2) \][/tex]

So, the solution in terms of natural logarithms is [tex]\( x = \ln(2) \).[/tex]

The decimal approximation for [tex]\( x = \ln(2) \)[/tex] is approximately [tex]( x \approx 0.69315 \).[/tex]

Therefore, the solution set is:

- In terms of natural logarithms: [tex]\( \{ \ln(2) \} \)[/tex]

- In decimal approximation: [tex]\( \{ 0.69 \} \)[/tex] (rounded to two decimal places)

Answer:

The proof with the statement is given below.

Step-by-step explanation:

Given:

Construction of angle bisector i.e SP is the bisector of angle RPQ.

To prove:

Δ PWS ≅ Δ PXS

Proof:

In  Δ PWS  and Δ PXS  

∠ WPS ≅ ∠ XPS    …………..{definition of angle bisector}

SP ≅ SP                .......…….{Reflexive property}

PW ≅ XP              ……....….{definition of ≅}

Δ PWS  ≅ Δ PXS  …...........{Side-Angle-Side test i .e SAS}

Angle bisector: A ray divides angle into two equal measures then the ray is called as angle bisector of the bisected angle.

In the construction SP is the bisector of the angle ∠ RPQ

SAS: This test is to prove the triangle congruent when two sides are congruent and angle between that sides should be congruent. then we can say the triangle is congruent by side angle side test.

Answer:

Option B

Step-by-step explanation:

multiplying 2/5 with 5/2 will give 1 on the left hand side of the equation

multiplying 10 with 5/2 will give 25 on the right hand side of the equation, ultimately resulting in  x=25

The number that we must use to multiply each side of the equation 2/5x = 10 to produce the equivalent equation x = 25 is; B: 5/2

We are given the equation;

(2/5)x = 10

Multiplying both sides by the same number is same as the original equation.

Thus, to make the left hand side only x, let us multiply both sides by the inverse of 2/5 which is 5/2 to get;

x = 10 × 5/2

x = 25

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Answer:

5/9 yards

Step-by-step explanation:

Just subtract 2/9 from 5/9 to find the difference, which is the answer.

Answer:

an = 4/3n - 13/3.

Step-by-step explanation:

The first term is a1,

a24 = a1 + 23d

83/3 = a1 + 4/3* 23

a1 =    83/3 - 92/3

a1 = -9/3 = -3.

So the nth term an =  -3 + 4/3(n - 1)

an = -3 + 4/3 n - 4/3

an = 4/3n - 13/3

To find the explicit formula for the general nth term of an arithmetic sequence, use the formula a_n = a_1 + (n - 1)d, where a_n represents the nth term, a_1 is the first term, and d is the common difference. In this case, the explicit formula is a_n = -3 + (n - 1)(4/3), based on given information a_24 = 83/3 and d = 4/3.

To find the explicit formula for the general nth term of an arithmetic sequence, we use the formula: a_n = a_1 + (n - 1)d, where a_n represents the nth term, a_1 is the first term, and d is the common difference. In this case, we are given that a_24 = 83/3 and d = 4/3. We can substitute these values into the formula and solve for a_1. From there, we can simplify the formula and express it in its lowest terms.

Given: a_24 = 83/3 and d = 4/3

We can rearrange the formula and solve for a_1 as follows:

Now that we have found a_1 = -3, we can simplify the formula and express it as:

a_n = -3 + (n - 1)(4/3)

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Answer:

Option C: Probability distribution for a random variable

Step-by-step explanation:

A probability distribution for a random variable describes the range and relative likelihood of all possible values for a random variable.

The probability distribution of a random variable is explained as a list of all the possible values of the variable and their probabilities. These probabilities sum up to 1.

Final answer:

The correct term is ' (c) probability distribution for a random variable,' represented by a probability density function for continuous random variables or a probability distribution function for discrete random variables.

Explanation:

The term that describes the range and relative likelihood of all possible values for a random variable is a (c) probability distribution for a random variable. For a continuous random variable, this is represented by a probability density function (pdf), which shows the likelihood of any given value or range of values. The pdf is depicted graphically, and the area under the curve represents the probability for a given range of values. The total area under the pdf curve is always one, signifying that the sum of all probabilities is one. Also, for a discrete random variable, the probability distribution function (PDF) lists all possible values and their associated probabilities, following the rules that each probability is between zero and one inclusive, and the sum of all probabilities equals one.

A) The function F(x) becomes F(x) = 500(sec x)²

B) The average force exerted by the press over the interval [0, pi/3] is 825.7 N.

Given that,

The force F (in newtons) of the hydraulic cylinder in a press is proportional to the square of sec x.

And, The domain of F is [0, pi/3], and F(0) = 500

A) For F as a function of x,

Since F is proportional to the square of sec x.

We are also given that F(0) = 500.

Let's denote the constant of proportionality as k.

Hence write the equation as:

F(x) = k(sec x)²

To find the value of k, substitute x = 0:

500 = k(sec 0)²

Since sec 0 = 1, we get:

k = 500

So, the function F(x) becomes:

F(x) = 500(sec x)²

B) For the average force exerted by the press over the interval [0, pi/3],  evaluate the average value of F(x) over this interval.

The average value of a function f(x) over an interval [a, b] is given by:

Average value = (1 / (b - a)) × ∫[a to b] f(x) dx

In this case, a = 0 and b = pi/3.

Average value = (1 / (pi/3 - 0)) × ∫[0 to pi/3] 500(sec x)² dx

Simplifying, we get:

Average value = (3/pi) × ∫[0 to pi/3] 500(sec x)² dx

Integrating (sec x)², we have:

Average value = (3/pi) [500 tan x] [from 0 to pi/3]

Evaluating this expression, we get:

Average value ≈ 825.7 N

Therefore, the average force exerted by the press over the interval [0, pi/3] is 825.7 N.

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The force F of the hydraulic cylinder is defined by the equation F(x)=500(secx)^2. The average force over the interval [0, pi/3] can be found by integrating this function over the interval and dividing by the interval length.

The force F of the hydraulic cylinder is directly proportional to the square of sec x, where sec x = 1/cos x. Given that F(0)=500, it implies that when x=0, F=500, so the proportionality constant k can be determined by substituting these values into the equation, as F=k(secx)^2. Where cos 0 = 1, therefore sec 0 = 1. So we get F=k*(1)^2 => k=500. Therefore, the equation that defines F as a function of x is F(x)=500(secx)^2.

To find the average force exerted by the press over the interval [0,pi/3], we need to integrate this function over the given interval and divide by the length of the interval. Therefore: F_avg = (1/(pi/3 - 0))∫ from 0 to pi/3 (500(secx)^2) dx. Solving this definite integral equation will yield the average force.

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Answer: option A is the correct answer

Step-by-step explanation:

The given triangle is a right angle triangle. This is because one of the angles is 90 degrees. The sum of the other two angles is 90 degrees. To determine sin C, we will apply trigonometric ratio

From the dimensions given and taking C as the reference angle,

Hypotenuse = AC = 17

Adjacent side = BC = 15

Opposite side = AB = 8

Sin# = opposite side / hypotenuse

Since # = C

SinC = 8/17

The value of angle C can be derived by finding Sin^-1(8/17)

Final answer:

The linear speed of the satellite is approximately 434.71 km/min. In kilometers per hour, it is approximately 26082.6 km/hr. In miles per hour, it is approximately 16206.26 miles/hr.

Explanation:

To find the linear speed of the satellite, we need to calculate the circumference of the circular orbit.

The radius of the orbit is the sum of the radius of the Earth and the altitude of the satellite:
Radius of orbit = Radius of Earth + Altitude of satellite = 6378 km + 1250 km = 7628 km

The circumference of a circle is given by the formula:
Circumference = 2π * Radius

Substituting the radius of the orbit into the formula:
Circumference = 2π * 7628 km ≈ 47818.16 km

In 110 minutes, the satellite completes one revolution around the Earth. Therefore, its linear speed is:
Linear speed = Circumference / Time taken = 47818.16 km / 110 minutes ≈ 434.71 km/min

To convert the linear speed from kilometers per minute to kilometers per hour, multiply by 60:
Linear speed = 434.71 km/min * 60 min/hr ≈ 26082.6 km/hr

To convert the linear speed from kilometers per hour to miles per hour, divide by the conversion factor of 1.60934:
Linear speed = 26082.6 km/hr / 1.60934 ≈ 16206.26 miles/hr

Answer:

  It takes the second worker 11 hours to do the job alone  

Step-by-step explanation:

The problem tells you how to work it.

  [tex]\dfrac{1}{11}+\dfrac{1}{x}=\dfrac{2}{11}\\\\x+11=2x \qquad\text{multiply by 11x}\\\\11=x \qquad\text{subtract x}[/tex]

x = 11 tells you the second worker takes 11 hours to do the job alone.

_____

You can also work directly with the fractions. Subtract 1/11 and you have ...

  1/x = 1/11

It should not be a real stretch to see that x=11. If you need, you can multiply both sides by 11x to get 11=x.

Answer:

[tex]77.4\ in^3[/tex]

Step-by-step explanation:

we know that

To find out how much empty space is left inside the box, subtract the volume of 18 cans of cola from the volume of the box

step 1

Find the volume of the box

The volume of the box is equal to

[tex]V=LWH[/tex]

substitute the given values

[tex]V=(12)(6)(5)[/tex]

[tex]V=360\ in^3[/tex]

step 2

Find the volume of the can of cola

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=1\ in[/tex]

[tex]h=5\ in[/tex]

substitute

[tex]V=\pi (1)^{2} (5)[/tex]

[tex]V=5\pi\ in^3[/tex]

Multiply by 18 (18 cans of cola)

[tex]V=(18)5\pi=90\pi\ in^3[/tex]

step 3

Find how much empty space is left inside the box

[tex]V=(360-90\pi)\ in^3[/tex] ---> exact value

assume

[tex]\pi =3.14[/tex]

[tex]V=360-90(3.14)=77.4\ in^3[/tex]

Answer:

77.4

Step-by-step explanation:

Answer:

The probability that the sample proportion of 80 LL70 batteries is within 0.03 of the population proportion is 0.44

Step-by-step explanation:

Sample proportion being within margin, or margin of error (ME) around the mean can be found using the formula

ME=[tex]\frac{z*\sqrt{p*(1-p)}}{\sqrt{N} }[/tex] where

Then 0.03=[tex]\frac{z*\sqrt{0.86*0.14}}{\sqrt{80} }[/tex] from this we get:

z≈0.773 and the p(z)≈0.439

Therefore, the probability that the sample proportion is within 0.03 of the population proportion is 0.44

Answer:

Part (A): There are 9 integers between 5 and 31 which are divisible by 3.

Part (B): There are 6 integers between 5 and 31 which are divisible by 4.

Part (C): There are 2 integers between 5 and 31 which are divisible by 3 and by 4.

Step-by-step explanation:

Consider the provided information.

Part (A) we need to find how many integers between 5 and 31 are divisible by 3.

Between 5 and 31 there are 25 integers.

According to quotient rule: [tex]\frac{25}{3} \approx8.33[/tex]

That means either 8 or 9 integers are divisible by 3 as 8.33 lies between 8 and 9.

The integers are: 6, 9, 12, 15, 18, 21, 24, 27, 30

Hence, there are 9 integers between 5 and 31 which are divisible by 3.

Part (B) we need to find how many integers between 5 and 31  are divisible by 4.

Between 5 and 31 there are 25 integers.

According to quotient rule: [tex]\frac{25}{4} \approx6.25[/tex]

That means either 6 or 7 integers are divisible by 4, as 6.25 lies between 6 and 7.

The integers are: 8, 12, 16, 20, 24, 28

Hence, there are 6 integers between 5 and 31 which are divisible by 4.

Part (C) we need to find how many integers between 5 and 31 are divisible by 3 and by 4

Between 5 and 31 there are 25 integers.

Integers should be divisible by 3 and by 4, that means integers should be divisible by 3×4=12.

According to quotient rule: [tex]\frac{25}{12} \approx2.08[/tex]

That means either 2 or 3 integers are divisible by 3 and by 4 or 12, as 2.08 lies between 2 and 3.

The integers are: 12, 24,

Hence, there are 2 integers between 5 and 31 which are divisible by 3 and by 4.

To find positive integers that are divisible by 3, 4, or both between 5 and 31, we can determine the multiples of each number. The multiples of 3 are: 6, 9, 12, 15, 18, 21, 24, 27, and 30. The multiples of 4 are: 8, 12, 16, 20, 24, and 28. The multiples of both 3 and 4 (or their least common multiple, 12) are: 12 and 24.

a) To find the positive integers between 5 and 31 that are divisible by 3, we need to look for numbers that are multiples of 3. Starting with 6, the first multiple of 3 in this range, we continue adding 3 to each number until we reach the highest multiple less than or equal to 31. So the multiples of 3 between 5 and 31 are: 6, 9, 12, 15, 18, 21, 24, 27, and 30.

b) To find the positive integers between 5 and 31 that are divisible by 4, we need to look for numbers that are multiples of 4. Starting with 8, the first multiple of 4 in this range, we continue adding 4 to each number until we reach the highest multiple less than or equal to 31. So the multiples of 4 between 5 and 31 are: 8, 12, 16, 20, 24, and 28.

c) To find the positive integers between 5 and 31 that are divisible by both 3 and 4, we need to find the common multiples of 3 and 4. This can be done by finding the multiples of the least common multiple (LCM) of 3 and 4, which is 12. So the multiples of 12 between 5 and 31 are: 12 and 24.

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Answer: Option (C)

Explanation:

Linear programming is referred to as the mathematical method designed in order to assist individuals to plan and thus make decisions which are necessary in order to allocate the resource. Under linear programming, first an individual defines the objective, thereby also looking at the limits i.e. constraints that are being put forth. Also defining the alternatives and the linearity.

A linear programming problem requires an objective, constraints, alternatives, and linearity. The objective is what you're trying to achieve, constraints are limitations or restrictions, alternatives are options available to reach your objective, while linearity necessitates that all functions in the problem must be linear.

The correct answer is C: An objective, constraints, alternatives, and linearity. These are the four requirements of a linear programming problem. The objective refers to what the problem is attempting to achieve, such as minimizing cost or maximizing profit. Constraints are the limitations or restrictions of the problem. Alternatives refer to the different options or decisions available to reach the objective. Finally, the requirement of linearity is that all functions in the problem, whether they are objective or constraints, must be linear.

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Answer: He traveled 10 km/hr through bike and 5km/hr by jogging.

Step-by-step explanation:

Let the speed of bike be 'x'.

Let the speed of his jogging be 'x-5'.

Distance covered = 10 miles

So the jog took 1 hour longer than the bike ride.

According to question, we get that

[tex]\dfrac{10}{x-5}-\dfrac{10}{x}=1\\\\10\dfrac{x-x+5}{x(x-5)}=1\\\\\dfrac{50}{x^2-5x}=1\\\\50=x^2-5x\\\\x^2-5x-50=0\\\\x^2-10x+5x-50=0\\\\x(x-10)+5(x-10)=0\\\\(x+5)(x-10)=0\\\\x=10\ km/hr[/tex]

Hence, he traveled 10 km/hr through bike and 5km/hr by jogging.

Answer:

18,471.6 cubic inches of wax will be needed

Step-by-step explanation:

We want the volume that will be required for 210 candles. We first find the volume of 1 candle by using volume of cylinder formula. Then multiply that answer by 210 to find volume of wax needed to make 210 such candles.

Volume of Cylinder is given by the formula:

[tex]V=\pi r^2 h[/tex]

Where

r is the radius

h is the height

Given,

r = 2 in

h = 7 in

We substitute and find 1 candle volume:

Volume of 1 candle = [tex]\pi r^2 h = \pi (2)^2 (7) = 87.96[/tex]

Hence,

Volume of 210 candles = 87.96 * 210 = 18,471.6 cubic inches

Answer:

18,471.6

Step-by-step explanation:

Answer:

The y-coordinate is changing by the rate of -70 cm per sec.

Step-by-step explanation:

Given equation,

[tex]y = 7x^2 + 4[/tex]

Differentiating with respect to time (t),

[tex]\frac{dy}{dt}=14x \frac{dx}{dt}[/tex]

We have,

[tex]\frac{dx}{dt}=-5\text{ cm per sec}, x = 1[/tex]

[tex]\frac{dy}{dt} = 14(1)(-5)=-70\text{ cm per sec}[/tex]

Answer:

Step-by-step explanation:

Let x = the number of pounds of oranges in the full box.

On a field trip, students ate 3/10 of a box of oranges. This means that the students ate 3/10 × x = 3x/10 pounds of oranges.

Altogether they ate 6 pounds of oranges. This means that

3x/10 = 6

3x = 6×10

3x = 60

x = 60/3 = 20

The full box contained 20 pounds of oranges

Each tenth of the model is 2 pounds because a tenth of 20 pounds is 20/10 = 2 pounds

Answer:

c. Multiple zero is 3; multiplicity is 2

Step-by-step explanation:

The factor is repeated, that is, the factor  ( x  −  3 )  appears twice. The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity. The zero associated with this factor,  x  =  3 , has multiplicity 2 because the factor  ( x  −  3 )  occurs twice.

Then

Multiple zero is 3; multiplicity is 2.

Answer:

multiple zero is -3 and multiplicity is 2

Step-by-step explanation:

Answer:

6 of the 8 oz one

Step-by-step explanation:

you need to buy 6 of the first to get 48 oz, and the price would be 9.54. you need 4 for the next with the price at 9.96. you need 3 for 16 oz and the price is 9.89. compare all of them and you get 9.54 as the lowest, which was the 8 oz one

Answer:

D. X= ± square root of 8 - 2

Step-by-step explanation:

Given quadratic equation is \[x^{2}+4x=4\]

Rearranging the terms: \[x^{2}+4x-4=0\]

This is the standard format of quadratic equation of the form \[ax^{2}+bx+c=0\]

Here, a=1 , b=4 and c=-4.

Roots of the quadratic equation are given by \[\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\]

Substituting the values and calculating the roots:

\[\frac{-4 \pm \sqrt{(-4)^{2}-4*1*(-4))}}{2*1}\]

= \[\frac{-4 \pm \sqrt{32}}{2}\]

= \[\frac{-2*2 \pm 2*\sqrt{8}}{2}\]

= \[-2 \pm \sqrt{8}\]

Hence option D is the correct option.

The solution of x² + 4x = 4 is x =  ± √8 - 2,

Hence, option D is correct.

The given quadratic equation is,

x² + 4x = 4

Here we have to solve it by completing square method

Now proceed the expression,

⇒ x² + 4x = 4

Adding 4 both sides,

⇒ x² + 4x + 4 = 4 + 4

⇒ x² + 4x + 4 = 8

Since we know that 2² is equal to 4, then

⇒ x² + 4x + 2² = 8

Since we know that, Formula of complete square,

(a+b)² = a² + 2ab + b²

Therefore,

⇒ (x+2)² = 8

Taking square root both sides we get,

⇒ (x+2) = ±√8

Hence,

x =  ± √8 - 2

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The total cost to join the website for one year is $34.00

Step-by-step explanation:

Onetime membership fee = $10

Per month newsletter charges = $2.00

One year = 12 months

Newsletter charges for 1 year = [tex]2.00*12=\$24[/tex]

Total cost = One time fee + newsletter charges for 1 year

[tex]Total\ cost=10+24.00=\$34.00[/tex]

The total cost to join the website for one year is $34.00

Keywords: addition, multiplication

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did you get the answer?? please let me know

Answer:

36

Step-by-step explanation:

Given:

Length of the cardboard = 27 inches

Width of the cardboard = 72 inches.

Let "x" be side of the square which is cut in each corner.

Now the height of box = "x" inches.

Now the length of the box = 27 - 2x and width = 72 - 2x

Volume (V) = length × width × height

V = (27 - 2x)(72 - 2x)(x)

[tex]V= (1944 -144x -54x + 4x^2)x\\V = (4x^2 - 198x +1944)x\\V = 4x^3 -198x^2 +1944x[/tex]

Now let's find the derivative

V' = [tex]12x^2 - 396x + 1944[/tex]

Now set the derivative equal to zero and find the critical points.

[tex]12x^2 - 396x + 1944[/tex] = 0

12 ([tex]x^2 - 33x + 162[/tex]) = 0

Solving this equation, we get

x = 6 and x = 27

Here we take x = 6, we ignore x = 27 because we cannot cut 27 inches since the entire length is 27 inches.

So, the area of the square = side × side

= 6 inches × 6 inches

The area of the square = 36 square inches.

Answer: Slope is 1/5

Step-by-step explanation:

Slope, m is expressed as

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the graph given, we would pick points for y2 and a corresponding x1 and also pick y1 and a corresponding x1

y2 = 4

y 1 = 3

x2 = 5

x1 = 0

Slope = (4-3)/(5-0) = 1/5

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

→The slope of the line given on the graph is [tex]\frac{1}{5}[/tex].

→You can tell because following the rise over run, the line goes up 1 unit, then to the right, 5 units.

→Since it is going to the right, it stays positive. However, if it were to go left, the 5 would be negative.

Answer: the other zeros are -3/2 and 5/3

Step-by-step explanation: