A rectangle has a length of 12 inches and a width of 2 inches whose sides are changing. The length is increasing by 10 in/sec and the width is growing at 4 in/sec. What is the rate of change of the perimeter?

Answer:

A.  1,500

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7cm}\underline{Sum of the first n terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the $n$th term.\\\end{minipage}}[/tex]

The given scenario can be modelled as a geometric series.

If Marcus' goal is to sell 15,000 t-shirts during the first 6 months, then:

If he projects that the number of t-shirts he sells will increase by 20% each month then the common ratio is:

Substitute these values into the formula and solve for a:

[tex]\implies 15000=\dfrac{a(1-1.2^6)}{1-1.2}[/tex]

[tex]\implies 15000(1-1.2)=a(1-1.2^6)[/tex]

[tex]\implies a=\dfrac{15000(1-1.2)}{1-1.2^6}[/tex]

[tex]\implies a=1510.586188[/tex]

Therefore, the approximate number of T-shirts Marcus needs to sell during the first month to meet his goal is 1,500.

Check:

Total = 1511 + 1813 + 2176 + 2611 + 3133 + 3760 = 15004

Check:

Total = 1500 + 1800 + 2160 + 2592 + 3110 + 3732 = 14894 ≈ 15000

By using unitary method, it can be calculated that

When input decreases by 30, output decreases by 36

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

This is a problem on unitary method

Slope = [tex]\frac{6}{5}\\[/tex]

When input decrease by 5, output decreases by 6

When input decrease by 1, output decreases by [tex]\frac{6}{5}[/tex]

When input decreases by 30, output decreases by [tex]\frac{6}{5} \times 30[/tex]

When input decreases by 30, output decreases by 36

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Answer:

Step-by-step explanation:

Step 1: Use point-slope form and substitute in the x and y values

y-y1=m(x-x1)

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

Step 2: Simplify the expression

y-1 = 2(x+3)

Add one to the other side

y= 2(x+3)+1

Multiple 2 by (x+3)

y=2x+6+1

Add common terms

y=2x + 7

Answer:

Step-by-step explanation:

24-29=-5

using the number line:)

Answer:

4-23=4b

Step-by-step explanation:

Answer:

y=5,-8

Step-by-step explanation:

Answer: hope this helps ♡

y = 5,   y = -8

Step-by-step explanation:

∣2y + 3∣ + 2 = 15

∣2y + 3∣ + 2 - 2 = 15 - 2

∣2y + 3∣ = 13,   ∣2y + 3∣ = -13

∣2y + 3 - 3∣ = 13 -3,   ∣2y + 3 - 3∣ = -13 - 3

2y = 10,   2y = -16

y = 5,   y = -8

80, 7, and 2.87 are not irrational numbers.

What is an irrational number?

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, etc all are irrational.

Given numbers: 80, 7, 2.87, √59

80 = It is a rational number

7 = It is a rational number

2.87 = It is a rational number

√59 = It is an irrational number.

Hence, 80, 7, and 2.87 are not irrational numbers.

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The solution of the given quadratic equation is x = 1.37, - 1.37.

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                            The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions .

Given quadratic equation:

9x² = 17

⇒ x² = (17 / 9)

⇒ x = ± √(17 / 9)

⇒ x = ± (√17) / 3

⇒ x = 1.37, - 1.37

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Value of contrast given is 4.043 , standard error is 1.4535 and t is 2.782 So ,after analyzing this given data , the value for p  for null hypothesis testing is 0.008

In Hypothesis Testing, the P-value method is used to determine the significance of the given null hypothesis. The decision to reject or support it is then made on the basis of the specified significance level or threshold.

This method computes a P-value, which is a test statistic. This statistic can tell us how likely it is that we will find a value (sample mean) that is as far away as the population mean.

P-value is an abbreviation for Probability.

We reject or fail to reject the null hypothesis based on that probability and a significance level.

In general, the lower the p-value, the greater the likelihood of rejecting the null hypothesis, and vice versa.

We also use the Z-table to complete this process.

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Answer:

4 916 083

Step-by-step explanation:

population in 1990

1.5 : 100 = x : 4 786 000

x = 1.5 · 4 786 000 / 100

x = 1.5 · 47 860

x = 71 790

4 786 000 + 71 790 = 4 857 790

population in 2000

1.2 : 100 = x : 4 857 790

x = 1.2 · 4 857 790 / 100

x = 0.012 · 4 857 790

x = 58 293.48

4 857 790 + 58 293.48 = 4 916 083.48

Answer:

13.3=c

Step-by-step explanation:

The hypotenuse can be found with the equation [tex]a^2+b^2=c^2[/tex].  For this problem, let

a=8.3

b=10.4

So,

[tex](8.3)^2+(10.4)^2=c^2\\177.05=c^2\\\sqrt{177.05}=\sqrt{c^2}\\13.31=c[/tex]

The equation of the new function is: f(x) = (x- 3)²

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

The translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

We know that the function f(x+m) is equals to the function f(x) translated 'm' times to the left.

Therefore, to find the translate the function f(x) = x² twelve units to the right, we have given;

f(x- 3) = (x- 3)²

Therefore, the new function is: f(x) = (x- 3)²

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The subtraction of significant figures between the distance is 5.01 × 10⁷km

In this problem, we have to subtract the difference between the distance of Venus and Mercury. When subtracting significant digits, the amount of significant digits that will be in the final answer is determined by the number of significant digits present after the decimal place in the numbers we are subtracting.

The distance between Venus and Mercury can be calculated as

1.08 × 10⁸ - 5.79 × 10⁷ = 50,100,000km

To express the value in significant figures, we will have

50,100,000 = 5.01 × 10⁷km

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Since a + b + c are vertically opposite angles, e = 130.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

d=70, opposite vertical angle

180 - 70 - 40 = 2 using angles on a straight line.

We now possess the two angles, and since they are perpendicular to one another, a and c = 35.

Because of the vertically opposed angles, b = 40.

4. Because 90-70, a=30.

Because an is 30, divide 90 by 30 to obtain b, 70.

vertically opposite angles, d=70

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4/4 is the most commonly used time signature. You will have 4 beats per measure and the quarter note will be one beat.

Two numbers make up a time signature, which is similar to a fraction. The time signature may alter throughout a work, but it always appears at the beginning. The bottom number is the note value that corresponds to one beat, and the top number is the number of beats in a measure. A song in 4/4 time, for instance, will have four quarter notes every measure, whereas a song in 9/8 time will have nine eighth notes per measure.

Here,

The most popular time signature is 4/4. The quarter note is one beat, and each measure has four beats.

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Answer:

D

Step-by-step explanation:

Since we know that both parabolas are on the y-axis, it can't be A or C.

We also know they are above (0,0), so it can't be option B.

That leaves option D.

Answer: 20%

Step-by-step explanation:

60 divided by 75 then times 100 = 80%

100% - 80% = 20%

The scale factor of Dilation is 2

The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.

We want to find the scale factor at which QRST is dilated to form Q'R'S'T'

We will find that the scale factor is 2.

In a general dilation, we will see that all the measures change in the same way, by the scale factor.

This means that:

QR*k = Q'R'

RS*k = R'S'

And so on, where k is the scale factor.

Then we can just find one of the equivalent measures in both trapezoids and find the value of k.

For example, we have:

Q'R' = 8

QR = 4

Replacing these on the above equation we get:

4*k = 8

k = 8/4 = 2

k = 2

Therefore the scale factor of dilation is 2.

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Answer:

= 408.16 or =20000/49

Step-by-step explanation:

= (78000/ 19110) x100

= (200/49)*100

=20000/49

The equation is 2w + 10 = 26.

The number of weeks the driving class lasts is 8 weeks.

With that,

Terrence signed up for the Safe Venture driving school.

He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.

When Terrence completes the 26 total hours of instruction, he will take his driver's test.

We have to determine,

Which equation can you use to find w, the number of weeks the driving class lasts.

According to the question,

He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.

Then, The equation of the number of weeks the driving class lasts,

= 2w + 10

When Terrence completes the 26 total hours of instruction, he will take his driver's test.

2w + 10 = 26

He spends 10 hours driving and adding on 2 more classes with a total of 26 hours.

Therefore,

The number of weeks the driving class lasts,

2W + 10 = 26

2W = 26 - 10

2W = 16

W = (16/2)

W = 8

Hence, The number of weeks the driving class lasts is 8 weeks.

Answer:-4x + 6

Step-by-step explanation:

7 + x - 1 - 5x

6 - 4x

The answer is -4x +6

The constant that must be added to both sides of the equation to find the perfect square is b/2a.

The 2nd equation in x is known as a quadratic function. Ax2 + Bx + c = 0 is the quadratic equation in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.

The presence of a non-zero component in the coefficient of x2 (a ≠ 0) is the first prerequisite for an expression to be a quadratic equation.

As per the given information in the question,

The equation for the quadratic equation is,

Ax² + Bx + c = 0

And for finding the roots,

d = b² - 4ac

Then, use the formula (-b±√d)/2a.

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The required values of the compound amount are $56740.76, $56982.05, $57191.25, $57232.60 and $57234.01 respectively.

What is compound interest?

Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has already accrued over the course of prior periods are used to calculate compound interest.

Given, Principal (P) = $42,400

interest rate(r) = 6% per year = 0.06

time(t) = 5 years

The compound amount is given by

[tex]A = P(1+\frac{r}{t} )^{nt}[/tex]

For compounded annually, n=1

[tex]A = 42400(1+0.06)^{1*5}[/tex] = $56740.76

For compounded semi-annually, n=2

[tex]A = 42400(1+\frac{0.06}{2})^{2*5}[/tex] = $56982.05

For compounded monthly, n=12

[tex]A = 42400(1+\frac{0.06}{12})^{12*5}[/tex] = $57191.25

For compounded daily, n=365

[tex]A = 42400(1+\frac{0.06}{365})^{365*5}[/tex] = $57232.60

For compounded continuously,

[tex]A=Pe^{rt} = 42400e^{0.06*5}[/tex] = $57234.01

Hence, these are the required values of the compound amount.

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Answer:

She spend $7 a month on downloads.

Step-by-step explanation:

y = the total spent on downloads

x = number of months

m = the amount spent each month

y = mx

45.50 = m(6.5)  Divide both sides by 6.5

7 = m

Answer:56

Step-by-step explanation:20% of 70 is 14 dollars so you have to subtract 70-14=56.

Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.

We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:

x + 28 = 2(y + 7)

x + 28 = 2y + 14

x - 2y = -14

Then, we can substitute the second equation into the first equation to eliminate the other variable:

y + 7 = 4(x + 28)

y + 7 = 4x + 112

y - 4x = -105

Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:

x - 2y = -14

y - 4x = -105

If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:

x - 2(4x - 105) = -14

x - 8x + 210 = -14

-7x = -224

x = 32

Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.

Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).

Answer:

  [tex]\bullet\quad(x^3+y^3)^\frac{1}{2}\\\\\bullet\quad\dfrac{81}{1}[/tex]

Step-by-step explanation:

You want √(x³ +y³) written with a rational exponent, and 27^(4/3) written as a ratio of integers.

The square root is the same as the 1/2 power. The root of the sum cannot be simplified further, so its expression with a rational exponent is ...

  [tex]\sqrt{x^3+y^3}=\boxed{(x^3+y^3)^\frac{1}{2}}[/tex]

The expression 27^(4/3) can be simplified to ...

  [tex]27^\frac{4}{3}=(\sqrt[3]{27})^4=3^4=81=\boxed{\dfrac{81}{1}}[/tex]

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The values of the expressions are x = √6, y = 2√3 and z = √2

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

[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]

[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]

[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]

We have

[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]

Take the square of both sides

So, we have

[tex]x^2 =12-3\sqrt{7} + 12 + 3\sqrt{7} - 2(\sqrt{12-3\sqrt{7} } * \sqrt{12 + 3\sqrt{7} })[/tex]

This gives

x² = 12 - 3√7 + 12 + 3√7 - 2√81

Evaluate the roots

So, we have

x² = 12 - 3√7 + 12 + 3√7 - 18

Evaluate the sum and the difference

x² = 6

Take the square roots of both sides

x = √6

Using the same steps above, we have

[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]

Square both sides

So, we have

[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * \sqrt{7-4\sqrt{3 } } * \sqrt{7 + 4\sqrt{3} }[/tex]

This gives

[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * 1[/tex]

Evaluate

y² = 12

Take the square root of both sides

y = 2√3

Lastly, we have

[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]

Square both sides

[tex]z^2 = 2 + \sqrt 3 + 2- \sqrt 3 - 2 * \sqrt{2 + \sqrt{3} } * \sqrt{2 - \sqrt{3} }[/tex]

This gives

z² = 4 - 2 *1

Evaluate

z = √2

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The probability that a given class period runs between 50.5 and 51.25 minutes is 15%.

Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make probability-based predictions, and also probability has extensive applications in this new area of artificial intelligence.

The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes. Also, the favorable number of outcomes cannot be negative.

[tex]P(50.5 < = X < = 51.25) =\frac{51.25-50.5}{54-49 } = \frac{0.75}{5} = 0.15[/tex]

P = 0.15 means that the probability is 15%.

Thus, the probability that a given class period runs between 50.5 and 51.25 minutes is 15%.

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