300 (1 - 0.25)to the power of t. what is the decay factor?

There are 2 hours of television must you watch in the eighth week to meet your goal.

What is television?

The transmission of audio and video data electronically between a source and a recipient.

The primary use of television is to transmit shows for entertainment, information, and education. Television is a system for transmitting visual images and sound that are reproduced on screens.

Given: You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period.

Suppose x is the hours of watching television in the 8th week.

Let the average of watching television per week is 1.5.

⇒

\(\frac{1 + 1.5 + 0.5 + 3 + 1.5 + 2 + 0.5 + x}{8} = 1.5\\ \frac{10+x}{8}=1.5 \\10+x = 12\\x = 12-10\\x = 2\)

Hence, there are 2 hours of television must you watch in the eighth week to meet your goal.

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Answer:

14x + 64

Step-by-step explanation:

3X x 3X + 7X + 64 - 2X =

9X + 7X + 64 - 2X =

16X + 64 - 2X =

14 X + 64

Hope that helps!

The value of θ from the given equation is 48.59degrees

Given the trigonometry function

Sin(θ)=3/4

We are to find the value of theta that will make the expression true

Take the arcsin of both sides

arcsin Sin(θ)= arcsin(3/4)

θ = arcsin(3/4)

θ = 48.59

Hence the value of θ from the given equation is θ = 48.59 defense

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Answer:

$9.77

Step-by-step explanation:

I hope this helps you out!

Answer:

None of them.

Step-by-step explanation:

log 15 could be log 3 + log 5

log3 + log 5 = 0.4771 + 0.69897 = 1.`17609

log 15 could also be log 45 - log 3 = 1.6532-0.4771=1.1761

But it cannot be any of the choices you have provided.

Answer:

The correct answer is log (15) - log (7)

Step-by-step explanation:

I took the quiz and got this question correct, hope it helps!

Hey there!

15% * 1.340

= 15/100 * 1.340

= 0.15 * 1.340

= .15 * 1.34

= 0.201

Therefore, the answer should be: 0.201

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The roots of the given quadratic function would be -

x = {- b - √(b² - 4c)}/2     &      x = {- b + √(b² - 4c)}/2

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

A quadratic function is of the form -

y = f(x) = ax² + bx + c

Given is the quadratic equation as -

x² + bx + c = 0

Using the quadratic formula, we can write the roots as -

x = {- b ± √(b² - 4c)}/2

We can write the two distinct roots as -

x = {- b - √(b² - 4c)}/2     &      x = {- b + √(b² - 4c)}/2  

Therefore, the roots of the given quadratic function would be -

x = {- b - √(b² - 4c)}/2     &      x = {- b + √(b² - 4c)}/2.

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Answer:

x= 7

Step-by-step explanation:

3x= 13+8

3x= 21

x= 21/3

x= 7

The radius of a cone with a curved surface area of 140π cm² and a slant height of 5 cm will be 28 cm.

The region with just curved surfaces, leaving the circular top and base, is referred to as the curved surface area. Total Surface Area is the combined area of the bases and the curved surface. The measurement of a solid's curved surface area is its outer area, which excludes the top and bottom extensions. Surface area of the cylinder that is curved: A right circular cylinder is the solid that results when a rectangle circles around one side and makes a full revolution. The curved surface area of a cylinder (CSA) is also known as the lateral surface area and is defined as the area of the curved surface of any given cylinder having a base radius "r" and height "h".

Here,

Curved surface area of cone=πrl

=140π

l=5 cm

140π=πr*5

r=140/5

r=28 cm

The radius of cone that has 5 cm as slant height and 140π cm² as the curved surface area will be 28 cm.

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Answer:

$0.65

Step-by-step explanation:

2.40-1.10=1.3

1.3/2=.65

2 x 10-7  is the probability of drawing a T, replacing it, then drawing a C.

What is Probability?

Probability is simply the chance that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics. 

There are 11 letters in MATHEMATICS which consist of 2 each of M, A and T and 1 each of H, E, I, C and S.  

P(M on 1st choice) = 2/11   since there are 2 M's out of 11 letters

P(A on 2nd choice) = 2/10   since there are 2 A's out of 10 remaining letters

P(T on 3rd choice) = 2/9     since there are 2 T's out of 9 remaining letters

At this point there are 8 letters remaining which are all distinct so they must be chosen in the correct order

P(H on 4th choice) = 1/8

P(E on 5th choice) = 1/7

P(M on 6th choice) = 1/6

P(A on 7th choice) = 1/5

P(T on 8th choice) = 1/4

P(I on 9th choice) = 1/3

P(C on 10th choice) = 1/2

P(S on 11th choice) = 1/1  

The probability of spelling the word correctly is the product of all the probabilities

P = 2*2*2 / 11! = 8 / 39916800 = 1 / 4989600 ~ 2 x 10-7

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The solution to the equation 2(t - 5) = 48 is t = 29.

To solve the equation 2(t - 5) = 48, we can use the following steps:

Distribute the 2 to the terms inside the parentheses:

2t - 10 = 48

Add 10 to both sides of the equation to isolate the variable term:

2t = 58

Divide both sides of the equation by 2 to solve for t:

t = 29

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Answer:

m∠B = 31°

Step-by-step explanation:

To find m∠B, we use the theory that in order to get it we must find the difference between the two arcs GM and VR and dividing it into 2

When putting this to equation we get:

m∠B = \(\frac{1}{2}\) * (VR - GM) = \(\frac{1}{2}\) * ( 94° - 32°) = \(\frac{1}{2}\)(62°) = 31°

Answer:

Step-by-step explanation:

This Website is On Goo gle By the way!

Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

(a) Let x = 3.12333…. Then 100x = 312.333… and 1000x = 3123.333…, so that

1000x - 100x = 3123.333… - 312.333…

==>   900x = 2811

==>   x = 2811/900 = 937/300

(b) x = 4.38555…   ==>   100x = 438.555… and 1000x = 4385.555…

==>   900x = 3947

==>   x = 3947/900

(c) x = 37.222…   ==>   10x = 372.222…

==>   9x = 335

==>   x = 335/9

(d) x = 16.292929…   ==>   100x = 1629.292929…

==>   99x = 1613

==>   x = 1613/99

(e) x = 2.333…   ==>   10x = 23.333…

==>   9x = 21

==>   x = 21/9 = 7/3

The z score on his first quiz was 1.29 and the z score on his second quiz was 1.73.

Alvin feels he did better on the second quiz than the first because he received a higher z score. A z score is a measure of how many standard deviations an individual score is from the mean. The higher the z score, the more standard deviations away from the mean the individual score is.

In this case, Alvin's score of 15 on his second quiz was 1.73 standard deviations away from the mean of 12.2, which is higher than his score of 16 on his first quiz which was 1.29 standard deviations away from the mean of 14.3.

This indicates that Alvin's second quiz score was further away from the mean than his first quiz score, which is why he feels he did better on the second quiz than the first.

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The correct formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests is 1950 + 100n.

To find the formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests, we can analyze the given information.

We are given two data points: the cost for 50 guests, which is $6,950, and the cost for 100 guests, which is $11,950. We can observe that the difference between these two costs is $11,950 - $6,950 = $5,000.

Since the cost forms an arithmetic sequence, the difference between consecutive terms will remain constant. In this case, the difference is $5,000.

Now, we need to find the initial term of the sequence. By examining the cost for 50 guests, we notice that the difference between the cost for 50 guests and the initial term is $6,950 - $5,000 = $1,950.

Putting it all together, we have the formula for the general term of the arithmetic sequence: initial term + (difference × (n - 1)).

Plugging in the values, the formula becomes: 1,950 + (5,000 × (n - 1)) = 1,950 + 5,000n - 5,000 = 5,000n - 3,050. Simplifying further, we get the final formula: 5,000n - 3,050.

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Answer:

A counterclockwise rotation of 270° about the origin

Step-by-step explanation:

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

Answer:

75 km

Step-by-step explanation:

(50km/h)(1.5h) = 75km

Answer:

-2.5?

Step-by-step explanation:

The solution is Option C.

The total amount of earnings of Sondra after 5 years is $ 169,113

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the annual salary of Sandra be A = $ 30,000

Now , the percentage increase in salary = 6 %

So , the equation will be

First year :

The increase in first year =  annual salary of Sandra + percentage increase in salary x annual salary of Sandra

The increase in first year = 30000 + ( 6/100 ) x 30000

                                        = 30000 + 1800

                                        = $ 31,800

Second year :

The increase in second year =  increase in first year + percentage increase in salary x increase in first year

The increase in second year = 31800 + ( 6/100 ) x 31800

                                        = 31800 + 1908

                                        = $ 33,708

Third year :

The increase in third year =  increase in second year + percentage increase in salary x increase in second year

The increase in third year = 33708 + ( 6/100 ) x 33708

                                        = 33708 + 2022.48

                                        = $ 35,730.48

Fourth year :

The increase in fourth year =  increase in third year + percentage increase in salary x increase in third year

The increase in fourth year = 35730.48 + ( 6/100 ) x 35730.48

                                        = 35730.48 + 2143.8288

                                        = $ 37,874.3088

Now , the equation is

The total earnings of Sondra is = First year salary + second year salary + third year salary + fourth year salary

The total earnings of Sondra is = 30000 + 31,800 + 33,708 + 35,730.48 + 37,874.3088

The total amount earnings of Sondra is = $ 169,112.7888

Therefore , the total amount earnings = $ 169,113

Hence , The total amount of earnings of Sondra after 5 years is $ 169,113

Answer:

C)  $199,797

Step-by-step explanation:

Adding 7% of a number to the number is the same as multiplying the number by 1.07

First year: $45,000

Second year: $45,000 × 1.07 = $48,150

Third year: $48,150 × 1.07 = $51,520.50

Fourth year: $51,520.50 × 1.07 = $55,126.94

Total = $199,797.43

Answer: C)  $199,797

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1230\\ r=rate\to 3.19\%\to \frac{3.19}{100}\dotfill &0.0319\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1230[1+(0.0319)(3)] \implies \stackrel{balance}{\boxed{A \approx 1347.71}}~\hfill \underset{interest}{\stackrel{1347.71~~ - ~~1230}{\boxed{117.71}}}\)

Answer:

B

Step-by-step explanation:

You had a balance of $535.07 from the previous month and only paid $450.00 so you didn’t pay off your balance in full.

The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;

The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors

Simultaneous equations are a set of two or more equations that have common variables.

Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station

According to the details in the question, after the first transaction, we get

Number of tractors at the first station = x - y - z

Number of tractors at the second station = y + y = 2·y

Number of tractors at the third station = z + z = 2·z

After the second transaction, we get;

Number of tractors at the first station = 2·x - 2·y - 2·z

Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z

Number of tractors at the third station = 2·z + 2·z = 4·z

After the third transaction, we get;

Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z

Number of tractors at the second tractor station = 6·y - 2·x - 2·z

Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y

The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)

6·y - 2·x - 2·z = 24...(2)

7·z - x - y = 24...(3)

Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;

12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24

16·y - 8·x = 24...(4)

Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;

14·z - 2·x - 2·y = 48

42·y - 14·x - 14·z = 168

42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168

40·y - 16·x = 216...(5)

Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;

40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168

8·y = 168

y = 168/8 = 21

The number of tractors initially at the second station, y = 21

16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24

8·x = 16 × 21 - 24 = 312

x = 312 ÷ 8 = 39

The number of tractors initially at the first station, x = 39

7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24

7·z = 24 + 39 + 21 = 84

z = 84/7 = 12

The number of tractors initially at the third station, z = 12

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The given quadrilateral PQRS do not have the properties of a parallelogram, but that of a square. Because we are to prove that its consecutive sides are congruent i.e : QP ≅ QR.

The required proofs are stated below:

                  Statement                                 Reason

1. <SPR ≅ <PRQ                                       Alternate angle property

2. PT ≅ TR                                               Definition of a mid-point

3. <PTS ≅ <QTR ≅ \(90^{o}\)                           Perpendicular bisector property

4. ST ≅ TQ                                              Mid-point of a segment

5. PQ ≅ SR                                             Opposite side congruent property

6. ΔPQs ≅ ΔQRS                                    Side-Angle-side (SAS) property

7. <PQR ≅ <SPQ                                    Right angle property

8. PQ ≅ QR                                            Congruent consecutive side property

Therefore given that PQ ≅ QR, then the given quadrilateral is a square.

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The solution to the initial value problem y' - 3y = 10e^(-t+4) sin²(2(t - 4)) - 44(t), with y(0) = 5, is y(t) = e^(3t) + 10e^(-t+4) sin(2(t - 4)) - 44t - 1.

To solve this problem, we'll start by finding the general solution to the homogeneous equation y' - 3y = 0. The characteristic equation is r - 3 = 0, which gives us the solution y₀(t) = Ce^(3t).

To solve the initial value problem y' - 3y = 10e^(-t) + 4sin(2(t - 4)) + 44t with y(0) = 5, we can use an integrating factor and the method of variation of parameters.

Step 1: Homogeneous Solution

First, let's find the homogeneous solution to the equation y' - 3y = 0. This means we solve the equation y' - 3y = 0 without the right-hand side term.

The characteristic equation is given by r - 3 = 0, which yields r = 3. Therefore, the homogeneous solution is y_h = C*e^(3t), where C is a constant.

Step 2: Particular Solution

Next, let's find a particular solution to the non-homogeneous equation y' - 3y = 10e^(-t) + 4sin(2(t - 4)) + 44t. We'll denote this particular solution as y_p.

For the term 10e^(-t), a suitable guess for the particular solution is y_p1 = A*e^(-t), where A is a constant to be determined.

Differentiating y_p1 with respect to t gives y_p1' = -A*e^(-t).

Substituting y_p1 and y_p1' into the differential equation, we have:

(-Ae^(-t)) - 3(Ae^(-t)) = 10e^(-t).

Simplifying, we get -4A*e^(-t) = 10e^(-t).

Comparing the coefficients on both sides, we find A = -10/4 = -5/2.

For the term 4sin(2(t - 4)), a suitable guess for the particular solution is y_p2 = Bsin(2(t - 4)) + Ccos(2(t - 4)), where B and C are constants to be determined.

Differentiating y_p2 with respect to t gives y_p2' = 2Bcos(2(t - 4)) - 2Csin(2(t - 4)).

Substituting y_p2 and y_p2' into the differential equation, we have:

(2Bcos(2(t - 4)) - 2Csin(2(t - 4))) - 3(Bsin(2(t - 4)) + Ccos(2(t - 4))) = 4sin(2(t - 4)).

Simplifying, we get (2B - 3C)cos(2(t - 4)) + (3B + 2C)sin(2(t - 4)) = 4sin(2(t - 4)).

Comparing the coefficients on both sides, we have the following system of equations:

2B - 3C = 0 (1)

3B + 2C = 4 (2)

Solving equations (1) and (2), we find B = 6/13 and C = 4/13.

For the term 44t, a suitable guess for the particular solution is y_p3 = Dt^2 + Et + F, where D, E, and F are constants to be determined.

Differentiating y_p3 with respect to t gives y_p3' = 2Dt + E.

Substituting y_p3 and y_p3' into the differential equation, we have:

(2Dt + E) - 3(Dt^2 + Et + F) = 44t.

Simplifying, we get -3Dt^2 + (2 - 3E)t + (E - 3F) = 44t.

Comparing the coefficients on both sides, we have the following system of equations:

-3D = 0 (3)

2 - 3E = 44 (4)

E - 3F = 0 (5)

Solving equations (3), (4), and (5), we find D = 0, E = -14/3, and F = -14/9.

Therefore, the particular solution is y_p = y_p1 + y_p2 + y_p3, which is:

y_p = (-5/2)e^(-t) + (6/13)sin(2(t - 4)) + (4/13)cos(2(t - 4)) - (14/3)t - (14/9).

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Answer:

Area of the rectangle - 144 in^2

Area of the circle - 28,26 in^2

Total shaded area - 115,74 in^2

Step-by-step explanation:

\(a(rectangle) = 18 \times 8 = 144 \: {in}^{2} \)

\(a(circle) = \pi \times {r}^{2} = {3}^{2} \times \pi = 9\pi = 9 \times 3.14 = 28.26 \: {in}^{2} \)

\(a(shaded) = a(rectangle) - a(circle)\)

\(a(shaded) = 144 -28.26 = 115.74 \: {in}^{2} \)