Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)

The proportional relationship y = 200x, showing the number of calories y burned as a function of the time swimming of x hours, is given as follows:

A proportional relationship is a special case of a linear function, as even though it has a constant rate of change, the intercept is of zero.

The general format of a proportional relationship is given as follows:

y = kx.

In which the constant of proportionality k represents the constant rate of change.

Supposing that for each hour swimming, the person spends 200 calories, the constant is given as follows:

k = 200.

Hence the proportional relationship that gives the number of calories y burned as a function of the time swimming of x hours is given as follows:

y = 200x.

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Answer:x=-2,5, -[tex]i\sqrt{2}[/tex], +[tex]i\sqrt{2}[/tex]

Step-by-step explanation:

Answer:

X=100

Step-by-step explanation:

I assume you want to find the value of x.

3/5x=60

5/3*60=x

x=20*5=100

The range of the sine function is:

R: {x ∈ R| -1 ≤ x ≤1}

It can also be written as [-1, 1], so that is the correct option.

For a function y = f(x) we define the range as the set of the outputs, this is, the set of the possible values of y.

In this case, our function is y = sin(θ)

Remember that the maximum value of the sine is sin(π/2) = 1

And the minimum is sin(3π/2) = -1

So the maximum value of y is 1 and the minimum is -1, thus, the range is the set of all real numbers between these two, then we can write the range as:

R: {x ∈ R| -1 ≤ x ≤1}

It can also be written as [-1, 1]

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To determine the gain or loss on the redemption of the bonds, you need to compare the redemption price to the carrying value of the bonds. The carrying value of the bonds is the amount that the bonds are recorded as being worth on the issuing corporation's balance sheet. This is calculated by adding the Bonds Payable balance and the Premium on Bonds Payable balance.

In this case, the carrying value of the bonds is $810,000 + $8,910 = $818,910. If the bonds are redeemed at a price of $102, the gain or loss on the redemption can be calculated as follows:

Gain or loss on redemption = Redemption price - Carrying value of bonds

= $102 - $818,910

= -$817,810

Since the gain or loss on the redemption is a negative number, this indicates that the redemption price was lower than the carrying value of the bonds, resulting in a loss. The correct answer is therefore: c. $7,290 loss.

Two index that are equivalent to the index (x^{1/3)² are:- 1) X⁽²/³⁾, 2) (∛X)²

What are index ?

An index can be assigned to a number or variable. A value raised to the power of a variable's (or a constant's) value is its index. The exponents or powers are other names for the indices. It displays how many times a particular number must be multiplied. It takes the following form:

a(m) = a × a × a ×……× a (m times)

The base in this case is a, and the index is m.

The index instructs a certain integer (or base) to be multiplied by itself a specified number of times, where the number of times is determined by the index raised to the base. It is a condensed way of expressing large sums of information and calculations.

[tex]X^b . X^A. X^n = X^b^a^n[/tex]

Example: 2^3 = 2 × 2 × 2 = 8

[tex][X^\frac{1}{3} ]^2[/tex][tex]= X^\frac{2}{3}[/tex]

We can also write the same index as;

[tex]A^\frac{1}{n}=\sqrt[n]{A}[/tex]

[tex]X^\frac{2}{3}=[\sqrt[3]{x}]^2[/tex]

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Between (5,10) and (15,70), a line runs. As a result, the slope of the line through the supplied locations is 3.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line.

A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-

P1 = (x1, y1) and P2 = (x2, y2)

Hence, Between (5,10) and (15,70), a line runs. As a result, the slope of the line through the supplied locations is 3.

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The dimensions of each of the rectangular pens are given as follows:

8.41m and 41.58 m.

The pen have rectangular format, as shown by the image given at the end of the answer, hence the dimensions are obtained from the area and the perimeter of the pen.

For each pen, the dimensions are given as follows:

For the entire pen, the dimensions are given as follows:

You have 200 meters of fencing to enclose two adjacent rectangular pens for livestock, hence the perimeter is given as follows:

2(2x + y) = 200

2x + y = 100.

The total area of the enclosed region is 1400 square meters, hence:

2xy = 1400.

From the first equation, we have that:

y = 100 - 2x.

Replacing in the second, the length x is obtained as follows:

2x(100 - 2x) = 1400

-4x² + 200x - 1400 = 0

4x² - 200x + 1400 = 0.

The solutions are of:

8.41m and 41.58 m.

Which gives the dimensions of the pen.

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Answer: y = 14/19x+15

Step-by-step explanation: using the equation y = mx+b, m is your slope and b is the y-intercept. plug your slope (14/19) and y-intercept (15) into the equation and you’ve got your answer in slope-intercept form

Y=mx+b is standard form.

y-2= -x-7

  +2      +2

y= -x-5

The equation that can be used to find the length of the side of the original square is 4(x+5) = 60. Option A. is the answer

Given that:

When the length of a side of a square is increased by 5, the perimeter of the new square is 60.

Let x represent the length of the side of the original square

when x is increased by 5, you have (x+5)

Perimeter (P) = 4 × length of the side

Thus, 4(x+5) = 60

Therefore,  the equation to find the length of the side is  4(x+5) = 60

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Preeti informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with Psychosis

Psychosis is a combination of symptoms resulting in an impaired relationship with reality. It can be a symptom of serious mental health disorders. People who are experiencing psychosis may have either hallucinations or delusions.

If someone is experiencing an episode of psychosis, the main symptoms include:

According to the question,

Preeti discovers that her roommate Shari recently experimented with methamphetamine. Preeti, worried about her roommate, informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with Psychosis

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we want to find the number of hours (or rather days) until only 4.25% of the drives fail.

that means for an exponential distribution we have

P(X < x) = 1 - e^(-Lx)

L = 1/mean = 1/12500

and we need to find x, so that P(X <x) = 0.0425 (that is 4.25% converted into a probability).

so, we get

0.0425 = 1 - e^(-x/12500)

0.0425 - 1 = -e^(-x/12500)

-0.9575 = -e^(-x/12500)

0.9575 = e^(‐x/12500)

ln(0.9575) = -x/12500

-x = ln(0.9575)×12500

x = -ln(0.9575)×12500 = - -0.043429558...×12500 =

= 0.043429558...×12500 = 542.8694741... hours

after 542.8694741... hours = 22.61956142... days

it is expected that 4.25% of the hard drives fail.

you left out to what decimal this should be rounded. and if you need hours or days. in case of doubt use hours (as the only other time information is given in hours).

please round yourself as you need.

According to the Dietary Guidelines for American 2015, you should limit your fat intake to 25% - 35% of your total calories. The correct option is B.

Food-based dietary guidelines also known as dietary guidelines are intended to serve as a foundation for public food and nutrition policies, health and agricultural policies, and nutrition education programs aimed at promoting healthy eating habits and lifestyles.

Calories are the units of energy released by your body when it digests and absorbs food. The higher the calorie content of a food, the more energy it can provide to your body. When you consume more calories than you require, your body stores the excess calories as fat. Even fat-free foods can be high in calories. In this case, the fay should not be more than 35%.

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The vertex (3, -16) is the maximum point on our quadratic equation.  

When we compare the given Quadratic function with the general form

ax² +bx +c,    

If the value of a is positive then the Quadratic function will have a minimum value, and the graph of the function opens up.  

If the value of a is negative then the Quadratic function will have a maximum value, and the graph of the function opens downwards.  

Here we have

f(x) = -2(x - 5)(x-7)

f(x) = -2 [x²-7x - 5x + 35 ]

f(x) = -2 [x²-12x + 35 ]

f(x) = -2x² + 12x - 35  

Compare f(x) with ax²+ bx + c  

=> a = -2, b = 12, and c = - 35  

Here,

a = -2 is a negative value then the function f(x) will have maximum value    

And the graph of the function opens down.  

The formula for the x coordinate of the vertex = -b/2a  

The coordinate of x = -(12)/2(-2) = 3    

Now substitute x = 3 in f(x) to find y-coordinate

=> f(3) = - 2(3)² +12(3) - 35    

=> f(3) = -2(9) + 36 - 35          

=> f(3) = - 16    

Therefore, y-coordinate = -16            

Therefore,

The vertex (3, -16) is the maximum point of the quadratic equation.              

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Answer:

44

Step-by-step explanation:

80*55/100 = 44

Answer:78

Step-by-step explanation:

Answer: To determine Alejandro's earnings for the first 4 weeks, we first need to calculate his weekly pay. To do this, we divide his annual salary by the number of weeks in a year:

Annual salary / 52 weeks/year = weekly pay

$71,500 / 52 weeks/year = $1,375/week

Next, we need to determine the agency fee that Alejandro will pay each week. The agency fee is equal to 40% of the first 5 weeks' pay, so we multiply Alejandro's weekly pay by 40% to get the agency fee:

Weekly pay * 40% = agency fee

$1,375/week * 40% = $550/week

Finally, to determine Alejandro's earnings for the first 4 weeks, we multiply his weekly earnings by the number of weeks:

Weekly pay * number of weeks = earnings

$1,375/week * 4 weeks = $5,500

So, Alejandro will earn $5,500 during the first 4 weeks of his new job, after paying the agency fee each week.

Answer: ???

Step-by-step explanation:

You have to put in the numbers for the percentages.

The position of the √7 on the number line is slightly right of the 2.6.

What is a number line?

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,

In general conclusion,

√4< √7 < √9

2 < √7 < 3

So, the value of the √6 lies between 2 and 3.

√6 = 2.6457

Hence, the position of the √7 on the number line is slightly right of the 2.6.

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There are 36 possible outcomes when rolling two dice, and only 1 of those outcomes results in a double. Therefore, the probability of rolling a double is 1/36, or approximately 0.028.

If you are willing to pay $20 to roll the dice, then you are effectively paying a premium of $20 for a probability of 0.028 of winning. This means that the expected value of rolling the dice is 0.028 * $20 = $0.56.

Therefore, you should be willing to pay up to $0.56 for the privilege of rolling the dice. Rounded to the nearest cent, this is $0.56.

Ling can therefore purchase 0 to 12 bags, but no more is the right decision.

Ling has been instructed to spend no more than $40.00 on party décor. She has already spent $10.00 on streamers but also plans to purchase bags of balloons. The price of a bag of balloons is $2.50.

Given her spending cap and how much she has already spent on streamers, the inequality  10 + 2.5x ≤ 40 indicates x, the number of bags she can purchase.

Subtracting 10 from both sides of our inequality, let's find x by reversing the inequality.

10 - 10 + 2.5 x ≤ 40 - 10

2.5 x ≤ 30.

We will now divide our inequality by 2.5 on both sides.

2.5 x / 2.5 ≤ 30 / 2.5

x ≤ 12.

Ling can therefore purchase 0 to 12 bags, but no more is the right decision.

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Answer:

Step-by-step explanation:

Ling can therefore purchase 0 to 12 bags, but no more is the right decision.

The bags of chips sold are 111.

The percentage is the term use to tell the hundredth part of something.

Given that, The snack bar sold 75% of its inventory of bags of chips, and the snack bar still has 37 bags of chips,

Let the original number of bags of the chips be x,

Since, 75% is already sold, so left number of bags are = 100%-75% = 25%

Therefore,

25% of x = 37

x = 37x4

x = 148

The number of bags sold = 75% of 148

= 75x148/100

= 111

Hence, they sold 111 bags of chips.

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Let n be a positive integer. Consider the  n+1 integers 1,11, 111,1111,... (where the last integer in this list is the integer with n+1 - 1s in its decimal expansion).

Note that there are n possible remainders when an integer is divided by n. Because there are n+1 integers in this list, by the pigeonhole principle there must be two with the same remainder when divided by n. The larger of these integers the smaller one is a multiple of n, which has a decimal expansion consisting entirely of 0s and 1s.

For example, take n=7

we have, 1,11, 111,1111,...,11111111

The remainder possible when any number is divided by 7 is 0,1,2,3,4,5,6

These are the remainders when the numbers in the first list are divided by 7 gives 1,4,6,5,2,0,1,4.

Now you can see that we have 7 pigeonholes {0,1,2,3,4,5,6} and 8 pigeons {1,11, 111,1111,...,11111111} so there needs to be at least one pigeonhole where 2 pigeons will reside.

In this case, we have 11%7=4 and 11111111%7=4

Their difference, i.e. 11111111-11=11111100 is divisible by 7.

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Answer:

$30.30

Step-by-step explanation:

$26.35*15%=$3.95

Then you add $26.35 and $3.95 to get $30.30

15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).

Given that,

We have to calculate let's now examine the Buffalo's collective data. How many Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).

We know that,

Theoretical hits= confidence interval × total no. of buffaloes

= 0.6×(buffaloes)

Sample hits = count among total no. of buffaloes, from which how many of inside 25000, that will be sample hits.

So,

=0.6×25000

=15000

Therefore, 15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).

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Answer: 59.50=8.25x + 10

Step-by-step explanation: so we know that It is 8.25 per sandwich making it the constant. Then we know that 10 is the the deléguente fee making it the y-intercept. Finally this all has to equal to 59.50. X represents how many sandwiches the person ordered.

Based on the elevation of the scientist after descending and traveling directly up, the number of feet she needs to ascend to get to sea level will be; 82.7 feet.

To find the number of feet that the scientist needs to travel up to get back to sea level, you need to find her current elevation.

The current elevation of the scientist is:

= 0 - 21.1 + 19.1 + 80.7

=  82.7 feet

In other words, the scientist is 82.7 feet below sea level.

To get back to sea level therefore, the scientist will need to travel 82.7 feet directly up.

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The dimensions of the piece are l = 8 and b =4.

What are dimensions?

The minimal set of coordinates required to specify any point within a mathematical space is the dimension of that space. Because only one coordinate is required to specify a point on a line, it has a dimension of one.

Here,

Let the length of a rectangular piece of metal = l cm

And the breadth of a rectangular piece of metal = b cm

Perimeter of a rectangular piece of metal = 2(l+b) = 24 cm

Or, l+b = 24/2

Or, l+b = 12 -------- (1)

Area of a rectangular piece of metal = l×b = 32 cm²

Or, l×b = 32 ------- (2)

We know that,

(l - b)² = (l+b)² - 4×l×b

(l - b)² = (12)² - 4×32

(l - b)² = 144 - 128

(l - b)² = 16

(l - b)² = 4

l - b = 4 --------- (3)

Adding equations (1) and (3), we get

l+b+l-b = 12 + 4

2l = 16

l = 8

Now, we put the value of l in equation(1) and we get

8 + b = 12

b =4

Hence, the dimensions of the piece are l = 8 and b =4.

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So the correct statement is A and D

What is a Quadrilateral?

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners.

The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides. 

These are the several kinds of quadrliaterals:

Quadrilateral A'B'C'D' = D8(ABCD) as we know two quadrilateral will be congruent in case of unit length scaling factor and corresponding side length corresponds like AB,BC,CD,DA

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