13 Here are the first three terms of a sequence. 26 20 32 Find the first two terms in the sequence that are less than zero.​

The interest earned by Peter after 42 months is $1,335.60 and the total amount in his account is $9,125.60.

The formula for compound interest is expressed as;

A = P(1 + r/n)^nt

Where A is accrued amount, P is principal, r is interest rate, n is compound, and t is time period.

Given the data in the question;

First, convert the interest rate to decimal.

Rate r = 4 5/8% = (4×8 + 5 )/8%

Rate r = 37/8%

Rate r = 4.625%

Rate r = 4.625/100 = 0.04625 per pear

Next, convert time from months to years

Time t = 42 month = ( 42/12 )years

Time t = 3.5 years

To determine the accrued amount, plug the given values into the compound interest formula and solve for A.

A = P(1 + r/n)^nt

A = $7,790(1 + 0.04625/1)^( 1 × 3.5 )

A = $7,790(1 + 0.04625 )^( 3.5 )

A = $7,790(1.04625 )^( 3.5 )

Accrued amount A = $9,125.60

Note that; Accrued amount A = Principal P + Interest I

Hence;

Interest I = A - P

Interest = $9,125.60 - $7,790

Interest = $1,335.60

Amount in the account after 42 months is the same as the accrued amount A, this is $9,125.60.

Therefore, the interest earned is $1,335.60 and the accrued amount is $9,125.60.

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The derivative dz/dt can be found using the chain rule. By differentiating each term with respect to t and applying the chain rule, we can calculate dz/dt as follows:

\(dz/dt = 2sin(t)cos(t) + 4e^tcos(t) + 4e^tsin(t) + 4e^t + 4sin(t)e^t.\)

By applying the chain rule, we can find dz/dt as follows: differentiate z with respect to x, then multiply it by dx/dt, and finally differentiate z with respect to y and multiply it by dy/dt.

The function z = x² + y² + xy can be rewritten as z = (sin(t))² + (4e^t)² + (sin(t))\((4e^t)\).

To find dz/dt, we need to find the partial derivatives of z with respect to x and y and multiply them by dx/dt and dy/dt, respectively.

The partial derivative of z with respect to x is (2x + y), and the partial derivative of z with respect to y is (2y + x).

Next, we differentiate x = sin(t) with respect to t, giving us dx/dt = cos(t).

Similarly, differentiating\(y = 4e^t\) with respect to t yields \(dy/dt = 4e^t.\)

Now we can apply the chain rule:

dz/dt = (2x + y) * dx/dt + (2y + x) * dy/dt

Substituting the expressions for x, y, dx/dt, and dy/dt:

\(dz/dt = (2sin(t) + 4e^t) * cos(t) + (2(4e^t) + sin(t)) * (4e^t)\)

Simplifying this expression will yield the final result.

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Answer: HL

Step-by-step explanation:

It tells you the triangle is a right triangle and it tells you that the hypotenuse of both triangles are congruent.

Answer:

it is 80⁰

Step-by-step explanation:

cuz the it vertical angle

and to find a just get

180-80-70

Answer:

See below for answers

Step-by-step explanation:

300° is in Quadrant IV, so its reference angle is 360°-300°=60°

225° is in Quadrant III, so its reference angle is 225°-180°=45°

480°=120° is in Quadrant II, so its reference angle is 180°-120°=60°

-210°=150° is in Quadrant II, so its reference angle is 180°-150°=30°

Answer: +1k

Step-by-step explanation: In order for you to be able to add two terms together, the terms need to be exactly the same except for the coefficients.

Here, since both terms contain a k, we can add them together.

So -6k + 7k simplifies to +1k.

Note that if you had said k,

that's also an acceptable answer.

Answer:

let x represent the time it took Caroline to complete the puzzle .

let 3x represent the time it took Felix to complete the puzzle.

let 0.25x represent the time it took Graham to complete the puzzle

the the ratio of their time would be

x:3x:0.25x

The ratio of their time is 4 :12 : 1.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

let the time taken by Caroline be x.

So, the time taken by Graham is x/4.

and, the time taken by Felix is 3x.

So, the ratio of time

Caroline time: Felix time: Graham time

= x: 3x : x/4

= 1 : 3 : 1/4

= 4 : 12 : 1.

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The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

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Answer:

3

Step-by-step explanation:

27=3^3

=3*3*3

27=27

i think it is clear &i hope it helps you

Answer:

y = -1/4 x+11/16

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = -1/4x+b

Substitute the point in for x and y

1 = -1/4(-5/4) +b

1 = 5/16 +b

16/16 = 5/16 +b

Subtract 5/16 from each side

11/16 = b

y = -1/4 x+11/16

Answer:

y = - \(\frac{1}{4}\) x + \(\frac{11}{16}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - \(\frac{1}{4}\) , then

y = - \(\frac{1}{4}\) x + c ← is the partial equation

To find c substitute ( - \(\frac{5}{4}\), 1 ) into the partial equation

1 = \(\frac{5}{16}\) + c ⇒ c = 1 - \(\frac{5}{16}\) = \(\frac{11}{16}\)

y = - \(\frac{1}{4}\) x + \(\frac{11}{16}\)

Answer:

Noah types faster because he can type more words per minute.

Step-by-step explanation:

For Andre you would divide 208 words by 4 minutes getting 52 words per minute. Then, for Noah divide 342 words by 6 minutes getting 57 words per minute.

Answer:

Step-by-step explanation:

Given vertices of triangle:

The centroid is found as the average of x- and y- coordinates of three vertices:

Substitute the coordinates into formula:

Correct choice is B

Answer:

B. (3, 2)

Step-by-step explanation:

Because it is the "Correct Answer"

The sample mean is significantly different from the population mean. The confidence level used was 95%.

To build a confidence interval to decide whether this example mean is fundamentally not the same as the populace mean, there are a few stages that should be taken.

To begin with, work out the standard error of the mean (SEM) for the example, which is the standard deviation separated by the square base of the example size (SEM = σ/√n). For this situation, the SEM is 3/5 = 0.6 mcg/dL.

Then, compute the critical value for the confidence interval picked by increasing the SEM by the t-esteem from the t-dissemination for the given confidence interval. For instance, in the event that a 95% confidence interval is picked, the t-esteem is 1.96. This provides us with a basic worth of 0.6 x 1.96 = 1.176 mcg/dL.

At last, build the certainty span utilizing the example mean and the basic worth. The certainty span is (15 - 1.176, 15 + 1.176), or (13.824, 16.176). This implies that we are 95% sure that the genuine populace mean exists in this reach.

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The triangle ABC must have an inradius of 2 units, following the given measure of sides.

To find the inradius of a triangle, you can use the formula:\(Inradius(r)= \dfrac{Area(\triangle abc)}{Semiperimeter(\triangle abc)}\)

Where the semi-perimeter of the triangle (s) is half of the sum of its side lengths, and the area of the triangle is given by Heron's formula:
\(Area=\sqrt{s(s-a)(s-b)(s-c)}\)

Given that the side lengths of △ABC are 6, 8, and 10, we can calculate the inradius as follows:

Calculate the semiperimeter s:
s= [6 + 8 + 10 ]/2
s = 12

Calculate the area triangle ABC:
\(Area=\sqrt{12(12-6)(12-8)(12-10)}\\Area=24\)

Calculate the inradius r:
\(r=32/12\\r=2\)

Therefore, the triangle ABC must have an inradius of 2 units,

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The inradius of triangle ABC is 2 units.

We have,

To find the inradius (r) of a triangle with side lengths a, b, and c, you can use the formula:

r = (A / s)

where A is the area of the triangle, and s is the semi-perimeter of the triangle given by:

s = (a + b + c) / 2

The semi-perimeter (s) of triangle ABC:

s = (6 + 8 + 10) / 2

s = 24 / 2

s = 12

The area (A) of triangle ABC using Heron's formula:

A = √(s * (s - a) * (s - b) * (s - c))

where a, b, and c are the side lengths of the triangle:

A = √(12 * (12 - 6) * (12 - 8) * (12 - 10))

A = √(12 * 6 * 4 * 2)

A = √(576)

A = 24

Now,

r = A / s

r = 24 / 12

r = 2

Thus,

The inradius of triangle ABC is 2 units.

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Answer: 9

Hope this helps

Answer:

9

Step-by-step explanation:

The solution of the mathematical statement is 102.5

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

"What is -5/2 times -41"

This means that

-5/2 times -41

Express as numbers

So, we have

-5/2 * -41

Divide 5 by 2

So, we have

-2.5 * -41

Evaluate the product

102.5

Hence, the result is 102.5

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There is 17.5 inches distance between the tee and the hole on the model.

According to the question we have been given that

length of hole#9 is = 175 yards

the scale for the model is given as = 2 inch : 20yards

We need to find the inches between the tee and the hole.

Let the length between the tee and the hole on the model be x inches

Thus the above condition can be written as

               2 inches / 20yards = x inches/175 yards

We have to solve this proportion for x we get

                       x inches = 175*2/20

                            x = 17.5 inches

Hence there is 17.5 inches distance between the tee and the hole on the model.

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Answer:

A

Step-by-step explanation:

A

The number of sides for a regular polygon that will not form a regular tessellation is 7. The correct option is C.

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

A tessellation or tiling is the seamless covering of a surface, frequently a plane, with one or more geometric shapes, known as tiles. One regular polygon can be used to create a single regular tessellation. Two or more regular polygons are used in a semi-regular tessellation.

Triangles, squares, and hexagons are the only three regular tessellations.

Now, the name of the polygon having 3, 4, and 6 sides is triangle, square, and Hexagon. Therefore, the only regular polygon that will not form a regular tessellation is heptagon, which has 7 sides.

Hence, the number of sides for a regular polygon that will not form a regular tessellation is 7.

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Answer:

4

Step-by-step explanation:

the answer is 4

x=2 and the hypotonouse is equal to 2x

Answer: if ur looking for an equation then y = -4 + 6

Step-by-step explanation:

Since the y intercept is 6 and it’s going 4 units down and 1 to the left

First you will get 4dz

Answer:

193 minutes

Step-by-step explanation:

We know

Boris paid an $8 fee to start the scooter plus 6 cents per minute of the ride.

Let y represent the total cost and x represent the number of minutes we have the equation

y = 0.06x + 8

Now, put $19.58 in for y and solve

19.58 = 0.06x + 8

11.58 = 0.06x

x = 193 minutes

So, Boris rides the scooter for 193 minutes.

Step-by-step explanation:

As the speed increases the time required to travel a distance is lessened.

 say you have to go 100 km

     if you go 20 km /hr it will take 5 hr....butif you increase your speed

( x axis) to 50 km/ hr it will take less time ....ony 2 hours    so the graph A is most representative       (look at the positive portion of the graph of

                                                   y = 100/x  )

The correct option  is option C: ∣s−82∣<4, which describes all possible values of s.

The correct option  is option C: ∣s−82∣<4, which describes all possible values of s

Option A (∣s - 82∣ = 4) would indicate that all the scores are exactly 4 units away from 82, which is not the case as some scores could be less than 82 or greater than 86.

Option B (∣s + 82∣ = 4) would indicate that all the scores are exactly 4 units away from -82, which is not relevant to the given situation.

Option C (∣s - 82∣ < 4) correctly indicates that the scores can vary within a range that is less than 4 units away from 82. This range includes scores between 78 and 86, as mentioned in the question.

Option D (∣s + 82∣ < 4) would indicate that all the scores are exactly less than 4 units away from -82, which is not relevant to the given situation.

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Answer:

You're right...

Step-by-step explanation:

(4-5)-(13-18+2)

(-1)-(-3)

-1+3

2

To determine how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis, we need to first establish a hypothesis test. A hypothesis test is a statistical procedure that helps us determine if there is enough evidence to support a particular hypothesis.

In a hypothesis test, we start with a null hypothesis (H0) which is a statement that there is no significant difference between two groups or variables. The alternative hypothesis (Ha) is the statement that there is a significant difference between the two groups or variables.

Once we have established our null and alternative hypotheses, we need to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The test statistic is the numerical value that we obtain from our statistical test, which we compare to a critical value to determine if we can reject the null hypothesis.

The critical value is determined by the level of significance (α) we have chosen for our test, which is the probability of making a type I error (rejecting the null hypothesis when it is actually true). Typically, the level of significance is set at 0.05 or 0.01.

So, to answer the question, how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis depends on the level of significance we have chosen, as well as the degrees of freedom and distribution of the test statistic. The critical value for a given level of significance and degrees of freedom can be found in statistical tables or calculated using software. If the test statistic is larger than the critical value, we can reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

x-2y+5=0

Step-by-step explanation:

y+1= \(\frac{x+7}{2}\)

y=\(\frac{x+7}{2}\) -1

y=\(\frac{x+7-2}{2}\)

y=\(\frac{x+5}{2}\)

2y=x+5

x-2y+5=0

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-1)=\dfrac{1}{2} (x-(-7)}\)

Simplify

\(\rm{y+1=\dfrac{1}{2}(x+7)}\)

Answer:

  see attached

Step-by-step explanation:

You want to use q=4 to show q×q³ = q⁴.

The attachment shows your calculator can help with this. It will compute and display the powers of values without requiring the intermediate calculations.

  4 × 4³ = 4 × 64 = 256

 4⁴ = 256 . . . . . . equivalent to 4 × 4³

An exponent signifies repeated multiplication in the same way a coefficient signifies repeated addition.

  4 × 4³ = 4 × (4·4·4) = 4·4·4·4 . . . . . using the associative property of multiplication

  4⁴ = 4·4·4·4 . . . . . . . equivalent to 4 × 4³

__

Additional comment

In literal terms, ...

  q×q³ = q·q·q·q = q⁴