Write an
explicit formula for an, the nth term of the sequence 5, 15, 25, ....

Answer:

Step-by-step explanation:

An acute angle of a right-angled triangle is twice the other acute ongle find them​

the sum of the internal angles of a triangle is 180 °, take away the right angle (90 °) and divide by three, and you find one of the unknown angles, you multiply it by 2 and you find the other unknown angle

(180 - 90) : 3 = 30

30 * 2 = 60

----------------------

check

90 + 30 + 60 = 180°

the answer is good

Answer: y= 1x+1

Step-by-step explanation:

The slope- intercept form is y=mx+b.

m is the slope(rise over run) and b is the y-intercept.

With this knowledge and the graph, m is 2/2 or 1, and b is 1.

When receiving ammunition, unit personnel perform three tasks: ensuring items requested match item numbers on DA Form 3151-R, loading and securing the ammunition, and placarding the vehicle.

The first task performed by unit personnel when receiving ammunition is to ensure that the items requested match the item numbers on DA Form 3151-R. This form serves as a record of the types and quantities of ammunition being received. By comparing the requested items with the item numbers on the form, personnel ensure accuracy and prevent any discrepancies or errors in the delivery.

The second task involves the loading and securing of the ammunition. Unit personnel are responsible for safely and efficiently loading the ammunition onto the designated vehicle or storage area. This includes following proper handling procedures, using appropriate equipment, and adhering to safety protocols. The ammunition must be securely stored and arranged to prevent shifting or damage during transportation.

The final task is to placard the vehicle. Placarding involves visibly displaying the necessary warning signs or labels on the vehicle that indicate the presence of ammunition. This step is crucial for safety and compliance purposes, as it alerts other personnel and drivers to exercise caution when approaching or handling the vehicle. Clear and prominent placarding helps prevent accidents and ensures that everyone involved is aware of the potential hazards associated with transporting ammunition.

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In part (b) of the previous question, we found that the power series representation of the function $f(x)=\frac{x^2}{1+x^2}$ is:

 \(\lim_{n \to \infty} (-1)^{n} x^{2n}\)

To find the interval of convergence of this power series, we can use the ratio test. Let $a_n=(-1)^n x^{2n}$ be the general term of the series. Then, the ratio of consecutive terms is:

\(\left[\begin{array}{ccc}an+1/an\end{array}\right] = \left[\begin{array}{ccc}(-1)^{n+1} x^{2(n+1)} )/ (-1)^{n}x^{2n} \end{array}\right] = \left[\begin{array}{ccc}x^{2}\end{array}\right]\)

The series converges if the limit of the ratio as $n$ approaches infinity is less than 1, and diverges if the limit is greater than 1. Therefore, we have:

\(\lim_{n \to \infty} \left[\begin{array}{ccc}(a_{n}+1)/a_{n} \end{array}\right] = \left[\begin{array}{ccc}x^{2} \end{array}\right]\)

The series converges if $|x|^2<1$, and diverges if $|x|^2>1$. If $|x|^2=1$, the test is inconclusive and we need to use other convergence tests.

Therefore, the interval of convergence of the series is $-1<x<1$. To check the convergence at the endpoints $x=-1$ and $x=1$, we can use the alternating series test. At $x=-1$, the series becomes:

\(\lim_{n \to \infty} (-1)^{n}(-1)^{2n} = \lim_{n \to \infty} 1\)

which diverges. At $x=1$, the series becomes:

\(\lim_{n \to \infty} (-1)^{n}1^{2n} = \lim_{n \to \infty} (-1)^{n}\)

which also diverges. Therefore, the interval of convergence of the series is $-1<x<1$, and the series diverges at the endpoints.

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Answer:

y=3x+5

Step-by-step explanation:

first you find the slope by doing rise over run. then you would put the slope into point-slope formula which is y-y1=m(x-x1), then you simplify into y=mx+b  (slope intercept form). which gets you your final answer.

Let's consider the facts at hand:

Based on the diagram, triangles BCE and triangles DCF are similar

   ⇒ based on the Angle-Angle theorem

      ⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC

         ⇒ the two triangles are similar

Hope that helps!

Definitions of Theorem I used:

Answer:

$1,816.00

Step-by-step explanation:

636 + 636 + 544 = 1816

Helping in the name of Jesus.

Answer:

Harris, Ian, Gia, Jackson.

Step-by-step explanation:

                   Exercising Distance (miles)       Time (minutes)

Gia              2                                                  30

Harris          5                                                  50

Ian               3                                                  40

Jackson      4                                                  80

The easiest thing to do here would be to calculate how many miles each person can walk in 1 minute.

Gia takes 30 minutes to walk 2 miles. That means that her speed is 2/30, or 1/15, or 0.0667 miles per minute.

Harris takes 50 minutes to walk 5 miles. That means his speed is 5/50, or 1/10, or 0.1 miles per minute.

Ian takes 40 minutes to walk 3 miles. That means his speed is 3/40, or 0.075 miles per minute.

Jackson takes 80 minutes to walk 4 miles. His speed is 4/80, or 1/20, or 0.05 miles per minute.

From here, we can see that Jackson can walk the least miles per minute, since his rate is just 0.05 miles per minute. Next is Gia, who walks 0.0667 miles per minute. Then Ian, who walks 0.075 miles per minute, and finally Harris, who walks 0.1 miles per minute.

So, the order from fastest to slowest is Harris, Ian, Gia, Jackson.

Hope this helps!

The list of ranks the students from fastest walker to slowest walker is;

⇒ Harris, Lan, Gia, Jackson

What is Speed?

The speed of an object is defined as;

Speed = Distance / Time

Given that;

The four students in the table below each recorded the time and distance traveled while exercising.

               Exercising Distance(miles)            Time (minutes)

Gia                    2                                                 30

Harris                5                                                 50

Lan                    3                                                 40

Jackson             4                                                 80

Now,

Find the speed of all the students as;

For Gia;

Speed of Gia = Distance / Time

                    = 2 / 30

                    = 0.067 miles/minutes

For Harris;

Speed of Harris = Distance / Time

                        = 5 / 50

                        = 0.1 miles/minutes

For Lan;

Speed of Lan = Distance / Time

                    = 3 / 40

                    = 0.075 miles/minutes

For Jackson;

Speed of Jackson = Distance / Time

                            = 4 / 80

                            = 0.05 miles/minutes

Thus, The list of ranks the students from fastest walker to slowest walker is;

⇒ Harris, Lan, Gia, Jackson

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Because the P-value is greater than \(0.10\), there is not convincing evidence that more than 80% of adults are honest is the correct answer.

Based on the information provided, the standardized test statistic is given as \(2 = 0.71\) and the P-value is \(0.2389\). The significance level is 0.10.

In hypothesis testing, the P-value is compared to the significance level to make a conclusion. If the P-value is less than the significance level, it is considered statistically significant, and we reject the null hypothesis. On the other hand, if the P-value is greater than the significance level, we fail to reject the null hypothesis.

In this case, the P-value is greater than the significance level of 0.10. Therefore, we fail to reject the null hypothesis. The null hypothesis states that 80% of adults are honest. Since there is not convincing evidence to suggest that more than 80% of adults are honest, we cannot conclude that the data provide convincing evidence for this claim.

Therefore, the correct conclusion is: Because the P-value is greater than 0.10, there is not convincing evidence that more than 80% of adults are honest.

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Answer:

∠A≅∠Y        AB≅YX

∠B≅∠X          AC≅YZ

∠C≅∠Z         BC≅XZ

ΔACB ≅ ΔYZX

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

Answer:

i think you should get brainly tutor even if you cant afford it you can use the free trail to see if you like it they could help you with that give the answer and an explanation

Step-by-step explanation:

Answer:

yeah its correct

Step-by-step explanation:

Answer:

\(\boxed {\mathfrak {B) 1.6}}\)

Step-by-step explanation:

B) \(r-value\) \(cant\) \(be\) \(1.6\)

\(-1 \leq r\leq 1\)

\(-----\)

Answer:

Present-day cells evolved from a common prokaryotic ancestor along three lines of descent, giving rise to archaebacteria, eubacteria, and eukaryotes.

Changed the composition of the oceans. Most of the iron was precipitated out by early life.

Changed the composition of the atmosphere.  Oxygen became available in abundance.

Answer:

258.75

Step-by-step explanation:

5x5=25

25x4.5=112.5

112.5x2.3=258.75

Answer:

Step-by-step explanation:

Formula

Area = 1/2 (b1 + b2)*h

Givens

b1 = 5

b2 = 11.5

h = 4.5

Solution

Area = 1/2 (5 + 11.5)* 4.5

Area = 1/2 (16.5)*4.5

Area = 1/2 (74.25)

Area = 37.125

Every integer n ≥ 1 can be written in the form

\(n = cr · 3^r + cr-1 · 3^(r-1) + ... + c2 · 3^2 + c1 · 3 + c0\), where

cr = 1 or 2 and

ci = 0, 1, or 2 for all integers i = 0, 1, 2, ..., r - 1.

To prove that every integer n ≥ 1 can be written in the form:

\(n = cr · 3^r + cr-1 · 3^(r-1) + ... + c2 · 3^2 + c1 · 3 + c0,\)

where cr = 1 or 2 and ci = 0, 1, or 2 for all integers i = 0, 1, 2, ..., r - 1, we can use a constructive proof.

Start with the base case: For n = 1, we have n = 1 = 1 · 3^0, which satisfies the given form.

Assume the statement holds for all positive integers up to k.

Consider the integer k + 1.

Divide k + 1 by 3: If k + 1 is divisible by 3, then set cr = 1 and use the remaining quotient (k + 1) / 3 as the next value for k in the assumption. Repeat this process until the quotient becomes 1.

If k + 1 is not divisible by 3, set cr = 2 and use the remaining quotient (k + 1 - 1) / 3 as the next value for k in the assumption. Repeat this process until the quotient becomes 1.

At each step, we update the values of cr, and the resulting expression follows the given form.

By repeatedly applying this process, we eventually reach 1, and the final expression satisfies the specified form.

Therefore, by induction, every integer n ≥ 1 can be written in the specified form.

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Answer:

(-7, 3)

Step-by-step explanation:

-6-1=-7  2+1=3

The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.

To understand this ratio, let's break it down using different units:

A. 1/3 part bleach and 2/3 part water:

If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.

B. 2 cups of bleach and 3 cups of water:

If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.

C. 3 cups of bleach and 2 cups of water:

If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.

Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

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1. The probability that the sample proportion will be greater than 0.34 is approximately 0.0192.

2. The probability that the sample proportion will be between 0.196 and 0.354 is approximately 0.8801.

1. Probability that the sample proportion will be greater than 0.34:

The sample proportion can be modeled as a normal distribution.

mean = 0.25

standard deviation = √(p(1-p)/n),

where p is the population proportion and n is the sample size.

Calculating the standard deviation:

σ = √(0.25 * 0.75 / 75)

σ  ≈ 0.0433

The z-score will be:

z = (0.34 - 0.25) / 0.0433

z ≈ 2.08

Using a calculator, the probability of obtaining a z-score greater than 2.08 is approximately 0.0192, or 1.92%.

2. Probability that the sample proportion will be between 0.196 and 0.354:

The z-scores for the two values are:

z1 = (0.196 - 0.25) / 0.0433 ≈ -1.25

z2 = (0.354 - 0.25) / 0.0433 ≈ 2.17

Using a calculator, the probability of obtaining a z-score less than -1.25 is approximately 0.1056, and the probability of obtaining a z-score less than 2.17 is approximately 0.9857.

Therefore, the between these two z-scores will be:

Probability = 0.9857 - 0.1056 ≈ 0.8801

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Complete question:

Nobel Dylan has determined that 25% of all its MP3-songs sales are credit sales. A random sample of 75 sales is selected.

1. What is the probability that the sample proportion will be greater than 0.34?

2. What is the probability that the sample proportion will be between 0.196 and 0.354?

The upper-tail critical value for the χ2 test with 10 degrees of freedom for α=0.01 is 23.209.

Chi-square is a statistical analysis technique that compares observed data with expected data. It is calculated as the sum of the squared difference between observed and expected data divided by the expected data.

The chi-square distribution is a probability distribution that is frequently used in hypothesis testing. The degrees of freedom for a chi-square test are determined by the number of categories being compared.The upper-tail critical value for the χ2 test with 10 degrees of freedom for α=0.01 is given by the chi-square distribution table as 23.209. The upper-tail critical value is the value that defines the boundary between the critical region and the noncritical region.

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Step-by-step explanation:

a negative exponent always means 1/...

so, e.g. 6^-2 means 1/(6²).

so,

\( {w}^{6} \times {w}^{ - 4} \)

= w⁶/w⁴

that means that if w⁶w⁴ is already prefilled, we need to counteract the w⁴ in the numerator of the fraction.

it would have to be then w⁶w⁴/w⁸

because we need to end up with w⁴ in the denominator (bottom part). and the only way we can do that, if we need to keep w⁴ in the numerator (top) part, is to put these w⁴ multiplied by another w⁴ (4+4 = 8, as multiplied exponents are added).

that would give us the expanded form of

w×w×w×w×w×w×w×w×w×w

---------------------------------------

w×w×w×w×w×w×w×w

and the simplified form

w²/1

\( {10}^{ - 3} \times {10}^{5} \)

gives us the same problem.

it is actually 10⁵/10³

but if 10³10⁵ is already predefined, then we must use the same trick as before. we must end up with 10³ in the denominator, so to compensate for the 10³ in the numerator, we must extra multiply this into the denominator :

10³10⁵/(10³10³) = 10³10⁵/10⁶

the expanded form of this would be

10×10×10×10×10×10×10×10

------------------------------------

10×10×10×10×10×10

with the simplified form

10²/1

and again similar with

\( {10x}^{3} \times {(10x)}^{ - 2} \)

which is actually

10x³/(10x)² = 10x³/100x²

again, if 10x³×(10x)² is predefined in the numerator, we need to compensate in the denominator for these extra (10x)².

so, we need then to put

10x³(10x)²/((10x)²(10x)²) = 10x³(10x)²/(10x)⁴

the expanded form would then be

10×x×x×x×10×x×10×x

-----------------------------

10×x×10×x×10×x×10×x

and the simplified form would be

x/10

if these entries (as seen in the picture) in the "make exponent positive" column are from you and not predefined by your teacher, then we use the example of the first line.

and then we have as indicated

w⁶/w⁴

wwwwww / wwww

w²/1

10⁵/10³

10×10×10×10×10 / 10×10×10

10²/1

10x³/(10x)²

10×x×x×x / 10×x×10×x

x/10

For the given lottery daily game, total number of choices player have to pick for three numbers from 0 to 9 where order does not matter is equal to 120.

As given in the question,

Total number have to pick by a player in a lottery daily game is equal to 3

Numbers  from which player have to pick the three numbers is 0 to 9

Total numbers from which player have to pick the three numbers = 10

Given condition : Order of the number does not matter

Total number of choices to pick three numbers from 0 to 9

= ¹⁰C₃

= ( 10! ) / ( 10 - 3 )! (3!)

= 10! / 7! 3!

= ( 10 × 9 × 8 × 7! ) / ( 7!) ( 3 × 2 × 1 )

= 10 × 3 × 4

=120 choices

Therefore, for the given lottery daily game, total number of choices player have to pick for three numbers from 0 to 9 where order does not matter is equal to 120.

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Answer:

12 R cm

Step-by-step explanation:

The power series representation of **sec(x)tan(x)** may have a limited radius of convergence based on the convergence of the power series for **sec(x)** and **tan(x)** individually

To find a power series representation for **sec(x)tan(x)**, we can use the given power series representation for **sec(x)** and the power series representation for **tan(x)**.

Given:

**sec(x) = 1 + 2x^2 + 24/5 x^4 + 7206/35 x^6 + 80642/63 x^8 + ...**

**tan(x) = x + 1/3 x^3 + 2/15 x^5 + 17/315 x^7 + ...**

To find the power series representation for **sec(x)tan(x)**, we will multiply the two power series term by term.

The first term of the resulting power series will be the product of the first terms of **sec(x)** and **tan(x)**, which is **(1)(x) = x**.

The second term will be the product of the second terms, which is **(2x^2)(1/3 x^3) = 2/3 x^5**.

The third term will be the product of the third terms, which is **(24/5 x^4)(2/15 x^5) = 8/25 x^9**.

Continuing this process, we can find the power series representation for **sec(x)tan(x)** as:

**sec(x)tan(x) = x + 2/3 x^5 + 8/25 x^9 + ...**

The power series continues with terms of increasing powers of **x**, where the coefficients are determined by multiplying the corresponding coefficients from the power series of **sec(x)** and **tan(x)**.

It's important to note that the power series representation of **sec(x)tan(x)** may have a limited radius of convergence based on the convergence of the power series for **sec(x)** and **tan(x)** individually.

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Answer:

40 miles per hour

Step-by-step explanation:

Driver a could be going 50 miles per hour

Driver c could be going 30 miles per hour

40 miles per hour is in the middle so that could be your answer

Answer:

jjjjjjjjjjhhhhhhhjjjjjjhhhhhh

Answer:

x = 8

Step-by-step explanation:

The measure of an arc is equal to the angle at the centre subtended by the arc.

The sum of the 3 arcs = 180° , then

5x + 6 + 83 + 51 = 180

5x + 140 = 180 ( subtract 140 from both sides )

5x = 40 ( divide both sides by 5 )

x = 8

Answer:

1. real number, irrational number

2. rational number, real number

Based on the provided information, the number of subjects examined is not explicitly mentioned. However, the given t-value (t(29) = 2.001) suggests that the study involved a sample size of 30 participants, as denoted by the degrees of freedom (df) in parentheses.

The notation t(29) = 2.001 represents a t-test, a statistical test used to determine if there is a significant difference between the means of two groups. In this case, the subscript "29" in t(29) denotes the degrees of freedom (df), which is calculated by subtracting 1 from the sample size. Therefore, df = 30 - 1 = 29.

Since the degrees of freedom are 29, it indicates that the sample size used in the study was 30 participants. The t-value of 2.001 represents the magnitude of the t-statistic, which measures the difference between the means of the two groups being compared.

The critical value for significance is not provided, but the statement "p < 0.05" suggests that the obtained p-value is less than 0.05, indicating statistical significance. However, the exact p-value is not given, so the level of significance cannot be precisely determined.

Overall, the information provided implies that the study involved a sample of 30 subjects, and the t-value and p-value suggest a significant result.

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Step-by-step explanation:

A triangle has an area of 30cm². The base and height are scaled by a factor of 3. What is the area of the resulting triangle? _cm²

Answer:

Zeke is 45.35 inches tall

Step-by-step explanation:

To find out how tall Zeke is, you must subtract 4.3 from 49.65 (Shorter means less - so subtraction)

49.65 - 4.3 = 45.35 inches tall

Answer:

45.35

Step-by-step explanation: