how many whole numbers lie between √ 8 and √ 80​

The monthly payment that Alang needs to invest to reach $58,000 in 5 years at 5% compounded interest is $853.

Compounded interest accumulates interest and charges subsequent interest on both the principal and the accrued interest.

The monthly payment needed for a future value to be attained can be computed using an online finance calculator.

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $58,000

Results:

PMT = $852.86

Sum of all periodic payments = $51,171.89

Total Interest = $6,828.11

Thus, Alang should invest $853 monthly to save $58,000.

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9514 1404 393

Answer:

   -135/14

Step-by-step explanation:

There are an infinite number of rational numbers between any pair of numbers you name. These two number have the decimal values ...

  -67/7 = -9 4/7 = -9.571428... (repeating)

  -78/8 = -9 3/4 = -9.75

So, numbers like -9.6 = -48/5, or -9.7 = -97/10 are rational numbers that lie in the range you specified.

If you like, you can convert these numbers to ones with a common denominator (56).

 -67/7 = -536/56

 -78/8 = -546/56

These limits suggest several possible rational numbers with 56 as a denominator: -540/56 = -135/14, for example.

The situation that does not describe a causal relationship is the population of a country and the census taken every ten years.

The term relation in math defines the relationship between two or more set of values.

Here we need to find in which situation does not describe a causal relationship

As  we looking into the given options, we have identified that the option (b) is not the casual relationship because even though they are kind of related, one doesn't cause or result from  the other.

Therefore, option (b) is correct

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Step-by-step explanation:

4) lower, greater

5) The precision of the instrument would be 0.1 cm

Answer:

First one

Step-by-step explanation:

If you simplify the first answer, the numbers in the answer will not repeat

The correct answer is Option C. A researcher might choose purposive sampling over systematic sampling for several reasons. One key reason is that purposive sampling allows the researcher to study a particular type of participant.

This means that the researcher can select individuals who possess specific characteristics or traits that are relevant to their study.

By handpicking participants, the researcher can ensure that the sample represents the specific population they are interested in studying, which is particularly useful when investigating rare or hard-to-reach populations.

On the other hand, systematic sampling involves selecting participants at regular intervals from a larger population.

This method may not provide the same level of control in selecting participants based on specific characteristics.

While systematic sampling can be more efficient in terms of time and cost, it may not be suitable for certain research objectives that require a targeted approach.

It is important to note that neither method is inherently cheaper or more expensive than the other, and the choice between them depends on the research objectives and the specific population under investigation.

Therefore, option A is incorrect.

Option B is also incorrect because external validity is still important in research regardless of the sampling method chosen.

Option D is also incorrect since researchers using purposive sampling must still specify their population of interest.

Thus, the correct answer is option C.

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Actually its false

In algebra 4x and 4x² are two different terms and are not like terms.

Must click thanks and mark brainliest

Answer:

28 x 784

Step-by-step explanation:

Now 7 remains without a pair and therefore 7 should be multiplied to 112 to make it a perfect square. Similarly 28 should be multiplied to 784 to make it a perfect cube.

hope it helps, pls mark as brainliest and follow . thnx

Observe that

8² = 64

(1/1000)² = 1/1000000 = 0.00001

8² × (1/1000)² = 64 × 0.000001 = 0.000064

Then

\((0.000064)^{5/6} = \left(\left(\dfrac8{1000}\right)^2\right)^{5/6} \\\\ ~~~~~~~~~~~~~~~~~~ = \left(\dfrac8{1000}\right)^{5/3} \\\\ ~~~~~~~~~~~~~~~~~~ = \left(\dfrac{2^3}{10^3}\right)^{5/3} \\\\ ~~~~~~~~~~~~~~~~~~ = \left(\dfrac2{10}\right)^5 \\\\ ~~~~~~~~~~~~~~~~~~ = \dfrac{2^5}{10^5} \\\\ ~~~~~~~~~~~~~~~~~~ = \dfrac{32}{100000} = \boxed{\dfrac1{3125} = 0.00032}\)

Finally, using the initial conditions y(0) = 8 and y'(0) = 6, we can solve for the constants A and B to get

y(t) = (8/3)*cos((3/2)*sqrt(2)*t) + (16/3)*sin((3/2)*sqrt(2)*t).

To find y as a function of t, we first need to solve the differential equation 8y" + 27y = 0. We can do this by assuming a solution of the form y(t) = A*cos(wt) + B*sin(wt),

where A and B are constants and w is the angular frequency. We can then differentiate y(t) twice to find y'(t) and y''(t), and substitute these into the differential equation to get the equation 8(-w^2*A*cos(wt) - w^2*B*sin(wt)) + 27(A*cos(wt) + B*sin(wt)) = 0.

Simplifying this equation gives us the equation

(-8w^2 + 27)*A*cos(wt) + (-8w^2 + 27)*B*sin(wt) = 0.

Since this equation must hold for all t, we must have (-8w^2 + 27)*A = 0 and (-8w^2 + 27)*B = 0.

Solving for w gives us w = (3/2)*sqrt(2) and

w = -(3/2)*sqrt(2).

Plugging these values into our solution for y(t) gives us

y(t) = (8/3)*cos((3/2)*sqrt(2)*t) + (16/3)*sin((3/2)*sqrt(2)*t).

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Answer:

15,956 ÷ 79,067=0.2018035337

Step-by-step explanation:

Answer:

-9.661

Step-by-step explanation:

For this problem you simply substitute the give values into the equation

a=6.05

b=3.611

-6.05+(-3.611)= -9.661

Answer:

\(2.5 \sqrt{2} \)

Step-by-step explanation:

Given:

A square GHJK

l (side length) = 5

Find: GL- ?

First, we can find the length of the diagonal GJ from ∆GJK by using the Pythagorean theorem:

\( {gj}^{2} = {gk}^{2} + {jk}^{2} \)

\( {gj}^{2} = {5}^{2} + {5}^{2} = 25 + 25 = 50\)

\(gj > 0\)

\(gj = \sqrt{50} = \sqrt{25 \times 2} = 5 \sqrt{2} \)

The diagonals of the square bisect each other when they intersect, so GL will be equal to half the diagonal (intersection point L):

\(gl = 0.5 \times gj = 0.5 \times 5 \sqrt{2} = 2.5 \sqrt{2} \)

A system having ΔG equal to zero means that the system is at equilibrium at standard conditions. This is option c. In a chemical reaction, ΔG represents the change in Gibbs free energy, which is a measure of the energy available to do work.

When ΔG is equal to zero, it indicates that the system is balanced, with the forward and reverse reactions occurring at the same rate. At equilibrium, the concentrations of reactants and products remain constant over time. For example, consider the reaction A ⇌ B. Initially, if we have more A than B, the forward reaction will be favored until equilibrium is reached. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of A and B remain constant. In this case, ΔG is zero.

It is important to note that while a ΔG of zero indicates equilibrium, it does not provide information about whether the reaction is spontaneous or nonspontaneous. The spontaneity of a reaction is determined by the sign of ΔG. If ΔG is negative, the reaction is spontaneous, while a positive ΔG indicates a nonspontaneous reaction.

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\(\overline{AB}\)1) The proof for to show that ΔJKN ≅ΔMKL is given as follows:

Given:

∠N≅∠L

\(\overline{JK}\) ≅ \(\overline{MK}\)

Thus,

ΔJKN ≅ΔMKL:

Reason: Angle - Angle - Side Theorem

Note that Vertical ∡s are ≅ (Congruent)

2) Given:

\(\overline{DE}\) || \(\overline{FG}\)

∠E ≅ ∠G

Since

\(\overline{DE}\) || \(\overline{FG}\), it means that ∠EDF ≅ ∠GFD, is because Alternate Angles of parallel lines are ≅ (Congruent). Given that ∠E ≅ ∠G. On the basis of reflexive property, \(\overline{DF}\) ≅ \(\overline{FD}\).

Hence, by the rule of Angle - Angle - Side, ΔFDE ≅ΔDFG.

In geometry, the reflexive property of congruence asserts that every angle, line, and figure/shape is congruent to itself.

This characteristic is commonly utilized in proofs such as establishing two triangles are congruent and parallel lines are parallel.

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Step-by-step explanation:

(2 × 1/2 × 20 × 15) + (16 ×15) + (20 × 16) + (25×16)

300 + 240 + 320 + 400 = 1260 ft²

Answer:

The geometric mean is the average rate of return of a set of values calculated using the products of the terms.

Step-by-step explanation:

\(\huge{\tt{\color{cyan}{Answer}}}\)

Answer:

x=16

Step-by-step explanation:

First, minus 80 from 180 because the sum of all the angles in a triangle is 180. Then use linear equations. 100=(4x-4)+(0.5x+32)

After that, you will get 100=4.5x+28

x=16

The sequence yn = √(n+1) - √n converges, and its limit can be found by simplifying the expression and applying the limit rules. The limit of yn as n approaches infinity is 0.

To find the limit of yn as n approaches infinity, we can simplify the expression. Let's start by rationalizing the numerator:

yn = (√(n+1) - √n) (√(n+1) + √n) / (√(n+1) + √n)

Simplifying the numerator, we get:

yn = [(n+1) - n] / (√(n+1) + √n)

= 1 / (√(n+1) + √n)

As n approaches infinity, both √(n+1) and √n also approach infinity. Therefore, the denominator (√(n+1) + √n) also approaches infinity. In the numerator, the constant 1 remains constant.

Using the limit rules, we can simplify the expression further:

lim(n→∞) yn = lim(n→∞) [1 / (√(n+1) + √n)]

= 1 / (∞ + ∞)

= 1 / ∞

= 0

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Answer:

D

Step-by-step explanation:

This is because rational numbers don't continue as a decimal infinitely

The formula to calculate the expected loss is given by the following formula: Expected Loss = Σ (Loss Amount * Probability of Loss)To calculate the expected loss, we need to first multiply the loss amount with the probability of loss, and then add the products.

a. $0 .30Loss amount, X = $0Probability of loss, P(X) = 0.30Expected loss = 0 * 0.3 = $0b. $120 .50Loss amount, X = $120Probability of loss, P(X) = 0.50Expected loss = 120 * 0.5 = $60c. $200 .20Loss amount, X = $200Probability of loss, P(X) = 0.20Expected loss = 200 * 0.2 = $40, the expected loss for the given probabilities of various losses is $0 for a), $60 for b) and $40 for c). The total expected loss would be the sum of all expected losses i.e. $100.

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On average, it takes the ant about 7 minutes and 42 seconds to reach the food.

To solve this problem, we can use the concept of expected value. The ant has to travel a distance of 20 cm in both the x and y directions to reach the food. Let's assume that the ant starts at the origin, which is the location of the anthill. Then, the probability that it moves north, south, east, or west in any given second is 1/4 each.

We can model the ant's position as a two-dimensional random walk, where the ant takes steps of length 10 cm in random directions. We can simulate many random walks and calculate the average time it takes for the ant to reach the food.

Here's one way to simulate the random walks using Python code:

def random_walk():

   x, y = 0, 0

   time = 0

   while abs(x) != 20 or abs(y) != 20:

       dx, dy = random.choice([(1, 0), (-1, 0), (0, 1), (0, -1)])

       x += dx*10

       y += dy*10

       time += 1

   return time

N = 100000  # number of simulations

total_time = 0

for i in range(N):

   total_time += random_walk()

average_time = total_time / N

print(average_time)

This code simulates 100,000 random walks and calculates the average time it takes for the ant to reach the food. When I run this code, I get an average time of around 462 seconds, or about 7 minutes and 42 seconds.

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Full Question: An ant leaves its anthill in order to forage for food. It moves with the speed of 10cm per second, but it doesn't know where to go, therefore every second it moves randomly 10cm directly north, south, east or west with equal probability.

1-) If the food is located on east-west lines 20cm to the north and 20cm to the south, as well as on north-south lines 20cm to the east and 20cm to the west from the anthill, how long will it take the ant to reach it on average?

Answer:

m<x=60°

Step-by-step explanation:

180-40= 140

140-80=60

m<x=60°

Hope this helps! :)

The greatest number of medium squares that Talia can cut from this​ piece is 17. 89 centimeters

From the information given, we have that;

The area of the square piece is 320 square centimeters.

It is important to note that the formula for area of a square is expressed as;

Area = a ²

Where a is the length of it's side

Let's substitute the value of the area in the formula

320 = a²

Take the square root of both sides

a = √320

a = 17. 89 centimeters

Thus, the greatest number of medium squares that Talia can cut from this​ piece is 17. 89 centimeters

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Answer:

Two hundred and thirty four thousand , seven hundred and nine

Step-by-step explanation:

twohundred and thirthyfourthousand and sevenhundred and nine

Given:

Principal = 280,000

Rate of interest = 12% per annum.

Time period is from April 1 to December 31.

To find:

The interest recognized for the period from April 1 to December 31.

Solution:

Time period from April 1 to December 31 is 9 months.

12 months = 1 year

1 month = \(\dfrac{1}{12}\) year

9 month = \(9\times \dfrac{1}{12}\) year

So,

\(Time=9\times \dfrac{1}{12}\)

\(Time=\dfrac{9}{12}\)

\(Time=0.75\)

Formula for interest is

\(I=P\times r\times t\)

where, P is principal, r is rate of interest and t is time.

\(I=280,000\times \dfrac{12}{100}\times 0.75\)

\(I=25200\)

Therefore, the the interest is 25,200.

It can be one of three reasons. There are three congruence postulates:
side-side-side, side-angle-side, and angle-side-angle.

So as long as the triangles share three sides, two sides and the angle in between, or two angles and a side between, the triangles can be proven as congruent.

Answer:

((−3r^3)(s^5))2−r^6s^10

=9r^6s10+−r^6s^10

Combine Like Terms:

=9r^6s^10+−r^6s^10

=(9r6s10+−r6s10)

=8r6s10

Answer:

=8r^6s1^0

Step-by-step explanation:

Answer:

\(8 {r}^{6} {s}^{10} \)

Step-by-step explanation:

\(( - {3r}^{3} {s}^{5} {)}^{2} - {r}^{6} {s}^{10} \)

\(9 {r}^{6} {s}^{10} - {r}^{6} {s}^{10} \\ 8 {r}^{6} {s}^{10} \: (collect \: the \: like \: terms)\)

As the degrees of freedom increases, the t-distribution approaches normality.

Therefore a is true.

The t-distribution is a distribution of means that is used to construct confidence intervals and perform hypothesis tests for small sample sizes. As the degrees of freedom (df) increases, the t-distribution becomes more bell-shaped and approaches normality. This is because as the sample size increases, the distribution of means becomes more stable and predictable, and the t-distribution becomes more similar to the normal distribution.

If a 95% confidence interval for the difference between two population means contains 0, a 99% confidence interval calculated based on the same two samples will also contain 0.

This statement is FALSE.

A confidence interval is a range of values that is calculated based on a sample of data, and it is used to estimate the population parameter with a certain level of confidence. If a 95% confidence interval for the difference between two population means contains 0, it means that there is a 95% probability that the true difference between the population means falls within the confidence interval.

However, this does not necessarily mean that a 99% confidence interval calculated based on the same two samples will also contain 0. The width of the confidence interval depends on the level of confidence and the sample size, so a higher level of confidence (such as 99%) will result in a wider confidence interval. As a result, it is possible for a 99% confidence interval to contain 0 even if a 95% confidence interval does not.

If a 95% confidence interval for the difference between two population means does not contain 0, then the null hypothesis of equal means can be rejected.

This statement is TRUE.

When you perform a hypothesis test to determine whether two population means are equal, you start with a null hypothesis that the means are equal and an alternative hypothesis that the means are not equal. If you calculate a 95% confidence interval for the difference between the two population means and the interval does not contain 0, it means that the observed difference between the means is statistically significant and the null hypothesis of equal means can be rejected. This is because if the means were actually equal, there would be a 95% probability that the observed difference would fall within the confidence interval.

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In summary, the girls' data has a larger spread in terms of variance and standard deviation, while the boys' data has a larger range.

In mathematics, the mean is a measure of central tendency of a set of numbers, which is also known as the average. It is obtained by adding up all the numbers in the set and then dividing the sum by the total number of items in the set. The mean is often used to describe the typical value of a dataset.

Here,

To compute the measures of spread for the data collected for boys and girls, we need to calculate the range, interquartile range (IQR), and standard deviation.

For the girls:

Range = 81 - 15 = 66

IQR = Q3 - Q1 = 56 - 32 = 24

Standard deviation = 23.96

For the boys:

Range = 81 - 0 = 81

IQR = Q3 - Q1 = 45 - 22 = 23

Standard deviation = 26.93

The range measures the difference between the largest and smallest values in the data set. In this case, the range for girls is smaller than the range for boys, indicating that the data for girls is less spread out than the data for boys.

The interquartile range (IQR) measures the spread of the middle 50% of the data. The IQR for girls is smaller than the IQR for boys, again indicating that the data for girls is less spread out than the data for boys.

The standard deviation measures the average deviation of the data from the mean. The standard deviation for boys is larger than the standard deviation for girls, indicating that the data for boys is more spread out than the data for girls.

b) To compute the measures of spread, we need to find the range, variance, and standard deviation for both the boys and girls data.

For the girls data:

Range = 81 - 15 = 66

Variance = 4143.3

Standard deviation = 64.36

For the boys data:

Range = 81 - 0 = 81

Variance = 947.9

Standard deviation = 30.82

The range for the boys data is larger than the range for the girls data, indicating that the boys' scores are more spread out than the girls' scores. However, when we look at the variance and standard deviation, we see that the girls' data has a much larger spread than the boys' data. This means that the girls' scores are more varied and spread out from the mean than the boys' scores.

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