on the day that virginia was born, her parents deposited $2500 into an account paying 3.6% interest compounded annually. a year later, on virginia's first birthday her parents deposited another $2500 and continued to do so for each of virginia's successive birthdays until she was 18 years old. on virginia's 18th birthday, her parents made the final deposit of $2500 and turned control of the account over to virginia. use the formula for a geometric series to find the value of the account on virginia's 18th birthday, to the nearest cent

Ron's average speed in bike race was 12miles/hour.

What is speed?

Speed is distance traversed per unit of time. It determines that how fast an object is moving. It is the scalar quantity so it has the magnitude of the velocity vector. It has no  direction. An object moving with higher speed means an object is moving faster. An object with lower speed means it is moving slower. If the object isn't moving at all, it has zero speed that is in rest.

The average speed of an object that travels a distance d in time t is d/t.

Ron finished a 15-mile bike race in 1.25 hours.

Here d= 15 miles and t= 1.25 hours.                                       15/1.25

so, average speed = 15/1.25                                                   = (15×100)/125

Dividing 15 by 1.25 we get,                                                     =12

                               = 12 miles/ hour.

Hence Ron's average speed in bike race was 12miles/hour.

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Answer:

yes it can

Step-by-step explanation:

yes

Answer:

No

Step-by-step explanation:

You need to use the Pythagorean Theorem.  This will show you if the ratio between the sides is accurate.

a² + b² = c²

8² + 11² = 13²

64 + 121 = 169

185 ≠ 169

The measurements will not fit in a right triangle.

The amount of aspirin that is left in her system after 6 hours is 2.344 mg.

In Mathematics and Statistics, a population or substance that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or substance that decreases by r percent per unit of time is an exponential equation of this form:

\(P(x) = I(1 - r)^x\)

Where:

By substituting given parameters into the formula, we have the following:

\(P(x) = I(1 - r)^x\\\\P(6) = 150(1 - 0.25)^6\\\\P(6) = 150(0.75)^6\)

P(6) = 2.344 mg.

In conclusion, we can reasonably infer and logically deduce that the decay rate is equal to 75%.

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The expression csc θ / cot θ = sec θ, is an identity.

Given:csc θ / cot θ = sec θWe are supposed to transform the left side of the above expression to the right side. We know that:csc θ = 1/sin θ cot θ = cos θ / sin θSubstituting these values in the above expression we get, csc θ / cot θ= (1/sin θ) / (cos θ/sin θ) (taking reciprocal of cot θ and substituting cot θ by cos θ/sin θ)csc θ / cot θ= 1/sin θ x sin θ/cos θ (multiplying the expression by sin θ/sin θ) csc θ / cot θ= 1/cos θ (sin θ gets cancelled from the numerator and denominator)Therefore, csc θ / cot θ = sec θ, is an identity.

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Answer:

2x^4 + x^3 - 2x -1

Step-by-step explanation:

Do each one at a time and add them after you are done is necessary, first multiply 2x times x^3 this gives 2x^4. Then multiply 1 times x^3 to get x^3. Then multiply 2x times -1 to get -2x. Then multiply -1 and +1 to get -1. Then combine them together. None of the terms are like terms so you don't need to worry about combining them further but keep that in mind for other problems. The final answer becomes 2x^4 + X^3 - 2x -1 because none of the terms are the same power.

Answer:

The answer is A) 14/12

Step-by-step explanation:

The common denominator here is 12.

1/3 is multiplied by 4 to get 12 on the bottom, and 4 on the top (4/12)

2/4 is multiplied by 3 to get 12 on the bottom, and 6 on the top (6/12)

4/12 stays the same

Now, we have 4/12 + 6/12 + 4/12

Add all the numerators to get 14/12 as your answer.

Answer:

d

Step-by-step explanation:

Answer:

your question Is not in Mark

Answer:

Value of n:

Since the first three terms in the binomial expansion are 1 + kx - x^2, we can compare this with the general binomial expansion formula:

(1 + bx)^n = 1 + n(bx) + (n(n-1)/2)(bx)^2 + ...

Comparing the terms, we see that n(bx) = kx, which means n = k.

Value of k:

From the given expression, we have 1 + kx - x^2. Since the coefficient of x is k, we can conclude that k = 1.

Therefore, the value of n is 1 and the value of k is 1.

Step-by-step explanation:

hope this helps :)

Answer:

The sum of 25 and 16 is 41.

Step-by-step explanation:

The sum of two numbers, 25 and 16, you can break apart the addends and add them separately to simplify the process. Here's how you can do it:

Break apart the numbers into their place values: For 25, you have 20 and 5, and for 16, you have 10 and 6. This step helps you work with the place values individually.

Add the tens place: In this case, you have 20 (from 25) and 10 (from 16). Adding them gives you 30.

Add the ones place: Now you add the ones place, which is 5 (from 25) and 6 (from 16). Adding them gives you 11.

Combine the sum of the tens place and the sum of the ones place: Take the sum of 30 (from step 2) and 11 (from step 3). Adding them together gives you 41.

So, the sun is 41.

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In thermodynamic system, Absolute Zero is that temperature implies Lowest energy level i.e.  option a) 0 K or -273° C.

Absolute Zero can describe as,  in  a thermodynamic system, there are certain energy levels depending upon the potentials of temperature. At Absolute zero the potentials of temperature  are  0 K in Kelvin scale and   -273° C in Celsius scale.

The question seem's to be incomplete. The option could be.

a) 0 K and -273° C
b) 273 K and 0° C
c) -273 K and 0° C
d) 0 K and 273° C

Hence, As per theory Value of The absolute zero is 0 K and -273° C

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We can approximate the mean and standard deviation temperature using these class midpoints.

To approximate the mean and standard deviation of the temperature for the given frequency distribution, we need to find the class midpoint for each class.

The class midpoints can be calculated by taking the average of the lower and upper class limits.

For the given frequency distribution:

Class 61-64: Class Midpoint = (61 + 64) / 2 = 62.5

Class 65-67: Class Midpoint = (65 + 67) / 2 = 66

Class 68-69: Class Midpoint = (68 + 69) / 2 = 68.5

Class 70: Class Midpoint = 70

Class 71-72: Class Midpoint = (71 + 72) / 2 = 71.5

Class 73-76: Class Midpoint = (73 + 76) / 2 = 74.5

Class 77-80: Class Midpoint = (77 + 80) / 2 = 78.5

Now, we can approximate the mean and standard deviation temperature using these class midpoints.

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Answer:

\(9 - x = 1\)

\(9-x-9=1-9\)

\(-x=-8\)

\(\cfrac{-x}{-1}=\cfrac{-8}{-1}\)

\(\boxed{x=8}\)

\(-252 = 21k\)

\(21k=-252\)

\(\cfrac{21k}{21}=\cfrac{-252}{21}\)

\(\boxed{k=-12}\)

Answer:

x= -6   k=-12

Step-by-step explanation:

15-9 is 6.   9+6=15 9-(-6)=15 because when two negatives are together they make a positive. (--)=+      K=-21 because -252/21 is -12.

Answer:

cos45° = \(\frac{1}{\sqrt{2} }\) = \(\frac{\sqrt{2} }{2}\)

Step-by-step explanation:

Using the 45- 45- 90 triangle with legs 1, 1 and hypotenuse \(\sqrt{2}\) , then

cos45° = \(\frac{1}{\sqrt{2} }\) = \(\frac{\sqrt{2} }{2}\) if the denominator is rationalised

these values into the formula, we get (655.20^2 / 48.28, 655.20^2 / 31.26), which simplifies to (15.07, 29.78). Therefore, we can estimate with 95% confidence that the population variance lies between 15.07 and 29.78.

To estimate the population variance, we use the chi-square distribution. The formula for calculating the confidence interval for the population variance is (n-1)s^2 / chi-square upper value, (n-1)s^2 / chi-square lower value, where n is the sample size, s^2 is the sample variance, and chi-square upper and lower values are determined based on the desired confidence level.

In this case, the sample size is 66, the sample variance is 5.20^2, and we want a 95% confidence interval. Using the chi-square distribution table or a statistical software, we find the chi-square upper value corresponding to a 95% confidence level with 65 degrees of freedom to be 48.28, and the chi-square lower value to be 31.26.

Plugging these values into the formula, we get (655.20^2 / 48.28, 655.20^2 / 31.26), which simplifies to (15.07, 29.78). Therefore, we can estimate with 95% confidence that the population variance lies between 15.07 and 29.78.

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Answer:

I think it is b and d .

Step-by-step explanation:

Answer:

Hello again! Both D and B are rectangles.

Step-by-step explanation:

You know that a rectangle has 4 sides like a quadrilateral but it is different. Both of the oppiosite sides are the same length. C would not be one because it is not connected therefore it is not a full shape. Because of  A´s even sides, A is not a rectangle. I hope this helps! :]

Sorry I messed up! :]

The answers to all the equations are:

So, f(x):

(A) f(x) = x + 3 when f(4)

(B) f(x) = 2x - 9 when f(5)

(C) f(x) = -6x + 2 when f(-3)

Therefore, the answers to all the equations are:

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Answer:

-2/-0.25=8

4/0.5=8

Step-by-step explanation:

both of their answers are 8

It is most important to have a random sample in inferential statistics, particularly in making statistical inferences about a population based on the sample data.

Random sampling is a critical component of inferential statistics because it helps to ensure that the sample is representative of the population. When a sample is randomly selected, each member of the population has an equal chance of being included in the sample, which reduces the risk of bias in the results. Without a random sample, the results of statistical analyses may not be accurate or generalizable to the population, and the conclusions drawn from the data may be flawed or misleading.

Therefore, random sampling is crucial in making valid statistical inferences about a population.

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Answer:

x = 36.27

Step-by-step explanation:

By using the steps to find sin θ backwards, we can find x, the hypotenuse.

sin θ = \(\frac{opposite}{hypotenuse}\) or side \(\frac{a}{c}\) (as seen in my example picture).

We already know the value for sin (α), which is 32° because its given. The opposite side (a) is 20 and the hypotenuse side (c) is x which are both also given.

So the equation now looks like:

sin 32° = \(\frac{20}{x}\)

Don't solve for the sin 32 yet! First, we have to isolate the variable.

To get rid of the x in the denominator you have to multiply both sides by x:

( sin 32 ) · x = ( \(\frac{20}{x}\) ) · x

( sin 32 ) x = 20

Then, you have to divide both sides by sin 32 to get x by itself:

(( sin 32 ) x ) ÷ ( sin 32 ) = 20 ÷ ( sin 32 )

x = 20 ÷ ( sin 32 )

Lastly, you have to use a calculator to find 20 ÷ ( sin 32 ), and it should give you 36.2695543766.

The question asks you to round to 2 decimal places so:

x = 36.27

If you want more like this^^^^^^^

Answer:

A

Answer:

y= 500+7x

Step-by-step explanation:

Given data

Total amount for the rent=  $500

Cost of food per night= $10

Family charges per night=$60

Let the number of nights be x

and let the total charges be y

Hence, the expression for the situation is given as

y=500+10x+60x

y= 500+7x

The sampling technique used in this scenario is a) random sampling. The researcher interviews all passengers on five randomly selected flights.

The sampling technique used in this scenario is random sampling. Random sampling involves selecting individuals from a population in such a way that each individual has an equal chance of being chosen. In this case, the researcher selects five flights at random, and then interviews all passengers on those selected flights.

Random sampling helps ensure that the sample is representative of the population and reduces the potential for bias. By randomly selecting flights, the researcher increases the likelihood of obtaining a diverse range of passengers, capturing a variety of opinions and experiences.

Other sampling techniques have different characteristics. Cluster sampling involves dividing the population into groups or clusters and randomly selecting entire clusters to be included in the sample. Stratified sampling involves dividing the population into subgroups or strata and then randomly selecting individuals from each stratum. Systematic sampling involves selecting every nth individual from a list. Convenience sampling involves selecting individuals based on their availability or accessibility, which may introduce bias into the sample.

In summary, the sampling technique used in this scenario is random sampling, as the researcher randomly selects five flights and interviews all passengers on those selected flights. This approach helps ensure a representative sample and reduces potential bias.

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Answer:

60^2-10/5 = 3600-2 = 3598

Step-by-step explanation:

Answer:

t=2.18n

Step-by-step explanation:

Total cost is 6.54 for 3 tickets so divide 6.54 by 3 and you get price per ticket which is 2.18. Multiply that by how many tickets you want and you get your final price.

Answer:

a= 126

b= 54

c= 126

d= 54

e= 126

f= 54

g= 126

Step-by-step explanation:

To find a you would subtract 54 from 180 which would give you 126

Since a and b are another linear pair they would also add up to 180.

Then you move to c which is a linear pair with 54 so it is 126.

Because a and g are alternate interior angles they are congruent and they you continue with the same process for the first and check by seeing if the angles would be obtuse or acute to see if the angle measures would be correct.

The measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

It is given that:

The diagram shows two parallel lines cut by a transversal.

As we know from the definition of the vertically opposite angles:

b = 54 degrees

a + c = 54 + b  (a = c)

2a = 54x2

a = 54 degrees

Since a and g are opposite interior angles, they are congruent, so you proceed with the process as you did for the first and check to see if the angles are acute or obtuse to ensure that the angle measurements are accurate.

Similarly:

b = 54

c = 126

d = 54

e = 126

f = 54

g = 126

Thus, the measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.

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It will create a torus shape.

The solid that resembles a doughnut and is called a torus has rotational symmetry around a vertical axis that runs through its center, and its outside edges are shaped like circles.

Rotations of two-dimensional objects can produce three-dimensional things. It will also be possible to identify and examine the two-dimensional cross-sectional forms of three-dimensional objects.

Every cross-section of a sphere is a circle, as is obvious. Remember that things may appear to be different from their true shapes depending on the viewpoint, even if certain cross-sections seem to be ellipses from various angles.

It will create a torus shape.

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Answer:

B for me

Step-by-step explanation:

Yun lang po correct me if iam wrong

The Required equation for the ellipse is given by   \(\frac{(x-4)^2}{49}+\frac{y+1}{100} = 1\) Option B. is correct

Ellipse is cross-section part of a cone structure when cutting it out a horizontal cross-section of a cone.

(x-h)^2/a^2 + (x-k)^2/b^2 = 1
(h,k) = centre of the ellipse.
a, b = semi minor or major axis,

\(\frac{(x-4)^2}{49}+\frac{y+1}{100} = 1\)

thus, the required equation of ellipse is given by \(\frac{(x-4)^2}{49}+\frac{y+1}{100} = 1\).

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