a nickel dime and a quarter are tossed what is the probability of getting 3 heads

An account with a starting balance of P accruing interest with rate r for time t, componunded continuously, ends up with a balance A according to

\(A=Pe^{rt}\)

Plug in everything you know and solve for r :

\(8624.97=6139e^{17r}\)

Divide both sides by 6139:

\(\dfrac{8624.97}{6139}=e^{17r}\)

Take the natural logarithm of both sides:

\(\ln\left(\dfrac{8624.97}{6139}\right)=\ln e^{17r}\)

Recall that \(\ln x^y=y=\ln x\), so that

\(\ln\left(\dfrac{8624.97}{6139}\right)=17r\ln e\)

and ln(e) = 1, so

\(\ln\left(\dfrac{8624.97}{6139}\right)=17r\)

Finally, divide both sides by 17:

\(r=\dfrac1{17}\ln\left(\dfrac{8624.97}{6139}\right)=\boxed{0.02}\)

So the account has an interest rate of 2%.

One of the species of trees is the Oak. If a seed of an Oak tree is planted, and it is assumed that the diameter of the seed is 0, the tree would grow by approximately 3.3 inches in year 1, 6.6 inches in year 2, 9.9 inches in year 3, and 33 inches in year 10. It cannot be said that the Oak tree would grow by the same amount each additional year.

Some years, the tree might grow more, while other years, it might grow less.Trees are perennial plants that have a single main stem, a supporting structure of branches and leaves, and the ability to produce wood.

A tree that is mature and has a single stem is known as a "single-trunked" or "single-stemmed" tree; trees with several stems originating at or near the ground are known as "multi-stemmed" or "clonal" trees.The height and trunk diameter of a tree increase as it matures.

The growth rate of each tree species is determined by various variables such as weather, altitude, and soil fertility.

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Answer:

4 games

Step-by-step explanation:

Hope this is right!!!

Answer:

4

Step-by-step explanation:

So first off, subtract the 800 from the 980, this leaves the amount of money left ofr games:

980-800

=

180.

Next divide this by how much each game cost, to get the amoutn per game:

180/45

=

4

So we know he got 4 games.

Hope this helps!

Answer: 1.25

Find my question since I had this question and look at the answer ok

Step-by-step explanation:

I hope my answer helps you out have a great day

Answer:

\(y=-x\,cos\,x+Cx\)

There are no transient terms.

Step-by-step explanation:

Given: \(x\,\frac{dy}{dx} -y=x^2\,sin\,x\)

To find: general solution of the differential equation and the transient terms in the general solution.

Solution:

For an equation of the form \(\frac{dy}{dx}+yp(x)=q(x)\),

solution is given by \(ye^{\int {p(x)} \, dx }\) = ∫ q(x)\(e^{\int {p(x)} \, dx }\) dx

The given equation \(x\,\frac{dy}{dx} -y=x^2\,sin\,x\) can be written as \(\frac{dy}{dx}-\frac{y}{x}=x\,sin\,x\)

Here,

\(p(x)=\frac{-1}{x}\,,\,q(x)=x\,sin\,x\)

\(e^{\int{p(x)} \, dx } =e^{\int{\frac{-1}{x} } \, dx } =e^{-ln(x)} =e^{ln(x^{-1} )}=x^{-1}=\frac{1}{x}\)

So,

the solution is \(\frac{y}{x}=\int \frac{1}{x}x\,sin\,x\,dx\)

\(\frac{y}{x} =\int\,sin\,x\,dx\\\\\frac{y}{x} =-cos\,x+C\\y=-x\,cos\,x+Cx\)

Here, C is a constant.

Transient term is a term such that it tends to 0 as x → ∞

Here, there does not exist any term that tends to 0 as x → ∞

So, there are no transient terms.

The value of Z in the similar triangles is 6

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

The triangle

Using the corresponding sides of similar triangles, we have

z/12 = (14 - z)/16

Cross multiply the equation

This gives

16z = 168 - 14z

So, we have

30z = 168

Divide

z = 5.6

Approximate

z = 6

Hence, the value of Z is 6

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ANSWER

66.3 m

EXPLANATION

We want to find the distance around the figure.

The figure is made up of a semi circle on a rectangle.

So, we have to find the perimeter of the semi circle (without adding the diameter) and the rectangle, but we will subtract 18 m from the perimeter of the rectangle since the person running does not run across that length.

The perimeter (circumference) of the semi-circle (without adding its diameter) is given as:

C = πr

where r = radius

The diameter of the semi-circle is 18 m, so its radius is:

r = D / 2 = 18 / 2

r = 9 m

So, the circumference is:

C = π * 9

C = 28.3 m

The perimeter of the rectangle is given as:

P = 2(L + B)

where L = length and B = breadth

So, the perimeter is:

P = 2(18 + 10) = 2 * 28

P = 56 m

Now, subtract 18 m:

P = 56 - 18

P = 38 m

Now, add the two of them:

P = 28.3 + 38

P = 66.3 m

So, if you run around the figure, you are traveling 66.3 m.

When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.

A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.

However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.

While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.

Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.

So, correct option is B.

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Answer:

2 Hours

Step-by-step explanation:

First you have to add up all the points which would be;

1 1/2 + 1 1/2+ 2 1/2+ 2 1/2= 8 hours

Then you have to divide by how many points to find the average;

8 hours divided by 4 points= 2 hours average

In total, she will practice 2 hours every day

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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Answer: 394.8

Step-by-step explanation:

if Amid needs 32.9 m for one tent  he will need

32.9 x 12= 394.8 m for 12 tents

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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The shape of the ABCD is a rhombus. The diagonals are not equal to each other.

What is the 2-dimensional shape?

A 2d shape is a two-dimensional shape with horizontal and vertical axes (x-axis and y-axis). 2D shapes are flat shapes with only length and width. These shapes have no thickness or height.

Given the vertices of ABCD are  A(-3,0), B (1,5), C(-3,10) and D(-7,5).

The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4

The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4

The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10

The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8

The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of AB is (5-0)/(1-(-3))=5/4

The slope of BC is (10-5)/(-3-1)=-5/4

The slope of CD is (5-10)/(-7-(-3))=5/4

The slope of AD is (5-0)/(-7-(-3))=-5/4

The number of vertices of the quadrilateral is 4.

Thus it is either a square or rectangle or rhombus or parallelogram.

Since the length of all sides is equal thus it is either a square or rhombus.

Since the diagonals are not equal it is a rhombus.

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Answer:

The answer is D.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

yawn

The expression when distributed is 3 + 2k

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

1/5(15 + 10k)

The distribution property states that

a(b + c) = ab + ac

using the above as a guide, we have the following:

1/5(15 + 10k) = 1/5 * 15 + 1/5 * 10k

Evaluate the products

1/5(15 + 10k) = 3 + 2k

Hence, the equivalent expression is 3 + 2k

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Answer:

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Step-by-step explanation:

Answer:

The original number is -22

Step-by-step explanation:

We'll label our mystery number x.

2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22

Plug in to confirm

-44 + 36 = -88/11S
8 = 8

Answer:

197

Step-by-step explanation:

So, if you catch 100 fish on both days, that means that you have caught 200 fish. 100 on one day and 100 on the next. But, since you've caught 3 fish twice, that means that three out of 200 fish are the same and cannot be counted as new fish. So 3 from 200 is 197 fish. Hope this helped!

Day 1: 100 (3 tagged)

Day 2: 97 (3 tagged)

100+97=197

or

Day 1: 100 (3 tagged)

Day 2: 100 (3 tagged)

100+100= 200

200-3=197

Answer, 197 fish.

Answer:

\(48\)

Step-by-step explanation:

Our expression:

\(6z\)

If we know \(z=8\), let's substitute \(z\), for \(8\), in our expression:

\(6(8)\)

Multiply:

\(6(8)=48\)

Given:

a² + b² = c²

a² + b² = n²

To find:

Substituting both equation to get a new equation

Steps:

We know,

a² + b² = c²

a² + b² = n²

Now if we substitute a² + b² to equal to c², in equation a² + b² = n² we get,

a² + b² = n²

       c² = n²

         c = n

Therefore we get the new equation as c = n

Happy to help :)

If you need any help, pls feel free to ask

The equation that we get after solving the given equation should be considered as the c = n.

As per the Pythagoras theorem, It defined that the area of the square i.e. hypotenuse is equivalent to the sum of the areas of the squares on the other two sides.

So based on this, we can considered the following equations:

Since

a² + b² = c²

a² + b² = n²

So here  

a² + b² = n²

 c² = n²

c = n

Therefore we get the new equation as c = n

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Answer:

i can help with the problem

The elements in the set (A u B)' are is {8,9,10,11,12,13}

The definitions of the sets and the elements are given as

The set to calculate is represented by the notation

(A u B)'

Start by calculating the set A u B

This means that we combine the sets A an B without repetition

So, we have

A u B = {1, 2, 3, 4, 5, 6, 7}

Next, we calculate (A u B)'

This represents the sets in U that are not in A u B

So we have

(A u B)' = {8,9,10,11,12,13}

Hence, the value of the set is {8,9,10,11,12,13}

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Answer:

$1.39

Step-by-step explanation:

4.59-3.20=1.39

The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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we know that

$320 --------> represents the 100% percentage

so

Applying proportion

Find out how much percentage represents $6.40

therefore

The answer is 2%

The area under the curve between two values on the x-axis represents the probability that the random variable falls within that range, with the total area under the curve being equal to 1.

In the graph, the PDF is represented by the smooth curve. The highest point on the curve corresponds to the most likely value of the random variable. In this case, the most likely value appears to be around x = 2.5.

The area under the curve between any two values on the x-axis represents the probability that the random variable falls within that range. For example, the probability that the random variable falls between x = 1 and x = 3 is equal to the area under the curve between those two values.

It's important to note that the probability density function must satisfy the following two conditions:

The total area under the curve must be equal to 1.

The probability of the random variable taking on any specific value is equal to zero, since the function only describes the likelihood of the variable taking on a range of values.

PDFs are often used in statistics to describe continuous distributions, such as the normal distribution, and to make statistical inferences about populations based on samples.

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In response to the given question, we can state that Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.

Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

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Answer:

Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.

Step-by-step explanation:

The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.

The equation from the fourth column is:

0.35x + 0.10(1300 - x) = 0.25(1300)

Solving for x, we get:

x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600