A coin collection consists of dimes and nickels. If there are a total of 500 coins valued
at $39. how many dimes are there?

If f(2) = 1 and the tangent line at x has slope (x − 1)ex2 − 2x. f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x).

To find f(x), we'll first integrate the given slope function to obtain the original function. The slope of the tangent line is given as (x - 1)e^(x^2 - 2x).

Let F'(x) = (x - 1)e^(x^2 - 2x). To find f(x), we need to integrate F'(x) with respect to x:

∫(x - 1)e^(x^2 - 2x) dx

Now, we can use substitution. Let u = x^2 - 2x, then du = (2x - 2) dx. Therefore, the integral becomes:

∫((u + 1)/2)e^u du

Now, we can integrate by parts. Let v = e^u, then dv = e^u du. Let w = (u + 1)/2, then dw = 1/2 du. Using integration by parts formula:

∫w dv = wv - ∫v dw

∫(u + 1)/2 * e^u du = ((u + 1)/2)e^u - ∫(1/2)e^u du

Now integrate the remaining part:

∫(1/2)e^u du = (1/2)e^u + C

Substituting back:

f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x) + C

Now, use the given condition f(2) = 1:

1 = ((2^2 - 2*2 + 1)/2)e^(2^2 - 2*2) + C

1 = (1)e^0 + C

C = 0

Know more about integration here;

https://brainly.com/question/18125359

#SPJ11

Answer:

25.5

Step-by-step explanation:

15% of 30.00 = 4.50 and 30.00 - 4.50 = 25.5. Hope this helps :)

Answer:

The discount is $4.50. The sale price is 25.50.

Step-by-step explanation:

Discount: 30(.15)=4.50

Sale Price: 30.00-4.50=25.50

The measure of angle \(RST\) is \(132\) degrees.

What is Isosceles triangle?

A triangle with two equal sides is known as an isosceles triangle. In other words, two of the three sides of an isosceles triangle are congruent. Along with being equal in size, the angles opposing the congruent sides are also.

Isosceles triangles are a typical geometric form with several uses in geometry, trigonometry, and everyday life.

We may determine the size of angle \(RST\) if  \(PQR\) is an isosceles triangle with \(QP = QR\) and \(QS = QT\) and angle \(PQS\) is 24 degrees.

Angles \(PQR\) and \(PRQ\) are equal because the triangle \(PQR\) is isosceles. Angle \(PRQ\)  is therefore \(24\) degrees as well.

A triangle's total number of angles is \(180.\)The sum of angles  \(PQR\) and  \(PRQ\)  can therefore be subtracted from \(180\) degrees to get the measure of angle  \(RST\).

Angle \(RST\) =\(180\) \(-\)(angle PQR \(+\) angle PRQ)

Angle \(RST\) = \(180 - (24 + 24)\)

Angle \(RST\) = \(180 - 48\)

Angle \(RST\) =\(132\) degrees

Therefore, the measure of angle \(RST\) is 132 degrees.

Learn more about Isosceles triangle:

https://brainly.com/question/29793403

#SPJ4

Answer:

$55.73

Step-by-step explanation:

i think this is right, sorry if it isn't

Approximately 12 percent of the people in Olde Town own both a goat and a chicken.

Let's assume there are 100 people in Olde Town. According to the given information, 40 percent of people own a goat, which means there are 40 goat owners. Additionally, 35 percent of goat owners also own a chicken, which means there are 35 percent of 40, which is 14 people, who own both a goat and a chicken.

Moreover, it is mentioned that 30 percent of people own a chicken. So, there are 30 chicken owners in Olde Town. However, we have already accounted for 14 of them who also own a goat. Therefore, there are 30 minus 14, which is 16 people who own only a chicken.

To find the number of people who own both a goat and a chicken, we add the number of people who own both to the number of people who own only a chicken: 14 + 16 = 30.

To calculate the percentage, we divide the number of people who own both by the total population of Olde Town (100) and multiply by 100: (30 / 100) * 100 = 30 percent. So, approximately 30 percent of the people in Olde Town own both a goat and a chicken, which is equivalent to 12 people.

For more questions like Populations click the link below:

https://brainly.com/question/27991860

#SPJ11

Strength and direction with a negative correlation so we cannot use a correlation close to 0 in predictions.

Given,

When using correlation for prediction.

Here,

When using correlation for prediction strength and direction with a negative correlation so we cannot use a correlation close to 0 in predictions.

Thus option F is correct.

Hence none of the above options are correct.

Know more about correlation,

https://brainly.com/question/9817086

#SPJ4

Answer:

B; 17/6

Step-by-step explanation:

4x-8=-2x+9

Combine like terms

6x=17

Solve

x=17/6

Answer: n = 0 and -2

Step-by-step explanation:

Equate the expressions to zero

n(n+2) = 0

n = 0 and n+2 = 0

n = 0 and n = -2

Answer:

0.8

Step-by-step explanation:

Divide the numerator and denominator together to find the answer.

19 / 24 = 0.79166...

Round to the nearest tenth.

0.79166... → 0.8

Best of Luck!

Answer:

0.8

Step-by-step explanation:

numerator ÷ denominator = 0.791..

19 / 24 = 0.791..

0.791 to the tenth is 0.8

Hope this helps :)

Answer:

y=5x

Step-by-step explanation:

If y is 25 and x is 5

25 = 5 (5)

25=25

Answer: BD = 9 units

Step-by-step explanation:

ABQ and CDQ are congruent triangles. That means their angle measures are the same but their lengths may be proportional.

19.2 / 32 = 0.6

15 * 0.6 = 9

So the length of side BD is 9 units.

Answer:

9 units

Step-by-step explanation:

When Grace spent 90% of the money she had, it means she spent 90% of the total amount she had available for shopping. To find out the amount of money she spent, we can calculate 90% of the total amount. Answer : Grace spent $4050 on shopping.

1. Determine the total amount of money Grace had available for shopping, which is given as $4500.

2. Calculate 90% of $4500 by multiplying $4500 by 0.90.

3. Multiply $4500 by 0.90: $4500 * 0.90 = $4050.

4. Therefore, Grace spent $4050 on shopping.

In summary, the amount of money Grace spent on shopping was $4050.

Learn more about amount : brainly.com/question/32202714

#SPJ11

\(\huge\boxed{25\%}\)

We need to find the number of students that study art first. This includes the students who study both art and biology (4) and the students who study art but not biology.

We know the counts for every category except for "art but not biology", so we can use subtraction.

\(26-4-5-5=12\)

This means that 12 students study art but not biology, which combines with the 4 who study both subjects to give us 16 art-studying students.

Now, we just need to find the probability that a student studies both subjects (4 students) given that they study art (16 students).

This is simple division.

\(4/16=0.25=25\%\)

Answer:

X = -11/4

Add all of the equations up and make them equal 180. For example:

-20x+3+-15+9+-40x+18=180

Then, solve for x.

X = -11/4

Answer:

can you copy and paste it on a question its kinda blurry for me

Step-by-step explanation:

Answer:

B / The Girl

Step-by-step explanation:

.

To solve this problem, we can use algebraic equations. Let's say that the number of weeks it takes for Ted and Carly to have the same account balance is "w".

Ted's account balance after "w" weeks can be represented by:

300 + 4w

Carly's account balance after "w" weeks can be represented by:

16w

We want to find out when their account balances will be equal, so we can set these two equations equal to each other:

300 + 4w = 16w

Simplifying this equation, we get:

300 = 12w

Dividing both sides by 12, we get:

25 = w

Therefore, it will take 25 weeks for Ted and Carly to have the same account balance.

The total capacity of the tank is 272.675 cubic meters.

Given that,

A storage tank consist of a hemisphere and a cylinder which share a common base.

The base of both hemisphere and cylinder will be the same circle with the same radius.

Also, we have,

Height of the tank = 16.5 m

Base diameter of the cylinder = 4.7 m

Radius of the base of the cylinder = 4.7 / 2 = 2.35 m

Radius of the hemisphere = 2.35 m

Height of the cylinder = Total height of the tank - Height or radius of the hemisphere

Total capacity of the tank = Volume of hemisphere + Volume of cylinder

                                          = 2/3 π r³ + π r² h

                                          = 2/3 π (2.35)³ + π (2.35)² (16.5 - 2.35)

                                          = 8.652π + 78.143π

                                          = 272.675 cubic meters

Learn more about Volume here :

https://brainly.com/question/28058531

#SPJ1

a)  The volume of paint left in the can is:

.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

b)  the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

(a) To convert gallons to cubic meters, we need to know the conversion factor between the two units. One U.S. gallon is equal to 0.00378541 cubic meters. Therefore, the volume of paint left in the can is:

0.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

(b) We can use the formula for the volume of a rectangular solid to find the volume of wet paint needed to coat the wall evenly:

Volume = area * thickness

We want to solve for the thickness, so we rearrange the formula to get:

Thickness = Volume / area

The volume of wet paint needed is equal to the volume of dry paint needed since they both occupy the same space when the paint dries. Therefore, the volume of wet paint needed is:

0.003321 m^3

The area of the wall is given as:

13.7 m^2

So the thickness of the layer of wet paint is:

0.003321 m^3 / 13.7 m^2 = 0.000242 m

Therefore, the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

Learn more about meters here:

https://brainly.com/question/29367164

#SPJ11

The solutions are:

sin(a)  = 24/25

tan(a) = 24/7

For a given point (x, y) and an angle "a" measured counterclockwise from the positive x-axis to a ray that connects the origin with our point, we can think on the situation as a triangle rectangle.

Where the ray is the hypotenuse, the x-component is the adjacent cathetus, and the y-component is the opposite cathetus.

So we have:

x = adjacent cathetus

y = opposite cathetus

h = hypotenuse = √(x^2 + y^2)

Then the trigonometric relations become:

cos(a) = x/√(x^2 + y^2)

sin(a) = y/√(x^2 + y^2)

tan(a) = y/x

Now, we know that we have:

cos(a) = 7/25

then we can see that:

x = 7

and

h = 25 = √(7^2 + y^2)

We can solve the above equation for y:

25 = √(7^2 + y^2)

25 = √(49 + y^2)

25^2 = 49 + y^2

625 - 49 = y^2

√576 = y = 24

Then we have:

x = 7

y = 24

h = 25

Now we can return to our known trigonometric relations and get:

sin(a) = y/√(x^2 + y^2) = 24/25

tan(a) = y/x = 24/7

If you want to learn more about trigonometry, you can read:

https://brainly.com/question/14746686

Answer:

there were 8 dog ears in all.

Step-by-step explanation:

Since the statement says that they saw two teachers each walking with two dogs, you have to multiply the number of teachers for the number of dogs each one had to find the total number of dogs they had:

2*2=4

Now, as the statement indicates that each dog had two ears you have to multiply the number of dogs for the number of ears each one has:

4*2=8

According to this, the answer is that there were 8 dog ears in all.

The population of the town in 5 years will be approximately 28,982.

A data pattern known as exponential growth exhibits faster expansion over time. Compounding generates exponential profits in finance. Exponential growth is possible in savings accounts with a compounding interest rate. Compound returns in finance lead to exponential development. One of the most potent forces in finance is the power of compounding. With the help of this idea, investors may generate sizable sums with little start-up money. Compound interest savings accounts are typical instances of exponential development.

Given that, population of a town increases by 3% each year.

The population after 5 years is calculated by:

Population in 5 years = Initial population x (1 + rate) raised to time.

That is,

Population in 5 years = 25,000 x (1 + 0.03)⁵

Population in 5 years = 25,000 x 1.159274

Population in 5 years = 28,981.85

Hence, the population of the town in 5 years will be approximately 28,982.

Learn more about exponential growth here:

https://brainly.com/question/11487261

#SPJ1

On solving the query we can say that As a result, the hemisphere's diameter, to the nearest tenth of a centimetre, is roughly 23.8 cm for a volume of 9103 cm3.

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

The equation (2/3)r3 yields the volume of a hemisphere. Given that the hemisphere's volume is 9103 cm3, we can use the following formula to get its radius:

(2/3)πr³ = 9103

When we simplify this equation, we obtain:

r³ = 9103 × 1.5 / π

r = (9103 × 1.5 / π)^(1/3)

Now, the hemisphere's diameter is equal to double its radius. We therefore have:

diameter = 2r diameter = 2 (9103 divided by 1.5) divided by 1/3

Calculating this expression yields the following results:

diameter: 23.8 centimetres (rounded to the closest tenth)

As a result, the hemisphere's diameter, to the nearest tenth of a centimetre, is roughly 23.8 cm for a volume of 9103 cm3.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

The diameter of the hemisphere to the nearest tenth of a centimeter is 23.9 cm.

What is hemisphere?

A hemisphere is a three-dimensional geometric shape that is formed by slicing a sphere in half along a plane that passes through its center. The resulting shape is a half-sphere with a curved surface and a flat base. A hemisphere has the same radius as the sphere from which it was derived and is therefore a symmetrical shape.

The volume of a hemisphere can be calculated using the formula: V = (2/3)πr³, where V is the volume and r is the radius.

Since we have the volume of the hemisphere, we can solve for the radius as follows:

V = (2/3)πr³

9103 = (2/3)πr³

r³ = (3/2) * 9103/π

\(r = (3/2 * 9103/\pi )^{(1/3)}\)

The diameter of the hemisphere is twice the radius, so:

diameter = 2r = 2 * \((3/2 * 9103/\pi )^{(1/3)}\) ≈ 23.9 cm

Therefore, the diameter of the hemisphere to the nearest tenth of a centimeter is 23.9 cm.

To learn more about hemisphere from the given link:

https://brainly.com/question/13625065

#SPJ1

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

\(12 {}^{ - 2} = 0.00694444444 = \frac{1}{144} \)

We need to find LM. Here, we can use the Pythagorean theorem to solve the given problem.Let’s assume, LM = x.We know that the Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

That is,if AC is the hypotenuse, AB and BC are the other two sides of a right triangle ABC, then according to the Pythagorean theorem:AB² + BC² = AC².Now, KM = AB = 52and NL = BC = 33And, LM = AC = x.Using the above information and Pythagorean theorem, we get:AB² + BC² = AC²52² + 33² = x²2704 + 1089 = x²3793 = x²Now, we need to find LM = √x² = x≈61.6 (rounded to the nearest tenth)Therefore, LM ≈ 61.6 (rounded to the nearest tenth).

Learn more about Pythagorean theorem here:

https://brainly.com/question/10368101

#SPJ11

Answer:Its B,C, and E man

Step-by-step explanation:

Answer:

B, C, and E

I did the quiz

the given expression is'

y = 13x - 5

compare this equation with the standard equation

y = mx + c

here m is slope

so m = 13

thus, the slope of the equation is m = 13

The solution of the equation is as follows:

\(\frac{8^{x} }{2^{y} } = 2^{12}\)

Therefore, the answer is A.

The equation 3x - y  = 12. Let's find the value of \(\frac{8^{x} }{2^{y} }\) as follows:

Let's apply the exponential law to solve the expression as follows:

Therefore, when dividing exponential values with the same base, we have to subtract the exponents.

Hence,

\(\frac{a^{x} }{a^{y} } = a^{x-y}\)

Therefore,

\(8^{x} = 2^{3x}\)

Hence,

\(\frac{8^{x} }{2^{y} } = \frac{2^{3x} }{2^{y} }\)

Applying the law,

\(\frac{8^{x} }{2^{y} } = \frac{2^{3x} }{2^{y} } = 2^{3x - y}\)

Using substitution,

3x - y = 12

Therefore,

\(\frac{8^{x} }{2^{y} } = \frac{2^{3x} }{2^{y} } = 2^{3x - y} = 2^{12}\)

learn more on exponential here: https://brainly.com/question/29301817

#SPJ1

The midpoint of the yearly number of unprovoked alligator attacks can be calculated by finding the class interval that contains the median value. In this histogram, the class intervals are not provided, so we cannot determine the exact midpoint.

However, we can estimate the midpoint by visually locating the point where the histogram is balanced or roughly in the middle. Based on the histogram, it appears that the midpoint is around 6-8 attacks per year.
The midpoint of the yearly number of unprovoked alligator attacks in Florida over 33 years can be found by first identifying the highest and lowest number of attacks in the histogram. Once you have those values, add them together and divide by 2 to find the midpoint.

Visit here to learn more about midpoint brainly.com/question/28224145

#SPJ11