Carolyn has $2.55 in her purse in nickels and dimes. The number of nickels in nine less than three times the number of dimes. Find the number of each type of coin

The rate at which shadow is decreasing On a morning of a day when the sun will pass directly overhead, the shadow of an 80-ft building on level ground is 60 ft long and is 10.4 inches per minute.

Given,

Height of the building, [tex]h[/tex] = 80 ft = 960 inches

Length of shadow, [tex]x[/tex] = 60 ft = 720 inches

The angle that the sun makes with the ground is increasing,

[tex]\frac{d\theta}{dt} = 0.27[/tex] degree [tex]= \frac{3\pi }{2000} rad/min[/tex]

[tex]tan\theta = \frac{960}{x} \\\frac{d }{dy} tan\theta = \frac{d}{dy} \frac{960}{x} \\sec^{2}\theta \frac{d\theta }{dt} = -\frac{960}{x^{2} } \\\\\frac{dx}{dt} = \frac{(60^{2})(\frac{5}{3})^{2} }{960} \\\\\\\frac{dx}{dt} = 10.4 inches /min[/tex]

Hence, the shadow is decreasing at a rate of 10.4 inches per minute.

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The number of years after 2003 that the car's value will be $11,250 is t = 7.5 years.

In 2003, the price of a certain automobile was approximately with a depreciation of 1,750 per year. After how many years will the cars value be $11,250 A) write an equation to model the problem. Let the represent the number of years after 2003.

A) The equation to model the problem is:

Price in year t = 2003 Price - (t - 1)(1,750)

B) To solve the equation for t, we can rearrange it to isolate t:

t = (2003 Price - 11,250) / 1,750

Therefore, the number of years after 2003 that the car's value will be $11,250 is t = 7.5 years. This means that the car's value will be $11,250 in the year 2010.5.

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The required total income generated by planting corn in 2008 is the amount of $1917.85.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The yield of corn on Mr. Geller's farm since 2001 can be modeled by the function N(t) = 10t + 88.5

Let's find the amount of corn produced in 2008:

N(7) = 10 x 7 + 88.5 = 158.5 (kilograms)

Next, let's find the price of corn in 2008:

P(7) = 81 - 10 x 7 + 1.1 = 12.1 ($/kilogram)

Finally, we can multiply the amount of corn by the price per kilogram to find the total income:

158.5 x 12.1 = 1917.85

Rounding to the nearest cent, the total income generated by planting corn in 2008 is $1917.85.

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The value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest. The solution is obtained by using the arithmetic operations.

What are arithmetic operations?

In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

We are given first expression as 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex]

The answer for this expression can be a positive or a negative number depending on the fact which of the terms is greater.

The second expression is (-7[tex]\frac{5}{6}[/tex] ) + (- 9[tex]\frac{3}{4}[/tex])

The answer for this expression will be a negative number because addition of two negative numbers is always negative.

The third expression is (-7[tex]\frac{5}{6}[/tex] ) . 9[tex]\frac{3}{4}[/tex]

The answer for this expression will be a negative number because multiplication of one negative number and one positive number is always  negative.

The fourth expression is (-7[tex]\frac{5}{6}[/tex] ) ÷ (- 9[tex]\frac{3}{4}[/tex])

The answer for this expression will be a positive number because division of two negative numbers is always positive. But, dividing two numbers will give us value close to 1 because the numbers 7 and 9 are very close to each other.

Hence, the value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest.

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The bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to describe the relationship between two quantities, or to express a rate or change in a quantity over time. The symbol for percent is "%".

For example, if a pizza is marked up by 20%, it means the price has increased by 20/100 or 1/5 of the original price. If a student scores 80% on a test, it means they got 80 out of 100 questions correct. If a stock's value increases by 10%, it means the value has gone up by 10/100 or 1/10 of the original value.

The current admission price is $3 + $3 * 50% = $3 + $1.50 = $4.50.

150% of the price 5 years ago is $3 * 150% = $3 * 1.5 = $4.50.

So, the bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.

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If a polynomial can be expressed as a polynomial divided by a polynomial, that function is deemed rational. x is 3, the sole zero in the denominator.

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The measure of the angle ∠ABC  is given by 45°

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: ΔABC with AB=√2, AM=1,BM=1 and BC=2

Now in ΔABM we have two sides equal AM=1,BM=1

and AB=√2

Thus AM²+BM²=AB²

Thus the triangle must be a right angled triangle with AB as its hypotenuse

let ∠B=Ф then we have TanФ=1/1

                                         ⇒ Ф=45°

Hence, The measure of the angle ∠ABC  is given by 45°

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$1.15

Let's call the cost of the bike horn "x".

Dirk paid $5.33 and received $4.18 in change, so he must have paid x + $4.18 = $5.33.

Solving for x, we get x = $5.33 - $4.18 = $1.15.

Therefore, the bike horn cost $1.15.

Answer:

she is 0 blocks away from home because you said she started at home

Answer:

a) Malavika is 8 blocks west from home

b) Traveled 20 blocks total

Step-by-step explanation:

a) According to a compass: 3 west (left), then 6 east (right) and that puts you at 3 east (right). Then back 11 west (left) puts you at 8 west (left)

b) Add up all blocks traveled: 3 + 6 + 11 = 20

Answer:0.3

Step-by-step explanation:

answer my question next please its about zara sells apples one

Answer:3/10

Step-by-step explanation: 4x3 is 12 and 4x10 is 40, so 12/40, the GCF of these numbers are 4 so 12/4=3 and 40/4= 10

So 3/10

Answer:

Your answer is: A) [tex]96cm^{2}[/tex]

Step-by-step explanation:

The area of the rectangle having a length of 12 cm and a width of 8 cm

is 96 cm².

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the area of a rectangle is (length×width).

Given, one side of a rectangle is 8 cm and the other side of the rectangle is 12 cm.

Therefore, The area of this rectangle is,

= (12×8) cm².

= 96 cm².

So, the area of the rectangle is 96 cm².

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Answer:

Cayley earned per day: 4 x 5 = 20

: Her earning per week-  3 x 20 = 60

: Her earning for 8 weeks- 8 x 60 = 480

Cayley earns $480 per week.

Smaller number = 7

Larger number = 14

An algebraic equation can be solved in a variety of ways.

The method you use to solve an equation depends on the type of equation and the information you are given.

Some of the most common methods to solve algebraic equations include using factoring, using the quadratic formula, completing the square, graphing, and using the substitution method.

This question uses the algebraic equation solving technique.

Step 1: Create an equation that relates the two numbers.

Let x = the smaller number

Let y = the larger number

2x + 3y = 86

Step 2: Substitute the given information into the equation.

We know that y = x + 7, so we can substitute that into the equation.

2x + 3(x + 7) = 86

Step 3: Solve the equation.

2x + 3x + 21 = 86

5x + 21 = 86

5x = 65

x = 13

Step 4: Substitute the value for x into the expression for y.

y = x + 7

y = 13 + 7

y = 20

Therefore, the two numbers are 7 and 14.

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Answer: ASA postulate

Step-by-step explanation:

There is a congruent side included between two pairs of congruent angles.

Answer:

-2

Step-by-step explanation:

y = −2− x 2 y = - 2 - x 2

Answer:

[tex]24x^{2}y^2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)!}\\\end{minipage}}[/tex]

We can use the Binomial Theorem to find any term of a binomial expansion.  

The first term is when k = 0, so the third term is when k = 2.

Compare the given expression (x + 2y)⁴ with the formula to find the values of a, b and n.  

Therefore:

Substitute the values into the formula to find the third term:

[tex]\implies \displaystyle\binom{4}{2}x^{4-2}(2y)^2[/tex]

[tex]\implies \dfrac{4!}{2!(4-2)!}x^{2}2^2y^2[/tex]

[tex]\implies \dfrac{4 \times 3\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}{2\times 1\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}\;x^{2}4y^2[/tex]

[tex]\implies \dfrac{12}{2}\:x^24y^2[/tex]

[tex]\implies 6x^{2}4y^2[/tex]

[tex]\implies 24x^{2}y^2[/tex]

If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B that is option E.

In mathematics, digits are single numbers that are used to represent values. In math, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in various combinations and repetitions to represent all of the values. A digit is a symbol that can represent any of the ten numbers from 0 to 9. If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B. A digit can be any of the following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A number is a measurement of something. It can be written with one, two, three, or more digits.

Here,

If a and b are nonzero digits, the number of digits (which does not have to be the same) in the sum of the three whole numbers is determined by the values of A and B that is option E.

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The incorrect code contained two errors. The first was that the variable 'resistance' was initialized with a string value from the prompt, and the second was that the inverse value was not rounded off to two decimal places.

// incorrect code

//

// let resistance = prompt("Enter the resistance: ");

// inverse = 1.0 / resistance;

// console.log("The inverse of resistance is " + inverse);

// correct code

let resistance = parseFloat(prompt("Enter the resistance: "));

let inverse = 1.0 / resistance;

console.log("The inverse of resistance is " + inverse.toFixed(2));

1. In the incorrect code we have a variable 'resistance' that is initialized with a string value from the prompt. To fix this we have used the parseFloat function to convert this string to a float value.

2. In the incorrect code the inverse value is not rounded off to 2 decimal places. To do this we have used the toFixed(2) method to round off the inverse value to 2 decimal places.

The incorrect code contained two errors. The first was that the variable 'resistance' was initialized with a string value from the prompt, and the second was that the inverse value was not rounded off to two decimal places. To fix these errors, the parseFloat function was used to convert the string value of 'resistance' to a float value, and the toFixed(2) method was used to round off the inverse value to two decimal places.

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Answer:

2290
ignore this--> (I need 20 words to answer the question lol)

Answer:

2290

Step-by-step explanation:

2290*3 gives 6870

the set of all z ∈ (-3,1) such that neither 2+z nor 2-3z is in the interval (-1,2].

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities.

the set of all z such that neither 2+z nor 2-3z is in the interval (-1,2].

here, we shall assume two cases,

case first.

z > -1,

2+z > -1

z > -1 -2

z > -3

and,

2-3z > -1

-3z > -3

z > 1

z belongs to ( -3 , 1)

case 2nd,

z<=2

2+z < = 2

z <= 2-2

z ≤ 0

and 2-3z ≤ 2

-3z ≤ 0

z ≤ 0

z is less than equal to 0

So, by above conditions

z belongs to (-3,1).

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An inequality which represents the value of t for which the water temperature is still safe is t ≤ 2 and it has been plotted in the graph attached below.

In order to write, solve, and graph an inequality that represents the value of t for which the water temperature is still safe, we would take note of the following important information;

Now, we can write an inequality that represents the value of t for which the water temperature is still safe as follows;

102 + t ≤ 104

By subtracting 102 from both sides of the inequality, we have the following:

102 - 102 + t ≤ 104 - 102

t ≤ 2

Next, we would use an online graphing calculator to graph the above inequality as shown in the image attached below.

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For equation 1, substitution x=4tanθ is the most helpful. For 2, substitution x=4sinθ is the most helpful. For 3, substitution x=4secθ is the most helpful. For 4, substitution x=4sinθ is the most helpful. For 5, substitution x=4tanθ is the most helpful.

Substitutions are often used to simplify indefinite integrals. For example, in the first integral ∫√(x^2-16) dx, substitution x=4tanθ is the most helpful. This is because it will allow us to simplify the expression under the radical. After substituting, we have ∫√(16tan^2θ-16) dθ. The 16tan^2θ can be factored to give 16(tan^2θ-1), which is equal to 16sec^2θ-16. This simplifies the integral, making it easier to integrate. In a similar way, substitution can also be used to simplify the other integrals. For example, for the fourth integral ∫(x^2 – 16)^(5/2) dx, substitution x=4sinθ is the most helpful. After substituting, we have ∫(16sin^2θ-16)^(5/2) dθ. This simplifies the integral, making it easier to integrate. In general, the substitutions chosen for each integral should be the ones that simplify the expression the most, allowing for easier integration.

1. A. x = 4tanθ

2. B. x = 4sinθ

3. C. x = 4secθ

4. B. x = 4sinθ

5. A. x = 4tanθ

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The third side is represented by the inequality 7 < x < 43, where x is the third side.

When you know two sides of a triangle, you can calculate the range for the third side.

Let x would be the third side.

First, since 25 - 18 = 7, the third leg must be greater than 13. Otherwise, the two smaller legs would not be able to connect to form the third leg.

Second, if we combine 18 with 25 and get 63, the third leg must be smaller than 69. Otherwise, the third leg would be able to reach further than the previous two legs.

This means 7 < x < 43.

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The total distance traveled by the particle over 5 units of time is 140 units.

What is the total distance?

To find the total distance a particle travels over a certain time interval, we need to find the definite integral of its velocity function over that interval. The velocity function is the derivative of the position function.

In this case, the position function of the particle is x(t) = t³ - 6t + 9t - 2 and we need to find the total distance traveled by the particle over 5 units of time.

The velocity function is x'(t) = 3t² - 6 + 9 = 3t² + 3

The total distance traveled over 5 units of time is the definite integral of the velocity function evaluated between 0 and 5.

∫(3t²+3) dt from 0 to 5

= [t³ + 3t] from 0 to 5

= (5³ + 3*5) - (0 + 0) = 125 + 15 = 140

The total distance traveled by the particle over 5 units of time is 140 units.

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The general statement for the previous question is that if a homogeneous system of equations has at least one non-zero solution, then it has infinitely many solutions, which can be found by taking multiples of the non-zero solution.

(a) (i)

Let p = (1,3,4) and q = (5,8,12) be two points in R3. The line joining p and q can be written as lq + (1-\p) where l is a real number. By substituting in the coordinates of p and q, we get l(5,8,12) + (1-\1,3,4) = (l + 1-\, l+3-\, l+4-\). This is the equation for the line joining p and q, where l can be any real number.

(ii)

To check that all points on the line joining p and q are also solutions to the system of linear equations, we substitute the equation of the line into the system of equations.

01111 + 212.22 + 213.43 = 21

(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 21

Simplifying, this gives: l + 6 - \ = 21. Therefore, all points on the line joining p and q are solutions to the system.

(b)

To check that any multiple of p, i.e., a vector of the form (1,3,4) where is any real number, is also a solution of the system, we substitute the equation of the multiple of p into the system.

01111 + 212.22 + 213.23 = 0

(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 0

Simplifying, this gives: l + 6 - \ = 0. Therefore, all multiples of p are solutions to the system.

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Answer:

=> A/Q,

m + 3m + 2m+ 3m 360° =

9m = 360°

m = 360/9

m = 40°

Angle A = m = 40°

Angle B = 3m = 120°

Angle C 2m = 80° =

Angle D = 3m = 120°

A specific example of a non-representative sample can be seen in the 2016 US presidential election.

The national polls indicated that Hilary Clinton had a lead in the polls, but Donald Trump went on to win the election. This is because the sample used in the polls was not representative of the population. The sample was disproportionately composed of college-educated individuals, when the actual electorate was more evenly balanced between college-educated and non-college-educated individuals. This caused the samples to be biased and not representative of the population.

For example, if we assume that the population is composed of 50% college-educated individuals and 50% non-college-educated individuals, then the sample should also be composed of 50% college-educated individuals and 50% non-college-educated individuals to be representative. If the sample is not composed of 50% college-educated individuals and 50% non-college-educated individuals, then the sample is not representative of the population.

This can be calculated by using the formula: (Number of College Educated Individuals in Sample/Total Sample Size) X 100.

For example, if the sample size is 100 and there are 75 college-educated individuals in the sample, then the sample is not representative of the population because (75/100) X 100 = 75%, which is not equal to the 50% of the population that is college-educated.

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In the given oblique triangle , the required value of c using cosine rule is given by c = 34.4.

As given in the question,

In the given oblique triangle ABC,

a = 12 feet

b = 30 feet

∠A = 20°

Let us consider in triangle side opposite to angle A, B, and C are a, b, and c respectively.

Using cosine rule we have,

a² = c² + b² - 2cbcos A

Substitute the values we get,

⇒ 12² = c² + 30² - 2(c )(30) cos 20°

⇒ 144 = c² + 900 - 60c ( 0.9396)

⇒ c² -56.376c + 900 - 144 = 0

⇒ c² -56.376c +756 = 0

using quadratic formula :

c = [ ( 56.376) ± √56.376² -4(1)(756) ]/ 2

  =  [ 56.376 ± 12.42 ] / 2

  =  (56.38 + 12.42) / 2 or (56.38 - 12.42) / 2

  = 34.4 or 21.98

Correct value is c = 34.4

Therefore, using the cosine rule the required values c of the triangle is equal to 34.4 .

The above question is incomplete, the complete question is :

One of the cases for the known measures of an oblique triangle is given. In triangle ABC, where a = 12 feet, b = 30 feet, and A = 20°. State whether the Law of Cosines can be used to solve the third side of the triangle .

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The interval over which the function is continuous equation is (-∞, 3) U (3, +∞).

The function f(x) = (x2 - 5x - 6)/(x - 3) is continuous over all real numbers except x = 3, since the denominator is equal to 0 at x = 3.

We can use the properties of combinations of continuous functions to determine the interval(s) over which the function f(x) is continuous equation.

First, we need to consider the function f(x) in two parts. The first part is f(x) when x ≠ 3, and the second part is when x = 3.

For the first part, when x ≠ 3, the function f(x) is continuous over all real numbers, since both the numerator and denominator are continuous over all real numbers.

For the second part, when x = 3, the function f(x) is discontinuous, since the denominator is equal to 0.

Therefore, the interval over which the function f(x) is continuous is (-∞, 3) U (3, +∞).

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Answer:

26

Step-by-step explanation:

32 - 14 + 26 - (81/9)2

Dividing

32 - 14 + 26 - (9)2

Multiplying

32 - 14 + 26 - 18

Adding & Subtracting from left to right

18 + 26 - 18

44 - 18

26