At Sparky' Candy World, Mile pent a total of $13. 75 on gummy bear and jelly bean. He bought 2. 5 pound of gummy bear at $3. 40 per pound. If jelly bean cot $1. 50 per pound, how many pound of jelly bean did he buy?

Answer:

\( \sqrt[3]{216} = \sqrt[3]{ {6}^{3} } = 6\)

this is your answer

The value of the integral comes out to be ∫(3t4 - 9)t3dt = ((30/7 + 6/5 + 6)√10).

To determine the change of variables from t to u, it is important to first calculate the function's derivative. Let's check it.  f(t) = (3t4 - 9)t3 f'(t)

= 3(3t4 - 9)t2 + (3t4 - 9)3t2

f'(t) = (9t2 + 3t4 - 27)t2

f'(t) = 3t2(3 + t2 - 9)

f'(t) = 3t2(t2 - 6)

We observe that the only linear expression is t2 - 6; thus, we can rewrite t2 as

u + 9. u + 9 - 6 = u + 3 u = t2 - 6 u = t2 + 9

Now we need to rewrite the integral in terms of u.

dt = (du/(2√u + 18))

t3 = (u + 3)3

Rewrite ∫(3t4 - 9)t3dt as ∫(3(u + 9)2 - 9)(u + 3)3(du/(2√u + 18))

 ∫(3u2 - 6)(u + 3)3(du/(2√u + 18)) ∫(3u2 - 6)(u + 3)3(1/2(√u + 9)du) ∫(3u2 - 6)(u + 3)3/2(√u + 9)du

Now we can evaluate the integral.

Let u + 9 = v2 v = √u + 9 du = 2vdv Change the limits of integration:

t = 0 → u = 0

t = 1 → u = 1 + 9 = 10

The new limits of integration are 0 → 3.

We integrate now using the substitution:

∫(3u2 - 6)(u + 3)3/2(√u + 9)du ∫(3(v2 - 9) - 6)(v2)(1/2)v(2)dv ∫(3v4 - 36v2 - 6v2 + 54)v dv ∫(3v5 - 42v3 + 54v)dv ∫3v(v - √14)(v + √14)5/2dv

= 3/7(v + √14)7/2 - 3/5(v - √14)5/2 + 3/3(v + √14)3/2  

= 3/7(√10)7/2 - 3/5(-√10)5/2 + 3/3(√10)3/2  

= 3/7(10√10) - 3/5(-10√10) + 3/3(2√10)  

= (30/7 + 6/5 + 6)√10 ∫(3t4 - 9)t3dt

= ((30/7 + 6/5 + 6)√10)

Thus, ∫(3t4 - 9)t3dt = ((30/7 + 6/5 + 6)√10)

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Answer:

its called a calculator division and multiplication

Step-by-step explanation:

Answer:

C. P = 30

Step-by-step explanation:

Parallelogram opposite (or parallel) sides are equal,

so:

2x = x + 2

5y - 9 = 2y + 3

For x:

2x = x + 2

2x - x = 2

x = 2

For y:

5y - 9 = 2y + 3

5y - 2y = 3 + 9

3y = 12

y = 4

the smallest sides are equal 2x and x + 2 => 2 * 2 = 4

the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11

P = 2 * (a + b)

P = 2 * (4 + 11)

P = 2 * 15

P = 30

Answer:

Step-by-step explanation:

a) Jamal spent:

Isaiah spent:

The equation is:

b) Solving the equation

c) Jamal's items cost

Isaiah's items cost

Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.

The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.

Congruence :

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.

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Answer:

the correct mean is greater than Eva's mean

Answer:

35

Step-by-step explanation: I used a protractor

Answer:

35 degrees.

Step-by-step explanation:

To figure this question out, we first need to understand how to solve it. We know that all the angles in a triangle add up to 180 degrees. we can imagine this is a massive triangle. We can do the following

73 + 51 + (21+x) = 180

we can do this, because we already know the other two angles, and we know part of the last angle is 21, and the other part of the last angle is x. We can add them all together.

124 + 21 + x =180

145 + x =180

35 = x

The population after 105 minutes is 282651.0114.

What is exponential growth?

Exponential growth is the process by which quantity rises over time. It occurs when a quantity's instantaneous rate of change with regard to time is proportionate to the quantity itself.

Here, we have

Given: The count in a bacteria culture was 200 after 15 minutes and 1500 after 40 minutes. Assuming the count grows exponentially.

Exponential growth is modeled by the equation: P(t) = P₀\(e^{kt}\)....(1)

where P(t) is the population at time t, P₀ is the initial population and k is the growth rate.

Given

200 after 15 minutes

Now, we put the values in equation (1) and we get

200 = P₀\(e^{15k}\)...(2)

Also, 1500 after 40 minutes

1500 = P₀\(e^{40k}\)...(3)

Now, we divide equation(3)by (2) and we get

1500/200 = \(e^{40k}\)/\(e^{15k}\)

15/2 = \(e^{25k}\)

Now, we take a log and we get

ln(15/2) = 25k

k = ln(15/2)/25

k = 0.0805

Now, we put the value of k in equation(2) and we get

200 = P₀\(e^{15(0.0805)}\)

Initial size of the culture P₀ = 59.702

Now, we find the doubling period:

f(t) = 2P₀

We know that f(t) = P₀\(e^{kt}\).

2P₀ = P₀\(e^{kt}\)

\(e^{kt}\) = 2

Now, we take a log and we get

ln(2) = kt

t = ln(2)/k

t = ln(2)/0.0805

t = 8.600

The time taken to doubling period is 8.600 minutes.

Population after 105 minutes:

f(t) = P₀\(e^{kt}\)

f(t) = 59.702\(e^{0.0805*105}\)

f(t) = 282651.0114

Hence, the population after 105 minutes is 282651.0114.

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True, Logarithms were used extensively for complicated calculations before the electronic calculator became widely available. A logarithm is a mathematical function that helps simplify complex arithmetic operations by converting multiplication and division into addition and subtraction, respectively.

By using logarithms, complex calculations could be broken down into simpler steps and performed more easily. Logarithms were particularly useful in fields such as astronomy, physics, and engineering, where large numbers and complicated formulas were common. However, with the advent of electronic calculators, the use of logarithms for everyday calculations declined. Today, logarithms are still used in certain fields and for specific applications, but they are no longer the primary tool for carrying out complicated calculations.

Before the electronic calculator became widely available, logarithms were used to carry out complicated calculations. Logarithms simplified complex calculations by turning multiplication and division operations into addition and subtraction.

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The measures of central tendency and measures of dispersion are complementary to each other and provide a complete description of the data distribution.

Measures of central tendency and measures of dispersion are complementary to each other while describing and analyzing a given set of data. Measures of central tendency describe the central location of the data distribution, whereas measures of dispersion describe the degree of variability in the data distribution. The measures of central tendency are the mean, median, and mode, which provide an indication of the location of the center of the data.

On the other hand, measures of dispersion include the range, variance, standard deviation, and interquartile range, which provide an indication of the spread of the data from the center. Measures of central tendency and measures of dispersion work together to give a complete description of the data distribution.

If we only describe the central tendency of the data, we would miss out on important information about the variability of the data.

Likewise, if we only describe the dispersion of the data, we would miss out on information about the location of the center of the data distribution.

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The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

Answer: The answer is x = 6.5

Answer:

63.25 KG

Step-by-step explanation:

Convert 15% to a decimal, then add 1 and multiply 15.

\(55 \times (1 + 0.15) = 63.25\)

To calculate the monthly principal + interest payments for a house with a down payment and a mortgage using an Excel formula, you can use the PMT function. Here's how:

Calculate the loan amount by subtracting the down payment from the house cost. In this case, the down payment is 25% of $300,000, so it would be $75,000.
  Loan Amount = $300,000 - $75,000 = $225,000    

Determine the monthly interest rate by dividing the annual interest rate by 12. In this case, the annual interest rate is 2.75%, so the monthly interest rate would be 2.75% / 12 = 0.00229.

Determine the loan term in months. Since it's a 30-year mortgage, the loan term would be 30 * 12 = 360 months.

Use the PMT function in Excel to calculate the monthly principal + interest payment.
  Monthly Payment = -PMT(0.00229, 360, 225000)

The negative sign is used because the payment is an outgoing cash flow.

By using this formula in Excel, you can find the monthly principal + interest payments for your mortgage. Remember to adjust the interest rate, loan amount, and loan term if they differ from the example provided.

To calculate the monthly principal + interest payments using an Excel formula, you can use the PMT function by inputting the appropriate parameters: the monthly interest rate, loan term in months, and loan amount.

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The given word phrase "C multiplied by eleven = C plus 2 whole square" into algebraic expression is "C × 11 = (C + 2)²".

The Algebraic Expression is defined as a mathematical phrase which contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

The left-hand side of the equation says that C is multiplied by 11.

Which is written as : C × 11 ;

The right-hand side says that C is increased by 2 and then squared.

It is written as : (C + 2)²;

So, on combining the left hand side and right hand side, the Algebraic Expression is "C × 11 = (C + 2)²".

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The given question is incomplete, the complete question is

Translate the given word phrases into algebraic expression

"C multiplied by eleven = C plus 2 whole square".

The price change that would lead to a margin call can be calculated using the formula: Price change = (Maintenance margin - Account balance) / (Number of contracts * Size of contract), Aprice decrease of 0.05 cents per pound would lead to a margin call.

1. Calculate the total initial margin:
  Total initial margin = Initial margin per contract * Number of contracts
  Total initial margin = $5,000 * 2 = $10,000
2. Calculate the total size of the contracts:
  Total size of contracts = Number of contracts * Size of contract
  Total size of contracts = 2 * 12,000 = 24,000 pounds

3. Calculate the account balance at which a margin call would occur:
  Account balance = Maintenance margin per contract * Number of contracts
  Account balance = $3,800 * 2 = $7,600
4. Calculate the price change that would lead to a margin call:
  Price change = (Maintenance margin - Account balance) / (Number of contracts * Size of contract)
  Price change = ($7,600 - $10,000) / (2 * 24,000)
  Price change = -$2,400 / 48,000
  Price change = -0.05 cents per pound
Therefore, a price decrease of 0.05 cents per pound would lead to a margin call.

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Answer

The triangle might be an equilateral triangle.

False

The triangle must be a right triangle.

False

The triangle might be an acute triangle.

True

Explanation

First of, we will explain the different types of triangles that exist based on side lengths and angle measures respectively,

Based on side lengths,

- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.

- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.

- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.

Based on angle measures,

- Acute triangle has all of the angles in the triangle being less than 90 degrees.

- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.

- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.

So, a sketch of the triangle described would look like

So, we can see that the triangle has two sides equal, hence, the two base angles will be equal to.

If we call those base angles, x,

x + x + 45° = 180°

2x = 180° - 45°

2x = 135°

Divide both sides by 2

(2x/2) = (135°/2)

x = 67.5°

Three angles of the triangle are 45°, 67.5° and 67.5°

So, taking the statements one at a time now

The triangle might be an equilateral triangle.

This statement is False since it is evident that all the angles of this triangle are not equal to one another, hence, the sides cannot all be equal too.

The triangle must be a right triangle.

This statement too, is False. None of the angles of the triangle is equal to 90°.

The triangle might be an acute triangle.

This statement is True. All of the angles of the triangle are less than 90°.

Hope this Helps!!!

Answer:

Rule 3

Step-by-step explanation:

The values correspond to the equation y=3^x

The correct answer is B i.e. Standard Error of the Mean (SE) = σ / √(n)

The measure of the variability of the sample means, also known as the standard error of the mean, can be calculated using the formula:

Standard Error of the Mean (SE) = σ / √(n)

sigma is the population standard deviation,

n is the sample size.

The standard error of the mean represents the variability or dispersion of the sample means obtained from repeated samples of size n from a population. It indicates how much the sample means are likely to differ from the true population mean.

The smaller the standard error of the mean, the less variability is expected among the sample means, indicating a more precise estimate of the population mean.

Therefore, the correct answer is B i.e. Standard Error of the Mean (SE) = σ / √(n)

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Given question is incomplete, the complete question is below

A measure of variability of the sample means xbar in repeated samples of n observations randomly selected from a given population is

a. s

b. σ/√(n)

c. s/√(n)

d. σ

Answer:

x = -23

Step-by-step explanation:

The absolute threshold is defined as the minimum detectable stimulus or intensity.

The absolute threshold refers to the minimum amount or level of a stimulus that is required for it to be detected or perceived by an individual. It is the point at which a stimulus becomes perceptible or noticeable to a person.

In sensory psychology, the absolute threshold is typically measured in terms of the lowest intensity or magnitude of a stimulus that can be detected accurately by a person at least 50% of the time. It represents the boundary between the absence of perception and the presence of perception.

The absolute threshold can vary depending on the sensory modality being tested. For example, in vision, it may refer to the minimum amount of light required for a person to see an object. In hearing, it may represent the minimum sound intensity needed for an individual to hear a tone.

Several factors can influence the absolute threshold, including individual differences, physiological factors, and the nature of the stimulus itself. Factors such as sensory acuity, attention, fatigue, and background noise can all affect an individual's ability to detect a stimulus.

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The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

Learn about the dimensions and components of matrices by starting your first introduction. A rectangular grid of numbers organized into rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. matrix, a collection of numbers lined up in rows and columns to create a rectangular array.  In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics. It is so named because there is just one row, and a row matrix has the order 1 n as a result.

given

Eigen values ( λ )

| A - λI | = 0

=  ( 7 - λ ) ( 11 - λ ) ( 11 - λ ) =0

= λ = 7 , 11 , 11

eigen vector for λ = 7

( A - IB ) X = 0

= Let y = 1 , n1 = ( -1  1  0 )

eigen vector for λ = 11

( A - λI ) X = 0

n2 = ( 0 1 0 ) let n3= ( -2 0 1 )

D = ( 7 0 0 ,  0 11 0 , 0 0 11 )

The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

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Answer:

4 hours

Step-by-step explanation:

Given that:

Initial height of red candle = 8 inches

Rate of burning of red candle = \(\frac{7}{10}\ inch/hr\)

Initial height of blue candle = 6 inches

Rate of burning of blue candle = \(\frac{1}{5}\ inch/hr\)

To find:

Time taken in hours such that both the candles have the same height.

Solution:

Let the time taken such that both the candles have the same height = \(t\) hours

Height of red candle after \(t\) hours = \((8 - \frac{7}{10}t) \ inches\)

Height of blue candle after \(t\) hours = \((6 - \frac{1}{5}t) \ inches\)

Writing both the expressions as equal:

\(8-\dfrac{7}{10}t=6-\dfrac{1}{5}t\\\Rightarrow 8-6=\dfrac{7}{10}-\dfrac{1}{5}t\\\Rightarrow 2 = (\dfrac{7-2}{10})t\\\Rightarrow \dfrac{5t}{10}=2\\\Rightarrow t=4\ hours\)

After 4 hours, height of both the candles will be same.

1.1 Using Laplace transforms, we can solve the given differential equation by transforming it into the frequency domain, determining the transfer function, and obtaining the solution through inverse Laplace transform.

1.2 Alternatively, the reduction of order method can be applied to solve the problem.

1.1 To solve the differential equation using Laplace transforms, we first apply the Laplace transform to the equation. Taking the Laplace transform of y" - y = sin(wt), we get \(p^2^Y\) - p - Y = 1/(p²+ w²), where Y is the Laplace transform of y and p is the Laplace transform variable.

Next, we determine the transfer function G(p) by rearranging the equation to isolate Y. Simplifying and applying partial fractions, we can express G(p) as Y = 1/(p²+ w²) + p/(p²+ w²).

Then, we solve for Y from the transfer function G(p). In this case, Y = 1/(p² + w²) + p/(p² + w²).

Finally, we determine L-¹(Y) by taking the inverse Laplace transform of Y. The inverse Laplace transform of 1/(p² + w²) is sin(wt), and the inverse Laplace transform of p/(p² + w²) is cos(wt).

Therefore, the solution y(t) obtained is y(t) = sin(wt) + cos(wt).

1.2 The reduction of order method is an alternative approach to solving the differential equation. This method involves introducing a new variable, u(t), such that y = u(t)v(t). By substituting this expression into the differential equation and simplifying, we can solve for v(t). The solution obtained for v(t) is then used to find u(t), and ultimately, y(t).

1.3 The Laplace transform method offers several advantages. It allows us to solve differential equations in the frequency domain, simplifying the algebraic manipulations involved in solving the equation. Laplace transforms also provide a systematic approach to handle initial conditions. Additionally, the use of Laplace transforms enables the application of techniques such as partial fractions for simplification.

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Answer:

10.60 inches

Step-by-step explanation:

18.45

-7.85

_____

10.60 inches

On solving the provided question we can say that - rate at which customers are entering the store in customers per minute is 4 minutes.

In order to calculate numerous unit values, a single unit value must first be determined. This is known as a unitary method. With the idea of dimensions and proportions, this strategy is mostly employed. The unit technique can be applied in either direct or indirect ways. A singular or unique entity is referred to by the word "unitary." The value will be determined using this procedure in terms of a single entity. The unit system, for instance, may be used to calculate the distance covered by a car on one liter of gasoline if it drives 44 km on two.

as per the question,

2 costumers enter over course of = 8 minutes

so, 1 costumers enter over course of = 8/2 =4 minutes

Hence,

rate at which customers are entering the store in customers per minute is 4 minutes.

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Answer:  \(\textsf{ab} > \textsf{0}\)

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Given: \(\textsf{a} > \textsf{0 and b} > \textsf{0}\)

Find:  \(\textsf{ab } \_\_\_ \textsf{ 0}\)

Solution: Since we know both a and b are positive this means that if they are multiplied against each other they would produce another positive. Therefore, this would cause the statement to be ab > 0.