Kathleen bought 8.3 ounces of walnuts. The next day, she used 1.7 ounces of them in a recipe. How many ounces does she have left?

Answer:

7/20

Step-by-step explanation:

Answer:7/10

Step-by-step explanation:

Here is the way that I think is the simplest method of changing a percentage a fraction. This percentage has two digits in it, so put it over a 1 and two zeros and then simplify. 35/100 is simplified to 7/20.

Answer:

7,802,000,000

Step-by-step explanation:

subtract: 1,020,000,000 - 239,800,000

A radian is denoted by rad and it's the standard unit that is used for the measurement of angles.

Your information is incomplete. Therefore, an overview of radians will be given. Radian is the standard unit for angular measurement.

A radian is a unit of measure for angles which is based on the radius of circles. The formula used for radians is simply put as:

= (Degrees × π) / 180°

For example 60° will be:

= (60° × π) / 180°

= π/3

Therefore, 60° converted to radians is π/3.

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Answer:

M(4, -3)

Step-by-step explanation:

Reflecting over the x-axis is simple:

If the x is positive, the reflection would be negative and vice versa.

In this case, the y isn't affected since it's only reflecting over the x-axis.

So, M is at the coordinates (4, -3)

i. Range (A): The space spanned by the columns of matrix A. It represents all possible linear combinations of the columns of A.

ii. Null (A): The set of all vectors x such that Ax = 0. It represents the solutions to the homogeneous equation Ax = 0.

iii. Row (A): The space spanned by the rows of matrix A. It represents all possible linear combinations of the rows of A.

iv. Null (A): The set of all vectors y such that ATy = 0. It represents the solutions to the homogeneous equation ATy = 0.

The equation Ax = b has a solution only when b is in the Range (A). It has a unique solution only when the Null (A) contains only the zero vector.

The equation ATy = d has a solution only when d is in the Row (A). It has a unique solution only when the Null (A) contains only the zero vector.

Assuming the size of A is m × n:

When Ax = b has a unique solution, the space Null (A) must be equal to Rn. This means there are no non-zero vectors that satisfy Ax = 0, ensuring a unique solution.

When ATy = d has a unique solution, the space Null (AT) must be equal to Rm. This means there are no non-zero vectors that satisfy ATy = 0, ensuring a unique solution.

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Answer:

x=5

Step-by-step explanation:

7 times x

7 times 2

7x-14= 21

14+14= 21+ 14

7x=35

x=5

7 times five equals 35

If the average rate of change is 18, then the value of the x is √(13/5). Then the correct option is B.

It's an average of how far the functions changed per unit throughout that time period.

Let f be the function given by f(x) = x³ + 5x.

Then the value in the closed interval [1,3] will be

The instantaneous rate of change will be

\(f'(x) = 3x ^2 + 5\)

Then the average rate of change will be

\(= \dfrac{f(3) - f(1)}{3-1} \\\\= \dfrac{(3^3 + 5\times 3) - (1^3 + 5 \times 1)}{3-1}\\\\= 18\)

Then we have

3x² + 5 = 18

Then the value of x will be

\(\begin{aligned} \rm 3x^2 + 5 &= 18\\\\\rm x &= \sqrt{\dfrac{13}{3}} \end{aligned}\)

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Answer:

x + y = 9

y = x + 2

Step-by-step explanation:

We need to write a system of equations to represent the given situation . The statements are ,

Statement 1:- The sum of x and y is 9.

Mathematically , we can write it as ,

\(\rm\implies x + y = 9 \)

Statement 2:- The value of y is two more than the value of x.

This simply means that y equals to 2 + x , that is

\(\rm\implies y = x+2\)

Therefore the system of equations will be ,

Also when we will try to solve the equations we will get ,

\(\rm\implies x + y = 9 \)

Put y = x + 2 , we have ,

\(\rm\implies x + x + 2= 9 \)

Add the like terms ,

\(\rm\implies 2x +2 = 9 \)

Transpose 2 to RHS ,

\(\rm\implies 2x = 9 -2 = 7\)

Divide both sides by 2 ,

\(\rm\implies \boxed{\blue{\rm\quad x = 3.5\quad}}\)

Similarly we will get the value of as ,

\(\rm\implies 3.5 + y = 9 \)

Transpose 3.5 to RHS ,

\(\rm\implies y = 9 - 3.5 \)

\(\rm\implies \boxed{\blue{\rm\quad y = 5.5\quad}}\)

Therefore ,

\(\begin{cases} \rm x = 3.5 \\\\\rm y = 5.5 \end{cases}\)

The energy released by this deuterium-deuterium reaction is 4.03 MeV.

a. i.  The half-life, T1/2 = 3.83 days or 3.31 x 105 s.

Initial number of radon atoms N0 = 3.0 x 107

Number of radon atoms that remain after 31 days =

We can find the number of remaining radon atoms by using the radioactive decay formula as:

N = N0 (1/2)n

where n = number of half-lives undergone.

Therefore, the number of half-lives undergone is given by

n = t/T1/2

  = 31/3.83

  = 8.09

Thus, the number of remaining radon atoms is given by

N = N0 (1/2)n

   = 3.0 x 107 (1/2)8.09

   = 3.0 x 107 (0.00457)

   = 137,190

ii. Initial activity = 100%

Number of radon atoms after sealing the basement against further entry of radon = 0

Activity after sealing the basement against further entry of radon = 0%

iii. Final activity =

Since the half-life is 3.83 days, it is easy to find the decay constant

λ = 0.693/T1/2

  = 0.693/3.83

  = 0.181/day

The activity of a radioactive substance is given by

A = λN

where N = number of radioactive nuclei present.

Substituting the values, we get

A = 0.181 x 137,190

   = 24,824 disintegrations/day.

The activity 31 days later would be the same as above as the number of radon atoms is the same.

b. The given reaction is deuterium + deuterium -> tritium + hydrogen.

The mass defect, Δm = [2.014102 u + 2.014102 u] - [3.016049 u + 1.007825 u]= 4.028204 u - 4.023874 u= 0.00433 u

The energy released E is given by Einstein’s mass-energy equation:

E = Δm c2where c is the speed of light.

E = (0.00433 u) (931.5 MeV/u) = 4.03 MeV

Therefore, the energy released by this deuterium-deuterium reaction is 4.03 MeV.

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The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

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The limit definition of a derivative is a mathematical method used to calculate the instant rate of change of a characteristic at a particular point. it is based at the idea of the limit of a function because the input techniques a certain cost.

The limit definition of a derivative is expressed as follows:

\(f'(x) = lim (h → 0) [f(x + h) - f(x)] /h\)

Wherein f'(x) represents the derivative of the function f(x) at a particular factor x. The expression \(( f(x + h) - f(x)) / h\) represents the common price of alternate of the characteristic over a small interval of size h, focused at x. The limit of this expression as h approaches 0 represents the instant fee of change of the characteristic at x, or the slope of the tangent line to the function at that factor.

The limit definition of a derivative is a fundamental concept in calculus and is used to calculate the slopes of tangent lines, to find maximum and minimum factors, and to clear up optimization issues in a huge variety of packages.

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Answer:

56

Step-by-step explanation:

Answer:

11.5652173913

Step-by-step explanation:

You might have to round

Answer:

Step-by-step explanation:

oh thats easy its 2

The term "resilience" encompasses the psychological processes and traits that enable individuals to deal with traumas and recover their healthy and effective functioning.

To understand resilience more deeply, let's consider a mathematical analogy.

Just as mathematical equations can be adjusted or modified to solve different problems, individuals need to adapt their coping mechanisms to match the specific demands of a trauma. Being adaptable allows people to assess the situation, identify necessary adjustments, and find effective strategies for recovery.

Resilience is not solely about returning to a pre-trauma state but also involves personal growth and transformation. In mathematics, this growth can be compared to solving a complex problem that requires expanding one's knowledge and skills.

It's important to note that resilience is not a fixed trait, but rather a dynamic process that can be developed and strengthened over time. Just as mathematical skills can be improved through practice and learning, individuals can cultivate resilience through various interventions, such as therapy, support groups, self-care practices, and building healthy relationships.

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Answer:

r=\(\frac{3t}{t-1}\)

Step-by-step explanation:

t(r-3)=r

tr-3t=r

tr-r=3t

r(t-1)=3t

r=\(\frac{3t}{t-1}\)

1. The height of the cone is equal to

2. You can solve for the slant height, s by applying Pythagorean's theorem.

3. To get from the base of the cone to the top of the hill, an ant has to crawl 29 mm.

In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:

Volume of cone, V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

8792 =  1/3 × 3.14 × 20² × h

26,376 =  3.14 × 400 × h

Height, h = 26,376/1,256

Height, h = 21 mm.

Question 2.

In order to solve for the slant height, s, we would have to apply Pythagorean's theorem since the height of the cone has been calculated above.

Question 3.

By applying Pythagorean's theorem, we have the following:

r² + h² = s²

20² + 21² = s²

400 + 441 = s²

s² = 841

Slant height, s = √841

Slant height, s = 29 mm.

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Polynomial \($-1+x^3-\frac{1}{3} x^3$\) and its conventional form, \(x^5-\frac{x^2}{3}-1$$\) , are both used.

\($$-1+x^5-\frac{1}{3} x^2=x^5-\frac{x^2}{3}-1$$\)

steps

\($$-1+x^5-\frac{1}{3} x^2$$\)

\(\begin{aligned}& \frac{1}{3} x^2=\frac{x^2}{3} \\& =-1+x^5-\frac{x^2}{3}\end{aligned}\)

rephrase in proper grammar

\(=x^5-\frac{x^2}{3}-1$$\)

The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial. You must consider each term's degree in order to write any polynomial in standard form.

Next, list each phrase in order of degree, left to right, highest to lowest. An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial.

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A(n) "correlational" design is used when the researcher wants to test a relationship between existing variables. This design aims to determine the degree to which two variables are related or associated with each other. In a correlational design, the researcher measures the variables of interest and examines the statistical relationship between them, typically using correlation coefficients.

On the other hand, a(n) "experimental" design is used when a researcher wants to test a causal link between variables. In an experimental design, the researcher manipulates one or more independent variables and measures the effect on a dependent variable. By controlling for confounding variables and using random assignment, an experimental design allows for causal inferences to be made.

It's important to note that while correlational designs can provide valuable insights into the relationships between variables, they do not establish causality. Experimental designs, on the other hand, provide stronger evidence for causal relationships by systematically manipulating variables.

A(n) \(\textbf{correlational}\) design is used when the researcher wants to test a relationship between existing variables.

A(n) \(\textbf{experimental}\) design is used when a researcher wants to test a causal link between variables.

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The amount of each monthly installment is $1,294 and the hire purchase of the car​ is: $4,158.

a.  Monthly installment

2 1/2 years=30 months

First step

Amount payable=[49,500×(1-.30)] /30 months

Amount payable=(49,500×.70)/30 months

Amount payable=$34,650/30 months

Amount payable=$1,155

Second step

Amount of monthly installment=[$1,155×(1+0.12)

Amount of monthly installment=$1,155×1.12

Amount of monthly installment=$1,293.6

Amount of monthly installment=$1,294 (Approximately)

b. Hire purchase

Hire purchase=$1,155×.12×30 months

Hire purchase=$4,158

Therefore the amount of each monthly installment is $1,294 and the hire purchase of the car​ is: $4,158.

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Answer: wouldn't that be 62 because line IJ is intersecting the parallel lines?

Sorry if i'm wrong but hope it helps.

The smallest value of x is 2 for which these three numbers 2, 60, and 240 have an LCM of 240.

LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.

Given, Are three numbers x, 60, and 240 of which x is unknown.

The lowest common multiple of these three numbers will be when x is the smallest.

Let x be 2 therefore the numbers are now, 2, 60, and 240.

And LCM of 2, 60, and 240 is 240 as it is the smallest number that is divisible by all these three numbers.

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Answer:

152 US quarts

Step-by-step explanation:

4 x 38 = 152

quarts = 4 of something

Answer:

152

Step-by-step explanation:

38 x 4 = 152

Compare the values of r for all three groups to determine which group has the strongest linear relationship.

Calculate the values of r for each group of linearly related bivariate data and compare them to determine the strongest linear relationship. The explanation step-wise involves calculating the correlation coefficient for each group.

In the first group, the bivariate data has a linear relationship.  we need to determine the value of r for each group. The explanation step-wise is as follows:

1. For group 1, the value of r is missing. To find it, calculate the correlation coefficient using the given data points.

2. Repeat the same process for group 2 and group 3 to find their respective values of r.

3. Compare the values of r for all three groups to determine which group has the strongest linear relationship.

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The name for a data value that is far above or below the rest is called an outlier.

An outlier is an observation that deviates significantly from other observations in a dataset. It is an extreme value that lies outside the typical range of values and may have a disproportionate impact on statistical analyses and calculations. Outliers can occur due to various reasons, including measurement errors, data entry mistakes, or genuine rare events. Identifying and handling outliers appropriately is important in data analysis to ensure accurate and reliable results.

When dealing with outliers, it is important to assess whether they are the result of errors or genuine extreme values. Statistical techniques, such as box plots, scatter plots, or z-scores, can be used to detect outliers. Once identified, the appropriate action depends on the nature and cause of the outliers. In some cases, outliers may need to be corrected or removed from the dataset, while in other cases, they may provide valuable insights or require further investigation.

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The employee's yearly salary is calculated as $37,440 using the arithmetic operations.  

The employee earns $18 per hour and works 40 hours per week. To calculate the weekly salary, we multiply the hourly wage by the number of hours worked:

Weekly salary = Hourly wage × Hours worked per week

Weekly salary = $18/hour × 40 hours/week = $720

Next, to calculate the yearly salary, we use the multiplication operation the weekly salary by the number of weeks in a year:

Yearly salary = Weekly salary × Weeks in a year

Yearly salary = $720/week × 52 weeks/year = $37,440

Therefore, the employee's yearly salary is $37,440. This calculation assumes a 40-hour work week and 52 weeks in a year. It's important to note that this calculation does not account for overtime pay or any other additional benefits or deductions that may affect the employee's total annual income.

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An appropriate statement of the null hypothesis, H₀ is that: A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.

In Mathematics, a null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (Ha) and it asserts that two (2) possibilities are the same.

For an experiment to test the contamination of medical personnel wrist-watches at a New York hospital, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:

H₀: p = 10.

Ha: p < 10.

In this context, we can logically that the proportion of contaminated wrist-watches would be the same for both sample proportion i.e., H₀: p = 46.6%.

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