Slices of cake were sold at a bake sale.
In total, Archie sold 33 cakes and Pam sold
7³ cakes.
How many more cakes than Archie did Pam
sell?
Give your answer as a mixed number in its
simplest form.

Jamie multiplied 3x and 7 by -5 to eliminate the parentheses.

This procedure is justified by the distributive property.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

When we need to multiply a number by the sum of two numbers, the distributive property of multiplication over addition comes into play. Let's multiply 7 by the sum of 20 plus 3 as an illustration. This can be expressed mathematically as 7(20 + 3).

The distributive rule of multiplication over addition and subtraction is another name for the distributive property. By its very name, the procedure implies that something will be divided or distributed. Both addition and subtraction are under the scope of the distributive law.

Jamie multiplied 3x and 7 by -5 to eliminate the parentheses.

This procedure is justified by the distributive property.

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There are 5 positive pair factors of 36 (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6).

Positive pair factors are factors that increase the likelihood of a successful relationship between two people. These factors include communication, trust, respect, understanding, appreciation, commitment, shared values, and mutual support. Communication is essential for a strong relationship. It allows two people to express themselves and share their thoughts, feelings, and experiences. Trust is another important factor in a positive relationship. It is important, to be honest, and open with one another and to feel secure that your partner is trustworthy. Respect is also important and involves treating each other with kindness and respect.  

Understanding is another important factor in a positive relationship, as it allows two people to understand each other’s perspectives and feelings. Appreciation is also important and involves recognizing the other person’s efforts, successes, and achievements. Commitment is another important factor, as it shows that both people are dedicated and committed to the relationship. Shared values are also important, as it allows two people to have shared goals, beliefs, and desires. Finally, mutual support is an essential factor in a positive relationship, as it allows two people to provide each other with emotional and practical support.

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The number of integral solutions of the given equation x₁ + x₂ + x₃ = 0 with [tex]x_{i}[/tex] ≥ (-5) is 136.

Suppose we wish to determine the number of integer -tuples (₁,…,[tex]x_{k}[/tex])

such that

₁ +⋯+ [tex]x_{k}[/tex] = , [tex]x_{i}[/tex] ≥ [tex]c_{i}[/tex] …(1)

The transformation [tex]y_{i}[/tex] = [tex]x_{i}[/tex] − [tex]c_{i}[/tex], 1 ≤ ≤ reduces (1) to

₁ +⋯+ [tex]y_{k}[/tex] = − (₁ +⋯+ [tex]c_{k}[/tex]), [tex]y_{i}[/tex] ≥ 0…(2)

The number of solutions to (2)

is given by the binomial coefficient [tex]\binom {(n-c_{1}- ... -c_{k})+k-1 }{k-1}[/tex].

For the given problem, = 3, = 0, and each [tex]c_{i}[/tex] = −5. Therefore, the number of solutions is

[tex]\binom {17}{2}=^{17}C_2=\frac{17!}{2!(17-2)!}[/tex]

= 136.

Thus, 136 integral solutions are there to x₁ + x₂ + x₃ = 0 with [tex]x_{i}[/tex] ≥ (-5).

--The given question is incorrect; the correct question is

"How many integral solutions does x₁ + x₂ + x₃ = 0 have if  [tex]x_{i}[/tex] ≥ (-5)?"--

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The type of sampling design like this is is a stratified random sampling design.

This is a stratified random sampling design. The population is divided into two strata, one for female applicants and one for male applicants, and a random sample is selected from each stratum.

Stratified random sampling is a method of sampling that involves dividing the population into smaller groups or strata based on certain characteristics, and then randomly selecting a sample from each stratum. In this case, the population of applicants is divided into two strata: female applicants and male applicants.

A random sample of 15% of the female applicants who were not hired and 15% of the male applicants who were not hired are then selected and compared with the records of the recent hires. This allows for a more representative sample of the population as it ensures that both genders are represented in the sample, and also allows for a comparison of the hiring process between the two groups.

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Since the function y = 80 + 2x represents his grade, y, after x weeks, the meaning of the slope of the line is: D. He increases his grade by 2 points each week.

In Mathematics, a slope is sometimes referred to as rate of change or gradient and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

Based on the information provided, we have the following function which represents Joseph's grade after a certain number of weeks;

y = 80 + 2x

where:

In this context, we can reasonably infer and logically deduce that Joseph's grade increases by 2 points each week.

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Answer:

24

Step-by-step explanation:

you multiply 5 by 3 to get 15 so you multiply 8 by 3 also

Answer:

  yes, for positive numbers

Step-by-step explanation:

You want to know if the number of arrays that represent a number is equal to the number of factor pairs of that number.

We assume that we're only concerned with Natural numbers (positive integers).

We assume that the factor pair 2×3 is indistinguishable from the factor pair 3×2, and that an array of 2 rows and 3 columns is indistinguishable from an array of 3 rows and 2 columns.

Each array corresponds to a factor pair. One factor of the pair specifies the number of rows; the other factor specifies the number of columns. The product of those factors is the number of interest.

Example

  12 = 1·12 = 2·6 = 3·4 . . . . . factor pairs listed with smallest factor first

The attachment shows arrays associated with these factor pairs.

If the number is a square number, then there will be an odd number of divisors. One of the divisors is repeated to make the factor pair. This results in a square array as one of the arrays that represent the square number. The second attachment shows arrays for the square number 9.

There will be as many arrays as there are factor pairs.

The measurement of angles C and F are 63°  and 59° respectively

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.

In the given image, you notice that angles A, B and C form a right-angled triangle. So the measurement of angle C is 90°. Also, the sum of angles in a triangle is 180°. Thus:

A + B + C = 180°

27° + 90° + C = 180°

117° + C = 180°

C =  180° - 117°

C = 63°

Likewise, angles D, E and F form a right-angled triangle. So the measurement of angle E is 90°. Also, the sum of angles in a triangle is 180°. Thus:

D + E + F = 180°

31° + 90° + F = 180°

121° + F = 180°

F =  180° - 121°

F = 59°

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If 1500 g can be divided evenly into batches of bread that are 70 g each, then the baker should choose the 1500 g package.

To check this, we can divide 1500 g by 70 g to see how many batches of bread can be made:

1500 g / 70 g = 21.428571428571427

Since this is a non-whole number, it means that some of the dough would be wasted if the baker chooses a package of 1500 g. The baker should choose the 1500 g package, as it can be divided evenly into batches of bread that are 70 g each.

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The nth term of the sequence 100 is 592

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

[tex]a, ar, ar^2, ar^3, \cdots[/tex]

 (till the terms to which it is defined)

Thus, the nth term of such sequence would be  [tex]T_n = ar^{n-1}[/tex] (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).

Given;

Sequence=-2,4...

D=4-(-2)

=6

Now, we have to find 100th term

So, n=100

an = a + (n – 1)d

=-2+(100-1)6

=-2+99x6

=592

Therefore, the answer of given sequence will be 592

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$a^4 - 3a^2 + 9$ can be factorised as $(a^2 - 3)(a^2 + 3)$

To factor $a^4 - 3a^2 + 9$ as a product of two monic quadratics with integer coefficients, we can use the difference of squares factorization.

When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b).

$a^4 - 3a^2 + 9$ can be factored as $(a^2 - 3)(a^2 + 3)$

Notice that both factors are monic quadratics with integer coefficients.

So, $a^4 - 3a^2 + 9$ = $(a^2 - 3)(a^2 + 3)$

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Since, 3 ¼ = ¾. So,  Â¾ is equivalent to 3 ¼. Since ¾ is written as 0.75 in fractional notation.

The fraction ¾, which is equivalent to 0.75, is shown by the fractional notation "â...". The bottom number, or denominator, must be multiplied by the top number in order to comprehend this fraction (top number). 4 times 3 in this instance equals 12, which is true. Find the fractional value by first dividing the numerator by the denominator. In this case, the result of 3 divided by 4 is 0.75, or 3/4.

To calculate a fractional value, use the following formula:

Fractional Value: Numerator / Denominator:

The numerator is multiplied by the denominator to arrive at 12 when calculating the fractional value of 3/4. Following that, the fractional value is obtained by dividing the numerator by the denominator:

Fractional value equals 3 / 4 = 0.75

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Answer:$917.59

Step-by-step explanation:

The formula for compound interest is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the initial deposit is $500, the annual interest rate is 4%, the number of times compounded per year is 12 (monthly), and the number of years is 12.

So, we can plug in the values into the formula:

A = $500(1 + 0.04/12)^(12*12) = $500(1.003333333)^(144) = $500(1.835170816) = $917.585

The final amount in her account after 12 years is $917.58

To round to the nearest cent, we can use the following method:

If the digit in the thousandths place is less than 5, we keep the hundredths digit as is.

If the digit in the thousandths place is greater than 5, we round up the hundredths digit.

In this case the digit in the thousandths is 5 so, we have to round up the hundredths digit of $917.58.

Step-by-step explanation:

By Arithmetic Progression,

The first term a1=70.1

Common difference, d= 72.2-70.1=74.3-72.2= 2.1

Nth term, T_n=a1+(n-1)d where n=time taken in minutes

T_n=70.1+[2.1*(n-1)]

(b) n=12

T=93.2°F

The value of x = -1 and y = 3.

To solve the system of equations using substitution, we can start by isolating one of the variables in one of the equations. For example, in the first equation, 7x - y = -10, you can add y to both sides to get y = 7x + 10.

Then we can substitute this expression for y into the second equation, 3y - x = 10, to get:

3(7x + 10) - x = 10

This simplifies to:

21x + 30 - x = 10

20x = -20

x = -1

Now we know that x = -1, we can substitute that back into the first equation or the expression we found for y to find the value of y

y = 7x + 10

y = 7(-1) + 10

y = -7 + 10

y = 3

So the solution of the system is x = -1 and y = 3

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The full question is:

Solve the given equations by substitution and find the value of x and y. Equationns: 7x-y=-10 and 3y-x=10

The equation of line is y= 1/4x -1

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Step1:

Given:

slope = 1/4 and y intercept = -1

Using slope- intercept form

Step2:

y= mx + b

y= 1/4x + (-1)

y= 1/4x -1

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Answer:

B. 0.4

Step-by-step explanation:

Probability (picking red paper) = preferred/sample

Preferred outcome (picking red) = 8 pieces.

Sample size is total outcome (paper in hat) = 20 pieces.

P(picking red paper) = 8/20

P(red) = 0.4 or 40%

Hope this helped :)

The system of equations shown is 4x + 2y = 200.

Where x represents the number of cookies with frosting and y represents the number of cookies without frosting, and x + y ≥ 75.

Equations are formulas used in mathematics to describe the connection between two or more variables.

They help with problem-solving and prediction by describing how physical systems behave.

Typically, an equation comprises of two expressions—one on either side of the equal sign (=)—and an equal sign.

The independent variable is referred to as the side of the equation on the right, while the dependent variable is referred to as the side on the left.

Engineering difficulties like the design of a bridge or an automobile can be solved using equations, which are also used to describe natural events like the answers to Newton's laws of motion.

The behaviour of chemical  reactions and biological activities is also described by equations.

There are numerous ways to express equations in writing.

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The y=5x-10 function is nonlinear.

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.  Although the linear functions are also represented in terms of calculus as well as linear algebra. The only difference is the function notation. Knowing an ordered pair written in function notation is necessary too. f(a) is called a function, where a is an independent variable in which the function is dependent. Linear Function Graph has a straight line whose expression or formula is given by; y = f(x) = px + q
Since you are using y, instead of f(x), I think it's more appropriate to call it a relationship. The equation y=5x-10 describes a set of points that fall on a line, but for it to be a linear function, it should be denoted as f(x)=5x-10.

The distinction isn't so interesting in this case, but how about the case x = y^2? This is a totally valid relationship, but it cannot be a function of x, since a function requires just one output for a given input.

No. If it was a linear function we should have y(λx)=λy(x), ∀x. But that's not what happens. Actually, this function is called an affine function. So, we can see that affine functions are obtained from the linear functions simply by performing a rigid movement.

The linear functions are those that have the form: y=ax.

Therefore, The y=5x-10 function is nonlinear.

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A maganitude 7.0 earthquake is hundred times stronger than magnitude 5.0 earthquake.

Richter's Magnitude Scale: Seismologists often use the Richter scale (developed by Charles Richter) when measuring the magnitude of earthquakes. There are many factors to consider, such as B. Amplitude for calculating this type of scale. An increment of magnitude 1 means that the actual size of the earthquake is multiplied by 10 (logarithmic signature). Let A (earthquake magnitude) be 7 and B (earthquake magnitude) be 4. Calculating how many time the A is approximately stronger than B:

=> 10ᴬ⁻ᴮ = 10⁷⁻⁵ = 10² = 100

The magnitude 7 earthquake is 100 times as strong as the magnitude 5 earthquake..

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Answer:

D) g²h-33/g

Step-by-step explanation:

The expression √gh³27g¹h³ can be simplified as follows:

√gh³27g¹h³ = √(gh)³(27g)¹(h³) = (gh)³/27gh = gh²/27g = g²h/27g

Option D is the equivalent to the original expression: g²h-33/g

The difference between tan and inverse tan functions is that, tan function has input as an angle whereas inverse tan function takes input as numbers.

In mathematics, the trigonometric functions sine, cosine and tangent are often represented by the symbols sin, cos and tan respectively.

The inverse of these functions, known as inverse trigonometric functions, are represented by the symbols sin^-1, cos^-1 and tan^-1.

These inverse functions are used to find the angle of a right triangle given the ratio of its sides.

In other words, if you know the values of the sides of a right triangle, you can use the inverse trigonometric functions to find the angles.

The inverse tangent function, also known as arctan, is particularly useful in finding the angle of a right triangle when the opposite and adjacent sides are known.

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The area of the parallelogram is 78ft².

The area of a parallelogram can be calculated with the following formula:

A= b*h

Where "b" is the length of any base of the parallelogram and "h" is the height.

In this case, you can identify the values of b and h from the question given, which:

b = 6ft

h= 13ft

Then, knowing those values, you can substitute them into the formula shown above, as below:

A= b*h= 6*13

Finally, you must evaluate in order to find the area of the given parallelogram.

A= 78ft²

Thus, the area of the parallelogram is 78ft².

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Answer:

x = 34 degrees

Step-by-step explanation:

angles TWU and PSR are vertical and equal

if TSU = 4x and QSR = x then PSQ = 3x

triangle PSQ has 180 degrees

we know the three interior angles of the triangle are:

x, x, 112

we found the 112 by subtracting 68 from 180 since PQR is a straight line which has 180 degrees

to find 'x' we do the following:

x + x + 112 = 180

2x + 112 = 180

2x = 68

x = 34

Answer: 240cm^3

Step-by-step explanation:

To find the answer to this question, you use the solution that is given; height x length x width. If you put in the numbers you have into that solution, you will get an answer of 240. I really hope this helps- because I'm not that good at explanation! :)

Answer:

The equation for the Ferris wheel is y=60sin(2π/110)(x-50)-3. The time you will be 40 feet above the ground for the second time is approximately 125.7 seconds

The sample space is -

{(6, 6), (5, 6), (6, 5), (4, 6), (5, 5), (6, 4), (3, 6), (4, 5), (5, 4), (6, 3)}

Given is that Nick is paid every other week. He has 390$ taken out of each paycheck for federal taxes.

       {(6, 6), (5, 6), (6, 5), (4, 6), (5, 5), (6, 4), (3, 6), (4, 5), (5, 4), (6, 3)}

Therefore, the sample space is -

{(6, 6), (5, 6), (6, 5), (4, 6), (5, 5), (6, 4), (3, 6), (4, 5), (5, 4), (6, 3)}.

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Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

"simplified" means that we calculate everything "away" we can calculate and end up with the minimum of an expression around the variable (in our case p).

18p⁴ - 4p = 2×(6p⁴ - p) + 2×width

the first simplification is that we can divide everything by 2

9p⁴ - 2p = 6p⁴ - p + width

3p⁴ - 2p = -p + width

3p⁴ - p = width

The number of real solutions to a quadratic equation depends on the coefficients of the quadratic equation.

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are real numbers. This equation can have either 0, 1, or 2 real solutions. If a is equal to 0, then the equation is not a quadratic equation and can have any number of real solutions.

If the coefficient a is not equal to 0, then the number of real solutions depends on the value of the discriminant, b2 - 4ac. If the discriminant is positive, then there are two real solutions to the equation. If the discriminant is zero, then there is one real solution. If the discriminant is negative, then there are no real solutions.

In summary, a quadratic equation can have 0, 1, or 2 real solutions depending on the value of the discriminant.

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