Joann had a vegetable stand where she sold tomatoes. She sold 15 tomatoes the first day. The second day she sold half of what was left. On the third day she sold 12 and sold half of what was left on the fourth day. On the fifth day there were 4 tomatoes left to be sold. How many tomatoes did she have to begin with?

Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8

Given the expression

(9¹⁺⁴)⁷⁺²

To simplify this expression using the power of a power property, we need to multiply the exponents:

(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)

Simplifying the exponents in the parentheses:

(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8

Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).

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Using binomial theorem, the generating function is G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256 while the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.

To find the generating function of (x+4)^4, we expand it using the binomial theorem:

[tex](x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)[/tex]

where C(n,k) denotes the binomial coefficient "n choose k".

Simplifying the terms, we get:

[tex](x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]

Therefore, the generating function of (x+4)^4 is:

[tex]G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]

The associated sequence can be read off by finding the coefficients of each power of x:

To find the generating function of (x+4)^4, we expand it using the binomial theorem:

(x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)

where C(n,k) denotes the binomial coefficient "n choose k".

Simplifying the terms, we get:

(x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256

Therefore, the generating function of (x+4)^4 is:

G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256

The associated sequence can be read off by finding the coefficients of each power of x:

The coefficient of x^k is the k-th term of the sequence.

In this case, the sequence is given by the coefficients of G(x):

a₀ = 256

a₁ = 256

a₂ = 96

a₃ = 16

a₄ = 1

Therefore, the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.

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In one of his experiments conducted with animals, Thorndike found that cats learned to escape from a puzzle box is increased gradually

To quantify the learning process, Thorndike used a mathematical formula known as the Law of Effect equation. The equation is:

B = f(log S1/S2)

where B represents the strength of the behavior, S1 represents the satisfaction of the positive consequence, and S2 represents the degree of frustration or negative consequence.

In the context of Thorndike's puzzle box experiment, the Law of Effect equation can be used to describe how the cat's behavior changed over time as it learned to escape the puzzle box more quickly and efficiently. Initially, the cat's behavior was weak because it did not know which actions would lead to a positive outcome.

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The sum of the arithmetic progressive sequence will be +∞, for common difference as positive that is d >0.

The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP).

A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by increasing 4 to the previous term. This annual income of a worker whose pay rises by a predetermined amount of $5000 each year serves as a real-world illustration of an AP.

The expression for an arithmetic progression:

a is the first term

l is last term

d is common difference

n is total number of terms

Sn = the sum of term

A.P =  a,a+d,a+2d,a+3d,…, a+(n-1)d

l = a+(n-1)d

Sum formula:

Sn=n/2 [a+(n-1)d]

Or, Sn=n/2 [a+l]

Thus, the sum of the arithmetic progressive sequence will be +∞, for common difference as positive that is d >0.

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ANSWER :

Answer is D.

Thanks for the question today.

Therefore, there are 20 girls in the class of fifth-graders.

In mathematics, a fraction represents a part of a whole or a division of two numbers. It is written in the form of a numerator and a denominator separated by a horizontal bar (also known as a fraction bar). The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts in the whole or the divisor of the division.

Here,

Let the number of girls in the class be represented by 'g'.

According to the problem, the number of boys is 3/4 as many as the number of girls. This means:

Number of boys = (3/4) * number of girls

Number of boys = (3/4) * g

The total number of students in the class is given as 35. So we have:

Number of girls + Number of boys = Total number of students

g + (3/4)g = 35

Simplifying the equation, we get:

(7/4)g = 35

Dividing both sides by 7/4, we get:

g = 20

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Answer:

88/25

Step-by-step explanation:

if you do 2.2 times 1.6 equals 3.52 and then a fraction.

Answer:

2.2 × 1.6 can be expressed as a fraction multiplication expression as follows:

(22/10) × (16/10)

Simplifying the expression by canceling out the common factor of 10, we get:

22 × 16 / 10 × 10

Multiplying the numerator and denominator, we get:

352 / 100

Simplifying the fraction by dividing both the numerator and denominator by 4, we get:

88 / 25

Therefore, 2.2 × 1.6 as a fraction multiplication expression is 88/25.

The volume of the new rectangular prism is 160 in³ after it has been dilated with a scale factor of 2.

In this case, the scale factor is 2, which means that the dimensions of the original figure will be multiplied by 2 to get the dimensions of the new figure.

Volume of rectangular prism = length x width x height

20 = l x w x h

Next, we need to find the new dimensions of the rectangular prism after it has been dilated by a scale factor of 2. We can do this by multiplying each dimension of the original rectangular prism by 2.

New length = 2 x l

New width = 2 x w

New height = 2 x h

Now we can find the volume of the new rectangular prism by using the same formula as before, but with the new dimensions:

Volume of new rectangular prism = (2 x l) x (2 x w) x (2 x h)

Simplifying this expression, we get:

Volume of new rectangular prism = 8 x (l x w x h)

We know that l x w x h is equal to the volume of the original rectangular prism, which is 20 in³. So we can substitute this value into the expression to get:

Volume of new rectangular prism = 8 x 20 in³

Volume of new rectangular prism = 160 in³

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There are no very large or small numbers inside the range of 38 to 92. The first data set [tex]48, 44, 41, 50, 38, 42, 92, 39.[/tex] is the one for which the mean would serve as the most accurate indicator of the center.

By adding every value in a collection and dividing by the total number of values, you may get the mean. The median is the value that falls in the center when a group of values are arranged from smallest to greatest. The value that appears the most frequently in the set is the mode.

The mean may be used as a benchmark for all observations since it can be used to reflect the typical value.

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y = 2x + 1...so sub in 2x + 1 for y in the other equation

x + 3y = 10

x + 3(2x + 1) = 10

x + 6x + 3 = 10

x + 6x = 10 - 3

7x = 7

x = 1

y = 2x + 1

y = 2(1) + 1

y = 2 + 1

y = 3

the difference : there can be 1 possible answer for this..

y - x = 3 - 1 = 2

Step-by-step explanation:

Use the 110 to find the 70 degree angle   (they form a straight line = 180°)

   then 70 + 64 + R angle = 180°    ( sum of angles of a triangle)

        then  :    R angle = 46°

then the R angle + 2x-10 = 90°    ( because the two lines are perpendicular)

(2x -10)°   + 46 °  = 90 °

x = 27

Answer:

Step-by-step explanation:

circumference c=2πr=5π

[tex]r=\frac{5\pi }{2\pi } =\frac{5}{2}~cm \\area=\pi r^{2} =\pi (\frac{5}{2} )^2\\=\frac{25}{4} \pi \\=6.25 ~cm^2[/tex]

Answer: 1/3 chance or 33.33333%

Step-by-step explanation: There are only 3 odd numbers on the die, 1,3,5 so there is a 1/3 chance it is 3

The Length of arcXY is 4π/3

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

Given, (radius) WX =3, it means, r = 3

given, m∠XWY = 80°

So, the length of arc XY;

arcXY = [tex]\frac{80}{360}* 2\pi r[/tex]        (by formula: length of arc)

arcXY = [tex]\frac{2}{9}* 2\pi *3[/tex]

arcXY = [tex]\frac{4}{3}\pi[/tex]

Therefore, the Length of arcXY is 4π/3

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Complete question-

Answer:

60 - 10 = 50

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Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.

calculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.

Change in temperature on Monday from High to low

=15-10=5°F

Change in temperature on Tuesday from High to low

=8-(-4)=12°F

Change in temperature on Wednesday from High to low

=-2-(-5)=3°F

Change in temperature on Thursday from High to low

=-3-(-7)=4°F

Change in temperature on Friday from High to low

=-1-(-12)=11° F

Days when change in temperature more than 10° F are Tuesday and Friday.

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The Complete question is attached below:

The  angles can be named with one letter  are 2.

Angles are a type of geometric shape which are formed when two straight lines intersect at a point. They are measured in degrees, usually between 0 and 360. Angles can be classified as acute, right, obtuse, straight and reflex, and the sum of any three angles in a triangle will always equal 180 degrees. Angles can be used in various ways, from providing stability in construction work to helping to identify other shapes. They can also be used to measure the size and shape of objects and to calculate distances and areas on maps. Angles are an important part of mathematics, geometry and trigonometry, and are used in a variety of applications in science and engineering.

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The kinetic energy of particle with a de Broglie wavelength of 0.50 nm is 82.6 eV.

The given de Broglie wavelength of 0.50 nm corresponds to photons. The formula for the kinetic energy of a particle with a given de Broglie wavelength λ is given by:

K = (hc/λ) - mc^2

where h is Planck's constant, c is the speed of light, and m is the rest mass of the particle.

For photons, the rest mass is zero, so the formula simplifies to:

K = hc/λ

Plugging in the given wavelength of 0.50 nm, we get:

K = (6.626 × 10^-34 J s × 3.00 × 10^8 m/s) / (0.50 × 10^-9 m)

K = 1.3252 × 10^-17 J

Converting to electronvolts (eV), we use the conversion factor 1 eV = 1.602 × 10^-19 J:

K = (1.3252 × 10^-17 J) / (1.602 × 10^-19 J/eV)

K = 82.6 eV (rounded to three significant figures)

Therefore, the kinetic energy of photons with a de Broglie wavelength of 0.50 nm is 82.6 eV (rounded to three significant figures).

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The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.

Compare Alice's utility from each option and choose the one that maximizes her utility.

Let us consider each option,

If Alice offers Bob $0, her utility will be,

If XA > XB then

UA (XA , XB )= 0.3x3 + 0.72A

UA(10,0)

= 0.3(10)³ + 0.72(10)

= 307.2

If Alice offers Bob $5, Bob's utility will be,

UB(10,5)

= 0.314 + 0.72(5)

= 0.314 + 3.6

= 3.914

And Alice's utility will be,

UA(5,10)

= -0.32(5) + 1.3(10)

= 11.4

Total utility for both Alice and Bob will be,

UA(5,10) + UB(10,5)

= 11.4 + 3.914

= 15.314

If Alice offers Bob $2, Bob's utility will be,

UB(10,2)

= 0.314 + 0.72(2)

= 1.754

And Alice's utility will be,

UA(2,10)

= -0.32(2) + 1.3(10)

= 12.4

So the total utility for both Alice and Bob will be,

UA(2,10) + UB(10,2)

= 12.4 + 1.754

= 14.154

If Alice offers Bob $10, Bob's utility will be,

UB(10,10)

= 0.314 + 0.72(10)

= 7.514

And Alice's utility will be,

UA(10,10)

= 0.3(10)³ + 0.72(10)

= 307.2

So the total utility for both Alice and Bob will be,

UA(10,10) + UB(10,10)

= 307.2 + 7.514

= 314.714

Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.

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Answer:

3.33 hours

Step-by-step explanation:

you have a total of 60mg, it is asked how much hours it takes to remove half the caffeine which is 30mg

1 hour removes 15%, 15% of 60 is 9g

(15/100×60) = 9

now it removes only 9g in an hour, we have to find out how long (hours) it'll take to remove 30g

30÷9= 3.33 hours

Answer:

Let's assume that the rate of interest is r (in decimals), and the time period is also r years. Then we can use the simple interest formula:

I = P * r * t

where I is the interest paid, P is the principal amount (the loan amount in this case), r is the rate of interest per year, and t is the time period in years.

Substituting the given values, we get:

324 = 900 * r * r

Simplifying, we get:

r² = 324/900

r² = 0.36

Taking the square root of both sides, we get:

r = ±0.6

Since the rate of interest cannot be negative, we can take r = 0.6. Therefore, the rate of interest is 0.6 or 60% per year.

Answer:

m = -3/4

Step-by-step explanation:

Calculation of the Slope of a line

The information provided about the line is that the line passes through the points  (-8, 9) to (-4,6)

Therefore, the first step consists in computing the slope. The formula for the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, by plugging the corresponding numbers is , we get that the slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-9}{-4-(-8)} =\frac{6-9}{-4+8} =-\frac{3}{4}[/tex]

So then, we find that the slope is [tex]m=-\frac{3}{4}[/tex] and that the line passes through the point  [tex](-8,9)[/tex].

The coordinates of point P that is 3/4 of the way along the directed line segment from C(6, -5) to D(-3, 4) are (-0.75, 1.75).

To find the coordinates of point P that is 3/4 of the way along the directed line segment from C(6, -5) to D(-3, 4), we can use the following formula:

P = (1 - 3/4)C + (3/4)D

First, we find the vector CD = D - C:

CD = (-3, 4) - (6, -5) = (-9, 9)

Then we can plug in the values and simplify:

P = (1 - 3/4)C + (3/4)D

P = (1/4)(6, -5) + (3/4)(-3, 4)

P = (3/4)(-3, 4) + (1/4)(6, -5)

P = (-2.25, 3) + (1.5, -1.25)

P = (-0.75, 1.75)

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Examination writing skills refer to a set of abilities that are essential for effective and successful writing in an exam context.

These skills include reading the question carefully, planning your response, writing a clear and concise answer, using appropriate terminology, providing evidence to support your argument, and presenting your answer in a logical and organized manner.

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Complete question:

State one way in which each of the examination writing skills below could effectively assist you when writing your examinations:

Answer: The total cost of buying 5 balls individually is $2.00 x 5 = $10.00.

The box costs $8.50, which means it is $10.00 - $8.50 = $1.50 cheaper to buy the box.

To calculate the percentage difference, we can use the formula:

% difference = (difference ÷ original value) x 100%

In this case, the difference is $1.50, and the original value is $10.00.

% difference = ($1.50 ÷ $10.00) x 100%

% difference = 0.15 x 100%

% difference = 15%

Therefore, it is 15% cheaper to buy the box than to buy 5 individual balls.

Step-by-step explanation:

Amelia uses 99 balls of yarn in all to make the sweaters and scarves.

What is addition ?

Addition is a basic mathematical operation that combines two or more quantities to find a total or a sum. It is denoted by the symbol "+" and is usually taught in elementary school. In addition, the order of the numbers does not matter, meaning that you can add them in any order and still get the same result. For example, 3 + 5 is the same as 5 + 3, and the answer is 8 in both cases.

According to the question:
To find the total number of balls of yarn that Amelia uses, we can start by finding the total number of balls of yarn she uses to make the sweaters and scarves separately, and then add those amounts together.

To make 7 sweaters, Amelia uses 7 x 9 = 63 balls of yarn.

To make 9 scarves, Amelia uses 9 x 4 = 36 balls of yarn.

Adding these together, we get:

63 + 36 = 99

So, Amelia uses 99 balls of yarn in all to make the sweaters and scarves.

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The equation of the line passing through A and B is y = (4/5)x - (2/5).

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. The y-axis intercept is denoted by the number c. A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.

The point-slope form of a linear equation can be used to find the equation of the line passing through points A and B:

y - y1 = m(x - x1) (x - x1)

where m denotes the slope of the line, (x1, y1) denotes the coordinates of point A or B, and (x, y) denotes the coordinates of any other point on the line.

To calculate the slope, we can use points A (3, 2) and B (8, 6).

m = (y2 - y1) / (x2 - x1) = (6 - 2) / (8 - 3)\s= 4 / 5

So the equation for the line connecting A and B is:

y - 2 = (4/5)(x - 3) (x - 3)

This equation can be simplified by multiplying both sides by 5:

5y - 10 = 4x - 12

Then we can rearrange it to form the slope-intercept equation, y = mx + b:

5y = 4x - 2

y = (4/5)x - (2/5)

As a result, the equation for the line connecting A and B is y = (4/5)x - (2/5).

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