The change in the total amount of Suki's allowance balance over the course of four weeks is shown in the table.



Week Change ($)
1 25.25
2 ─5.75
3 12.40
4 ─14.35


Based on the average change in her allowance balance per week, how much money can Suki expect to save or spend over the course of a year?

A rigid motion maps each part of a figure to an Rotation.

What is rotation ?

In physics, rotation refers to the movement of an object around an axis or a fixed point. When an object rotates, every point on the object moves in a circle around the axis of rotation, and the object typically completes one full rotation or revolution after it has moved a full 360 degrees around the axis.

The study of rotation in physics is important in many fields, including mechanics, electromagnetism, and quantum mechanics. Rotational motion is characterized by several key parameters, including the angle of rotation, the angular velocity (how fast the object is rotating), and the angular acceleration (how quickly the angular velocity is changing).

In addition, rotational motion is subject to a number of physical laws and principles, such as Newton's laws of motion, which describe the relationship between the forces acting on a rotating object and its resulting motion. Other principles, such as the conservation of angular momentum, relate to the conservation of the rotational energy of a system as it undergoes rotational motion.

Therefore, a rigid motion maps each part of a figure to an Rotation.

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Answer: 2.3716 <-------- This is the Code

Step-by-step explanation:

1.4 x 2.5 = 3.5

2.2 x 2.5 = 5.5

1.4 x 0.2 = 0.28

2.2 x 0.2 = 0.44

3.5 x 0.28 = 0.98

5.5 x 0.44 = 2.42

Then:

X         1.4           2.2

2.5      3.5          5.5

          - x -          - x -    

0.2      0.28        0.44

           - = -           - = -

        0.98  x    2.42 = 2.3716 <-------- This is the Code

Answer: 3.8 minutes!

Step-by-step explanation:

The answer is 3.8 minutes. To solve for t, we need to set up an inequality where the calories burned in routine #1 is equal to or greater than the calories burned in routine #2. We can write this as 22 + 5.75t ≥ 8.5t. Then, we can subtract 8.5t from both sides to get 22 ≥ -2.75t. Finally, we can divide both sides by -2.75 to get t ≤ -8/2.75, which simplifies to t ≤ 3.8. Therefore, Jane needs to run for 3.8 minutes in Routine #1 in order to burn at least as many calories as Routine #2.

Answer:

Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.

Step-by-step explanation:

In Routine #1, the total number of calories burned is:

C1(t) = 22 + 5.75t

The first term represents the calories burned while walking, and the second term represents the calories burned while running.

In Routine #2, the total number of calories burned is:

C2(t) = 8.5t

This represents the calories burned while running, as there is no walking in Routine #2.

We want to find the values of t for which C1(t) is greater than or equal to C2(t). So we can set up the following inequality:

C1(t) ≥ C2(t)

Substituting the expressions for C1(t) and C2(t), we get:

22 + 5.75t ≥ 8.5t

Simplifying the inequality, we get:

22 ≥ 2.75t

Dividing both sides by 2.75, we get:

t ≤ 8

So Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.

A medium-sized orange contains 68 calories. Which is one-fifth the number of calories in a slice of cheese pizza.

If one slice of cheese pizza contains 340 calories, and a medium-size orange has one-fifth that number of calories, we can find the number of calories in a medium-size orange by dividing 340 by 5. Calories in a medium-sized orange = [tex]\frac{340}{5}[/tex] calories = 68 calories. The division is an arithmetic operation used to find out how many times one number is contained within another number. The result of a division operation is called the quotient.

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The length of the rectangular prism is 20.35

The diagonal of the base is calculated using Pythagoras theorem. This is a side that will use to find the length of the box.

The diagonal A - B given as 2 feet = 24 inches is the hypotenuse while solving for the length of the prism

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 9² + 9²

x² = 81 + 81

x = √162

x = 12.728

The length of the rectangular prism is solved as follows

let y be the required distance

24² = y² + 12.728²

y² = 24² - 12.728²

y = √413.998

y = 20.35 in

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Answer:

10 packs

Step-by-step explanation:

Allie wants to give each of her classmates 3 pencils, so she needs a total of 3 pencils * 26 classmates = 78 pencils.

The pencils come in packs of 8, so she needs 78 pencils / 8 pencils per pack = 9.75 packs of pencils.

Since you can't buy a fraction of a pack, Allie needs to buy 10 packs of pencils.

The standard deviation lies in the range of 0 to 1. The numerical value of standard deviation can never be negative.

The standard deviation is a measure of amount of variation or dispersion of a set of values. When we compare two unequal observations, the result is always greater than zero i.e., always positive.

Standard deviation is the square root of the variance of the observations and the root always gives values either positive or zero, it can never be negative.

Therefore, the numerical value of the standard deviation can be positive. The value of standard deviation is always greater or equal to zero.

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Answer:

Step-by-step explanation:

Answer: 25 inches

Step-by-step explanation:

The equation for area of a rectangle is Length x Width, since we have the width which is 20 in., we can multiply it by a variable and set it equal to 500.

20(b)=500

divide both sides by 20

b=25

The value of the expression is -8. Option A

It is important to note that algebraic expressions are expressions that are made up of variables, terms, coefficients, constant and factors.

From the information given, we have that;

3x-6= 5x - 2

collect like terms

3x - 5x = -2 +6

subtract the like terms

-2x = 4

Make 'x' subject

x = -2

Substitute the value in the equation

2x - 4

2(-2) - 4

expand bracket

-8

Hence, the value is -8

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Answer:

622.03

Step-by-step explanation:

Answer:

If the cost price (CP) is 380 and the gain percentage is 25%, we can use the following formula to find the selling price (SP):

SP = CP + (gain percentage/100) * CP

Substituting the given values, we get:

SP = 380 + (25/100) * 380

SP = 380 + 95

SP = 475

Therefore, the selling price is 475.

Step-by-step explanation:

Option a is correct- The length of MC is 16mm.

The equilateral triangle has its three sides with the same length.

So if the perimeter is 96 mm, we have,

perimeter = 3 * side

3 * side = 96

side = 32mm

The segment MA is the height of the equilateral triangle, and its length can be calculated with the equation,

height = (side * root(3))/2

height = 16root(3)

Using the Pythagoras' theorem in the triangle ACM, we have,

side^2 = MC^2 +height ^2

1024 = MC^2 + 768

MC^2 = 256

MC = 16mm

so, The length of MC is 16mm.

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Answer:

<P = 41

Step-by-step explanation:

we can consider this first figure as a quadrilateral and the trianlgle attached to be is equilateral triangle (as it is already shown in the figure that sides are equal)

we know that each angle of equalateral triangle is 60°

we can see that angle 79° is attached to it and even other angle is also attached

let the other angle be x

we can notice that x and the angle of equi triangle make a linear pair

so 180 - 60

= 120°

the opposite angle to the angle x will be also equal as angles on the same side of qual sides will be equal

now we know that total angle sum of quadrilateral is 360°

so

79 + 120 + 120 + <P = 360

319 + <P = 360

<P = 360 - 319

<P = 41

The  triangle is rotated 90° counterclockwise about the origin shown below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

we have to rotate 90° counterclockwise about the origin.

as, the rule for 90° counterclockwise about the origin is (x, y) becomes

(-y, x).

As, the coordinates after rotation are :

(-8, 3)---> (-3, -8)

(-2, 8)---> (-8, -2)

(-5, 7) -----> (-7, -5)

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Answer:

47% for rolling a blue and 33% for rolling a red

Step-by-step explanation:

The length of the side AB in triangle ABC is 6.58 units.

What are trigonometric ratios in terms of a right-angle triangle?

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjacent/hypotenuse and

tan = opposite/adjacent.

From the given figure we can conclude that we have length of the adjacent

with an angle of 20° and we have been asked to find the hypotenuse.

We know cos = adjacent/hypotenuse.

∴ cos20° = adjacent/7.

0.937 = adjacent/7.

adjacent = 7*0.937.

adjacent = 6.58.

Hence , the length of the side AB in triangle ABC is 6.58 units.

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The 4-2-1 rule is a guideline used to help determine the amount of water an individual needs to drink each day.

The rule states that an individual should drink 4 liters of water for every 50 pounds of body weight, 2 liters of water for every 50 pounds of body weight if they are exercising, and 1 liter of water for every 50 pounds of body weight if they are in a hot or dry environment.

To calculate how much water you need to drink using the 4-2-1 rule, simply follow these steps:

1. Determine your body weight in pounds.
2. Divide your body weight by 50 to get the number of 50-pound increments in your weight.
3. Multiply the number of 50-pound increments by 4 to get the amount of water you need to drink if you are not exercising or in a hot or dry environment.
4. Multiply the number of 50-pound increments by 2 to get the amount of water you need to drink if you are exercising.
5. Multiply the number of 50-pound increments by 1 to get the amount of water you need to drink if you are in a hot or dry environment.
6. Add the amounts from steps 3, 4, and 5 together to get the total amount of water you need to drink each day.

For example, if you weigh 150 pounds, you would need to drink 4 liters of water for every 50 pounds of body weight (150 / 50 = 3), 2 liters of water for every 50 pounds of body weight if you are exercising (3 x 2 = 6), and 1 liter of water for every 50 pounds of body weight if you are in a hot or dry environment (3 x 1 = 3). Therefore, you would need to drink a total of 13 liters of water each day (4 + 6 + 3 = 13).

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Answer:

3,293 yards are more than a mile

Step-by-step explanation:

1 mile is 1,760 yards. Thereby, we know that 3,293 is more than 1,760.

Answer: 3,293 yards is more than a mile since a mile is 1,760 yards

Step-by-step explanation:

2 miles are 3,520 yards which can further prove that 1 mile is way less the 3,293 yards

Hope this helped

Answer: You can make 5/3 * (1/1) = 5 servings with a cup of macaroni.

And, with 5 servings, you can make 5 * (3/1) = 15 1/3 servings of pasta salad.

Step-by-step explanation:

The value of f(3/4) is 5/4.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a function.

f(x) = 2x - 1/4

We have to find the value of the function when the input value x = 3/4.

For that, substitute 3/4 in place of x.

f(3/4) = (2 × 3/4) - 1/4

         = 6/4 - 1/4

         = 5/4

Hence the value of the function is 5/4.

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3/5 = 0,6, it is 0.6 × 100 = 60%

Therefore, 3/5 is expressed as 60% in terms of percentage.

Percentage:

In mathematics, a percentage is a number or ratio that represents a fraction of 100. This is one way of representing a dimensionless ratio between two numbers. Other methods include ratios, fractions, and decimals. Percentage is often indicated by writing a "%" sign after the number.

According to the Question:

To convert a fraction to a decimal, it's always best to look at the denominator first. If the denominator only has prime factors of 2 and 5, you can easily pick a number multiplied by the denominator and convert it to a denominator that is a power of 10, and the result is the final prime number. If you have prime factors other than 2 and 5, converting to decimal takes longer and can result in infinite but repeating decimals.

In this case, the denominator is 5, so you can easily convert to decimal by multiplying the denominator and numerator by 2.

(3 × 20) / (5 × 20) = 60/100

Now,

To convert a fraction to a percentage, simply multiply by 100 and put a % sign next to the result.

As 3/5 = 0,6, it is 0.6 × 100 = 60%

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Answer:

This is Non-terminating

decimal: 0.777

Step-by-step explanation:

To represent the data, the display used is histogram.

A frequency distribution shows how often each different value in a set of data occurs. A histogram is the most commonly used graph to show frequency distributions. Histograms visualize quantitative data or numerical data, whereas bar charts display categorical variables.

Given,

Data of 24 students eating vegetables in the frequency table.

The data is quantitative.

Histograms are visual displays of frequencies using columns plotted on a graph. The Y-axis (vertical axis) generally represents the frequency count, while the X-axis (horizontal axis) generally represents the variable being measured.

Hence, Histogram will be used to represent the data.

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Answer: (0,6), (1,5), (2,4), (3,3)

Step-by-step explanation:

I don't think I can add a picture but I can give you points and you can just draw a line through all of them

(0,6), (1,5), (2,4), (3,3)

If you want to, you can use a graphing calculator and just put the equation in. If you don't have an actual graphing calculator, I recommend using desmos online graphing calculator because it works really well.

1.The beginning balance should be $4,000

2.The amount to be adjusted is $2554

3.The ending balance of the account after the adjustment $2554

4. Office Supplies Account is $14846

"Information available from the question"

The Office Supplies account started the year with a $4,000 debit balance

The company purchased supplies for $13,400,

The inventory of supplies available at the end of the year totaled $2,554.

Now, According to the question:

1. The beginning balance should be $4,000

2.The adjusted amount is

Opening balance = 4000

Add: New purchases = 13400

Balance after Purchase = 17400

Less: Year end balance = 2554

3. The ending balance is $2,554

4. The adjusting journal entry is

Dr. Supplies Expense Account is 14846

Adjustment in the year = Cr. 14846 (subtracted from the balance)

Office Supplies Account is 14846

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The horizontal distance between Ryan and the dolphin is  57.87 feet.

The airplane is 10735.96 feet away from the control tower

The angle of depression from the top of the lighthouse to the boat is 0 degrees.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Using trigonometry, we can find the horizontal distance x:

tan(15) = x / 228

x = 228 tan(15)

x = 57.87 feet

Therefore, the horizontal distance between Ryan and the dolphin is  57.87 feet.

2. Using trigonometry, we can find the horizontal distance between the airplane and the control tower:

tan(56) = x / 7450

x = 7450tan(56)

x = 10735.96 feet

Therefore, the airplane is approximately 10735.96 feet away from the control tower

3. We want to find the angle of depression from the top of the lighthouse to the boat. Since the lighthouse is 275 feet above the water, we can use trigonometry to find the height of the lighthouse above the boat:

tan(90) = 275 / x

x = 275 / tan(90)

x = undefined

Therefore, the angle of depression from the top of the lighthouse to the boat is 0 degrees.

Hence,  the horizontal distance between Ryan and the dolphin is approximately 57.87 feet.

the airplane is approximately 10735.96 feet away from the control tower

the angle of depression from the top of the lighthouse to the boat is 0 degrees.

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Answer:

b

Step-by-step explanation:

Use the Avogadro constant of 6.02 x 10^23

One must evaluate the function as the independent variable gets closer to the point from the provided side.

So in order to determine the limit of a function at a point from one side, one must evaluate the function as the independent variable gets closer to the point from the provided side. Take the subsequent function, for instance: scss. Copy the code f(x) = (x2 - 4) /. (x - 2)

You can evaluate the function for x values that are getting closer to 2 but always greater than 2 in order to determine the limit of this function as x approaches 2 from the positive side (i.e., as x goes closer and closer to 2 from values greater than 2). The function can be evaluated, for instance, at x = 2.1, x = 2.01, x = 2.001, and so forth. The function values will approach the target value as x approaches 2, which is 2. In order to determine the limit of this function as x approaches 2 from the positive side (i.e., as x goes closer and closer to 2 from values greater than 2). The function can be evaluated, for instance, at x = 2.1, x = 2.01, x = 2.001, and so forth.

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H0: mean=1.45

H1: mean< 1.45

=-3.175

The result is significant at p < .01.

Reject Null Hypothesis

the mean level of exhaust emitted for this model reduces emissions

A)

Null hypothesis:

H0: mean=1.45

Alternative hypothesis:

H1: mean< 1.45

b)

estimate - the value we hypothesize standard error test statıstıc - t-statisticS

[tex]\begin{gathered}\text { test statistic }=\frac{\text { estimate }-\text { value we hypothesize }}{\text { standard error }} \\\text { t-statistic }=\frac{\bar{x}-\mu_o}{s / \sqrt{n}}\end{gathered}[/tex]

t=1.21-1.45/0.4/sqrt(28)

=-3.175

c)

t=-3.175

df=28-1=27

alpha=0.01

The P-Value is .001863.

The result is significant at p < .01.

d)

p=0.001

< alpha of 0.01

Reject Null Hypothesis

e)

there is sufficient evidence

the mean level of exhaust emitted for this model reduces emissions

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