Compute the variances in dollar amount and in percentage. (round to the nearest whole percent.) indicate whether the variance is favorable (f) or unfavorable (u).


budgeted amount - expense $106.00


actual amount $100.00


dollar variance $



percent variance


%


f or u

The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.

dA ≈ (dA/dx)dx

At the lower end of the possible range for x, we have:

x = 9 31/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches

At the upper end of the possible range for x, we have:

x = 10 1/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches

Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(b) The percent error in computing the area of the square is given by:

(percent error) = (error / actual value) x 100

(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.

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Step-by-step explanation:

Let the other rational number be represented by "x". We know that the difference of the two rational numbers is 17/28, which can be written as:

x - (-9/14) = 17/28

Simplifying the left-hand side:

x + 9/14 = 17/28

Multiplying both sides by the least common multiple of 14 and 28, which is 28, we get:

28(x + 9/14) = 28(17/28)

Simplifying:

4(2x + 9) = 17

Expanding:

8x + 36 = 17

Subtracting 36 from both sides:

8x = -19

Dividing by 8:

x = -19/8

Therefore, the other rational number is -19/8.

The old coordinates are;

W (3, 14)

Y (12, 14)

X (6, 11)

While the new coordinates for the reflected triangle are:

W'' (3, -14)

X'' (6, -11)

Y'' (12, -14).

See the attached image.

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line.

A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.

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To build a ramp with a 15-inch rise for rolling gym equipment into your school, following ADA specifications, we should create a ramp with a run of 180 inches to maintain a 1:12 slope.

For building a ramp with a rise of 15 inches for rolling gym equipment into your school, following ADA specifications. Let's use these terms in our step-by-step explanation:

1. ADA specifications: The Americans with Disabilities Act (ADA) specifies that the slope of a ramp should be no more than 1:12, which means that for every 1 inch of rise, there should be 12 inches of run.

2. Ramp rise: In this case, the rise is 15 inches.

3. Calculate ramp run: To find the ramp run, we can use the ADA specification of 1:12. Multiply the rise (15 inches) by 12.

15 inches x 12 = 180 inches

4. Ramp run: Based on the calculation, the run for the ramp should be 180 inches.

5. Ramp length: To ensure a safe and accessible ramp, follow the ADA specifications and use a ramp length of 180 inches to achieve the 15-inch rise.

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Answer:

Obese

Step by Step Explanation:

looked it up :)

The sum of the heights of the two trees with given volumes and radius is equal to  9 cm (nearest whole number ).

Volumes of the cylindrical trunks of first tree = 904.78 cm³

and Volumes of the cylindrical trunks of first tree =113 cm³.

radius of the  first tree = 6cm

Radius of the second tree = 6cm

The formula for the volume of a cylinder is V = πr²h,

where r is the radius of the cylinder,

h is the height of the cylinder,

and π is the constant approximately value equal to 3.14.

For the first tree,

⇒904.78 = π(6)²h

⇒h = 904.78 / (π(6)²)

⇒h ≈ 8.004 cm

For the second tree, we have,

⇒113 = π(6)²h

⇒h = 113 / (π(6)²)

⇒h ≈ 0.9996 cm

This implies,

The sum of the heights of the two trees is equal to,

= 8.004 + 0.9996

= 9.003 cm

= 9 cm ( nearest whole number)

Hence, the sum of the heights of the two trees is approximately 9 cm nearest whole number.

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The given question is incomplete, I answer the question in general according to my knowledge:

The two trees trunk are in cylindrical shape. one with radius 6cm and volume 904.78 cm³ and  another one with radius 6cm and volume 113 cm³.

What is the sum of the heights of the two trees? Round your answer to the nearest whole number

The probability of Henry choosing a Milky Way and then a Snickers is 2/27.

1. First, let's find the total number of candy pieces in Henry's candy jar:
3 Snickers + 1 Reese's + 1 Twix + 2 Milky Ways + 2 Skittles Packs = 9 pieces of candy.

2. Next, we'll calculate the probability of choosing a Milky Way on the first pick:
There are 2 Milky Ways and 9 total pieces of candy, so the probability is 2/9.

3. Since Henry puts the candy back, there are still 9 pieces of candy for the second pick. Now, we'll calculate the probability of choosing a Snickers on the second pick:
There are 3 Snickers and 9 total pieces of candy, so the probability is 3/9 (or 1/3).

4. Finally, we'll multiply the probabilities of each individual event to find the probability of both events occurring together (choosing a Milky Way and then a Snickers):
(2/9) * (1/3) = 2/27

So, the probability of Henry choosing a Milky Way and then a Snickers is 2/27.

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Answer:

250+25d= P

Step-by-step explanation:

How to say it aloud: "$250 plus 25 times miles ran is equal to total amount earned"

250 is a fixed amount that is apart of the equation. In order to get a correct total at the end, $250 must be added to 25d.

25d stands for $25 times the amount of miles ran, which according to the word problem is represented by d. The reason we multiply 25 times d is because Marcus is getting $25 for every mile he runs. At the end of his run, we need to multiply $25 by those miles.

The reason everything equals P is because according to the word problem, P is the amount of money earned.

I hope that makes sense.

The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).

To find the coordinates of the points on the curve x(t) = 3t^2 + 1 and y(t) = t^3 - 1, where the tangent line has a slope of 1/2, follow these steps:

1. Calculate the derivatives of x(t) and y(t) with respect to t:

dx/dt = 6t
dy/dt = 3t^2

2. The slope of the tangent line is given by dy/dx, so calculate dy/dx using the chain rule:

dy/dx = (dy/dt) / (dx/dt) = (3t^2) / (6t) = t/2

3. Set the slope equal to 1/2 and solve for t:

t/2 = 1/2
t = 1

4. Plug the value of t back into the original equations for x(t) and y(t) to find the coordinates of the point:

x(1) = 3(1)^2 + 1 = 4
y(1) = (1)^3 - 1 = 0

The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).

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This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices

In this scenario, we can think of the slot machines as experts providing us with advice on which machine to play each day. The cost of taking advice from each expert, represented by cti, is the amount we lose by playing that particular machine.

To minimize our losses and regret, we want to choose the expert (i.e., slot machine) with the lowest cost each day. However, it's important to note that the cost of taking advice from each expert may change each day, so we need to constantly evaluate and adjust our choices.

To formalize this problem as an optimization task, we can use the concept of regret. Regret measures how much worse off we are by not knowing the best expert in advance. In other words, it's the difference between our cumulative losses if we always chose the best expert versus the losses we actually incur by following different experts each day.

To minimize our regret R, we need to choose the best expert as often as possible. One way to achieve this is by using an online learning algorithm that updates our choice based on the outcomes of each day's play. By continuously monitoring the performance of each slot machine, we can adjust our strategy and minimize our losses over time.

In summary, to minimize our losses while gambling at a casino, we need to treat each slot machine as an expert providing us with advice. We must choose the expert with the lowest cost each day and constantly update our strategy to minimize regret.

This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices.

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The area enclosed by the figure at the right is 2856 square meters.

To find the area enclosed by the figure at the right, we first need to find the area of the square and the two semicircles on each side. The square has sides of 40 meters, so its area is 40 x 40 = 1600 square meters. Each semicircle has a radius of 20 meters (half the side length of the square), so its area is 1/2 x pi x r^2 = 1/2 x 3.14 x 20^2 = 628 square meters. Since there are two semicircles on each side, the total area of all four semicircles is 2 x 628 = 1256 square meters.

To find the total area enclosed by the figure, we add the area of the square and the area of the four semicircles:

1600 + 1256 = 2856 square meters

Therefore, the area enclosed by the figure at the right is 2856 square meters.

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a. FA5.6₁₆ = 15x16² + 10x16 + 5 + 6/16 = 4005.375₁₀

b. 725.38₁₀ remains the same in decimal form

c. 3F4.8₁₆ = 3x16² + 15x16 + 4 + 8/16 = 1012.5₁₀

d. 73.25₈ = 7x8 + 3 + 2/8 = 59.3125₁₀

e. FF.F0₁₆ = 15x16 + 15 + 15/16 + 0/256 = 255.9375₁₀

Decimal form is a way of representing numbers using the base 10 number system. In this system, there are 10 digits from 0 to 9 that are used to represent all possible numbers. Each digit in a decimal number has a place value that is determined by its position. The rightmost digit represents units, the next digit to the left represents tens, and so on, with each successive digit representing higher powers of 10.

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The mover is communicating that the weight of the table and 4 chairs combined, represented as t+4C, is greater than or equal to 100 pounds.

The expression t+4C represents the total weight of the table and 4 chairs. The mover's invoice states that this total weight is greater than or equal to 100 pounds, which means that the combined weight of the table and chairs is at least 100 pounds. Therefore, the correct answer is D, "The table and 4 chairs weigh at least 100 pounds."

To solve this mathematically, we can use algebraic inequalities. The inequality t+4C >_ 100 can be rearranged as t >_ 100-4C. This means that the weight of the table t must be greater than or equal to 100 minus four times the weight of a single chair C.

If each chair weighs less than 25 pounds, then the total weight of the table and 4 chairs combined will be at least 100 pounds. So D is correct answer.

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The function that can be used to find the total area is: (x^2 + 25) sq. ft.

A square is a type of quadrilateral which has an equal length of sides. So then its area can be calculated as;

area of a square = length x length

We have from the question that; a square surface that has a side length of x feet. So that;

area of the square surface = length * length

                                            = x * x

                                            = x^2 square feet

But since the contractor always adds 25 square feet to the area, he buys extra paint, then the function required is:

total area = (x^2 + 25) sq. ft.

The function is (x^2 + 25) sq. ft.

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Answer:

----------------------

In order to find the total area, we need to consider both the area of the square surface and the extra paint he always adds.

Find the area of the square surface:

Add the extra 25 square feet of paint:

Combining these steps, the function is:

The limit of (sin(9x))/x as x approaches 0 is equal to 9.

To evaluate this limit analytically, we can use L'Hopital's Rule.

Taking the derivative of the numerator and denominator with respect to x, we get:lim (sin(9x))/x = lim (9cos(9x))/1as x approaches 0.

Substituting x = 0, we get:lim (sin(9x))/x = 9cos(0)/1 = 9Therefore, the limit of (sin(9x))/x as x approaches 0 is equal to 9.

We know already how to apply or make the procedures mathematically talking so this short program will eventually help you how to find logic.

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The width of the rectangle is approximately 5.39 meters.

Let's denote the width of the rectangle by x. According to the problem, the length of the rectangle is 4 meters more than the width, which means that the length can be represented as x+4.

The formula for the area of a rectangle is A = length x width. In this case, we know that the area of the rectangle is 77 square meters, so we can set up the following equation:

77 = (x+4)x

Expanding the brackets, we get:

77 = x² + 4x

Rearranging this equation into standard quadratic form, we get:

x² + 4x - 77 = 0

To solve for x, we can use the quadratic formula:

[tex]x = \frac{(-b ± sqrt(b^2 - 4ac))}{ 2a}[/tex]

Plugging in the values for a, b, and c, we get:

[tex]x = \frac{(-4 ± sqrt(4^2 - 4(1)(-77)))}{ 2(1)}[/tex]

Simplifying this expression, we get:

[tex]x = \frac{(-4 ± sqrt(336)} { 2}[/tex]

[tex]x = \frac{(-4 ± 4sqrt(21))}{ 2}[/tex]

x = -2 ± 2[tex]\sqrt{(21)}[/tex]

Since the width of a rectangle cannot be negative, we discard the negative solution and get:

x = -2 ± 2[tex]\sqrt{(21)}[/tex]

Therefore, the width of the rectangle is approximately 5.39 meters (rounded to two decimal places).

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Step-by-step explanation:

there is no explanation about x so wierd

Answer:

First Problem:

Transformation: Reflection across the x-axis, shift 2 units rightward

Equation: g(x)=-5^(x-2)

Second Problem:

Transformation: Reflection across the y-axis, shift 4 units upward

Equation: 10^-x+4

Step-by-step explanation:

Imagine folding a piece of paper and using the x or y axis as the crease marks. By folding them and comparing them, we can find out whether it is either the x-axis, y-axis, or both-axis. Then, we move the graph, to match the position in the second picture.

As for equations, exponential functions have the parent function of y=b^(x+c)+h. By plugging in any points given, let's say (1,5), we can see that 5=b^1 and simplifying shows 5=b. Therefore, the function is y=5^x. Using that first equation, we transform it. If over the x-axis, convert y=b^x to y=-b^x. If over the y-axis, convert y=b^x to y=b^-x. For horizontal shift, if going rightward, it is x-c. If going leftward, it is x+c. For vertical shift, if going up, b^x+h. If going down, b^x-h.

If unsure, plug-in points to see if your answer checks out with the equation :)

Answer: 5

Step-by-step explanation:

10 + 7h = 45

-10         -10

     7h = 35

divide by 7 to both sides

        h = 5

Ms. Brock can now fill up to 88 spray bottles with her preparation.

It is calculated that:

hence we have that

1 gallon = 128 fluid ounces

1 pint = 16 fluid ounces  

cross multiplying

16 fluid ounces x 1 gallon = 128 fluid ounces x 1 pint

1 gallon = (128 fluid ounces x 1 pint) / 16 fluid ounces

1 gallon = 8 pints

Consequently, there are 8 pints in one full gallon.

Ms. Brock blended 1 gallon of cleaner with 10 gallons of water, thus resulting in 11 gallons.

To figure out the total number of pints Ms. Brock has in her solution, we must multiply 11 gallons by 8 pints/gallon:

11 gallons x 8 pints/gallon = 88 pints

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If each locker is identified by one letter and one digit, the total number of lockers built in the school is 229.

There are 26 letters in the alphabet (A to Z), and if each locker is identified by one letter and one digit, then there are a total of 26 × 10 = 260 possible locker identifications using the letters A to Y and digits 0 to 9.

Out of these, there are 4 digits used to identify the lockers with the letter Z. So, there are 10 − 1 = 9 digits left to use for the remaining lockers, as we cannot use the digit already used for the lockers with the letter Z.

Similarly, there are 25 letters left to use for the remaining lockers, as we cannot use the letter Z.

Therefore, the number of remaining lockers is 9 × 25 = 225. Adding the 4 lockers with the letter Z, the total number of lockers built in the school is 225 + 4 = 229.

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The only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

The temperature on Skylar's thermometer is measured using a scale that indicates the degree of hotness or coldness of the atmosphere. In this case, we know that the temperature on her thermometer last night was −3°F. The negative sign indicates that the temperature was below the freezing point of water.

We are asked to determine what the temperature could be on her thermometer this morning. Since we are told that the temperature is colder than −3°F, we can eliminate 0°F and 2°F as possible options, as they are warmer than −3°F.

Similarly, −1°F is only slightly colder than −3°F, so it is unlikely to be the temperature on Skylar's thermometer this morning. Therefore, the only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

It is important to note that temperature can have a significant impact on our daily lives. Extreme cold temperatures can cause frostbite, hypothermia, and other health hazards, while hot temperatures can lead to dehydration, heat exhaustion, and heat stroke. It is important to dress appropriately and take necessary precautions when the temperature is too low or too high.

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The range of x values between which a zero can be found is -9/4 < x < -4.

Since x + 4 and 4x + 9 are linear factors of the quadratic expression, the quadratic expression can be written as:

Q(x) = k(x + 4)(4x + 9)

where k is some constant.

To find the values of x for which Q(x) = 0, we can set each factor equal to zero and solve for x:

x + 4 = 0 --> x = -4

4x + 9 = 0 --> x = -9/4

Therefore, the zeros of Q(x) are x = -4 and x = -9/4.

To find the range of x values between which a zero can be found, we need to determine the sign of Q(x) in each of the three intervals:

1. x < -9/4

2. -9/4 < x < -4

3. x > -4

For x < -9/4, both x + 4 and 4x + 9 are negative, so Q(x) = k(negative)(negative) = k(positive), which is positive.

For x > -4, both x + 4 and 4x + 9 are positive, so Q(x) = k(positive)(positive) = k(positive), which is also positive.

For -9/4 < x < -4, x + 4 is positive and 4x + 9 is negative, so Q(x) = k(positive)(negative) = k(negative), which is negative.

Therefore, the range of x values between which a zero can be found is -9/4 < x < -4.

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Deloria is analyzing the relationships between relative frequencies of nuts.

She has found that the relative frequency of a specific type of nut is 15%, which is calculated by dividing the number of that nut (3) by the total number of nuts (30).

Deloria might be comparing this relative frequency to other types of nuts to determine their prevalence or importance in a given context.

To calculate the relative frequency, we can divide the number of occurrences of the specific nut (3) by the total number of nuts (30):

Relative frequency = (Number of occurrences of specific nut) / (Total number of nuts)

Relative frequency = 3 / 30 = 0.1 = 10%

Therefore, the relative frequency of the specific type of nut is 10%, not 15%. It seems there was an error in the initial statement.

By analyzing relative frequencies, Deloria can compare the prevalence or importance of different types of nuts in a given context.

By calculating and comparing the relative frequencies of different types of nuts, Deloria can gain insights into the distribution and significance of each nut type within the dataset or sample.

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The given expression, 14⁻³ · 14¹², written as a single, positive exponent is 14⁹

From the question, we are to write the given expression using a single, positive exponent

From the given information,

The given expression is

14⁻³ · 14¹²

This means

14⁻³ × 14¹²

To solve this, let us revise some of the laws of indices

Thus,

The expression

14⁻³ × 14¹²

can be written as

14⁻³ ⁺ ¹²

14⁹

Hence, the expression written as a single exponent is 14⁹

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the price of one apple after solving the simultaneous equations is $1.45.

Let's denote the price of one apple by "a" and the price of one banana by "b". We can then set up a system of two equations to represent the given information:

4a + 9b = 12.70 (equation 1)
8a + 11b = 17.70 (equation 2)

To solve for the price of one apple, we want to isolate "a" in one of the equations. One way to do this is to multiply equation 1 by 8 and equation 2 by -4, which will allow us to eliminate "b" when we add the two equations together:

(8)(4a + 9b) = (8)(12.70) --> 32a + 72b = 101.60 (equation 3)
(-4)(8a + 11b) = (-4)(17.70) --> -32a - 44b = -70.80 (equation 4)

Adding equations 3 and 4 gives:

28b = 30.80

Solving for "b" yields:

b = 1.10

Substituting this value of "b" into equation 1 gives:

4a + 9(1.10) = 12.70

Solving for "a" yields:

a = 1.45

Therefore, the price of one apple is $1.45.

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