an old refrigerator consumes 202 w of power. assuming that the refrigerator operates for 18 hours every day, what is the annual operating cost of the refrigerator if the cost of electricity is $0.09 per kwh? answer to two decimal places without a unit.

Answers

Answer 1

The Annual operating cost of the refrigerator = Energy consumed × Cost of electricity= 1324.74 kWh × $0.09 per kWh = $119.22 (approx.)Hence, the answer is $119.22 (approx.)

Given:Power consumed by the old refrigerator = 202 WAssuming the refrigerator operates for 18 hours every day.Cost of electricity is $0.09 per kWh.Solution:Power consumed by the old refrigerator in an hour = 202 WTime for which the refrigerator operates every day = 18 hours Energy consumed by the refrigerator in a day = Power consumed × Time = 202 W × 18 hours = 3636 Wh Energy consumed by the refrigerator in a year (365 days) = 3636 Wh × 365 days= 1324740 Wh = 1324.74 kWhCost of electricity is $0.09 per Therefore, Annual operating cost of the refrigerator = Energy consumed × Cost of electricity= 1324.74 kWh × $0.09 per kWh = $119.22 (approx.)Hence, the answer is $119.22 (approx.).

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Related Questions

I have been stuck on this/ that

Answers

The coordinates of the graph when reflected over x-axis is given as A' (7, -8) and B' (2, -3).

What are transformations?

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The mapping of reflection over the x-axis is depicted as follows:

(x, y) to (x, -y)

The coordinates of A and B are:

A (7, 8)

B (2, 3)

After the reflection over x-axis the coordinates are transformed as follows:

A' = (7, -8)

B' = (2, -3)

Hence, the coordinates of the graph when reflected over x-axis is given as A' (7, -8) and B' (2, -3).

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What’s of the following describes a situation in which there is a linear relationship between time and population. 1. The population doubles each year. 2. The population increases by 500 the first year, by 1000 the next year, by 1500 the next year, and so on. 3. The population increases by 2000 people each year. 4. The population increases by 10% each year.

Answers

The statement that describes a linear relationship between time and population is 3. The population increases by 2000 people each year.

What is a linear relationship?

A linear relationship is an association between two variables, for example, time and population.

In a linear relationship, there is a straight-line relationship between the two variables, which can be expressed graphically or as a mathematical equation, y = mx + b.

There is a positive linear relationship when the slope is positive such that as the independent variable increases, the dependent variable increases.

A negative linear relationship exists when one increases while the other variable decreases.

Finally, a linear relationship can show a neutral relationship when the slope is 0, then as one variable increases, the other remains constant.

Thus, the linear relationship between time and population is best described by Option 3.

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You select a sample of 20 kids in the Valley Kindergarten and observe that their ages are
9; 9.5; 9.5; 10; 10; 10; 10; 10.5; 10.5; 10.5; 10.5; 11; 11; 11; 11; 11; 11; 11,5; 11,5; 11.5
Find the sample standard deviation of the age distribution in the Wenatchee Valley Kindergarten.
Solution. Please write your detailed solution here:

Answers

Standard deviation of the following data is 0.655.

What is standard deviation?

The standard deviation is equal to the variance's positive square root. It is a fundamental statistical analysis method. The amount by which data values deviate from the mean is referred to as "standard deviation," or "SD."

Whereas a big standard deviation implies that the values are much outside the mean, a low standard deviation shows that the values are frequently only a few standard deviations from the mean.

Here in the question,

Total kids = 20.

Mean = 9+9.5+9.5+10+10+10+10+10.5+10.5+10.5+10.5+11+11+11+11+11+11+11.5+11.5+11.5/20

= 10.52

Now square of distance between mean and ages.

(9-10.52) ² = 2.31

(9.5-10.52) ² = 1.04

(10-10.52) ² = 0.27

(10.5-10.52) ² = 0.0004

(11-10.52) ² = 0.23

(11.5-10.52) ² = 0.96

Now sum of all the differences = 2.31 + 1.04 + 1.04 + 4×0.27 + 4× 0.0004 + 6× 0.23+ 3×0.96

= 8.73

Now standard deviation = √8.73/20

= √0.43

= 0.655

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N + 2/5 = 4/5
What is “N”?

Answers

Answer:

2/5

Step-by-step explanation:

same denominator so ignore it.

2 + 2 = 4

2/5 + 2/5 = 4/5

simple way.

2/5 because 2 plus 2 is 4 and you keep the same denominator

i need this answer for my hw please help me

Answers

In order for ΔCAM≅ΔCOM to be proved, all three sides and all three angles must be equal. So the correct answer is E. ΔCAM≅ΔCOM.

What is corresponding sides?

Corresponding sides are two sides in a polygon that are directly across from each other. This can be seen when two sides are connected by a line that is perpendicular to the other two sides.

ΔCAM≅ΔCOM can be proved when the two triangles have three corresponding sides and three corresponding angles that are equal.

However, option E does not provide proof of this as it only states that two angles are equal.

The other four options provide such proof.

Option A states that two angles are equal, Option B states two lines are equal and two angles are equal, Option C states two lines are equal and two angles are equal, and Option D states two lines are equal and two lines are equal. All of these provide the proof that ΔCAM≅ΔCOM.

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In order for ΔCAM≅ΔCOM to be proved, all three sides and all three angles must be equal. Option E does not provide proof of this as it only states that two angles are equal. So the correct answer is E. ΔCAM≅ΔCOM.

What is corresponding sides?

Corresponding sides are two sides in a polygon that are directly across from each other. This can be seen when two sides are connected by a line that is perpendicular to the other two sides.

ΔCAM≅ΔCOM can be proved when the two triangles have three corresponding sides and three corresponding angles that are equal.

However, option E does not provide proof of this as it only states that two angles are equal.

The other four options provide such proof.

Option A states that two angles are equal,

Option B states two lines are equal and two angles are equal,

Option C states two lines are equal and two angles are equal, and Option D states two lines are equal and two lines are equal.

All of these provide the proof that ΔCAM≅ΔCOM.

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Graph the following inequality on a number line. Upload your picture.
x > 3

Answers

Answer:

x>3

Step-by-step explanation:

please answer it i need to know what the value of x is and thank you so much

Answers

Answer:

54

Step-by-step explanation:

the angle measures of any triangle add up to 180 degrees, so we need to add all of the given measures and set it equal to 180.

(x) + (40) + (2x - 22) = 180

3x + 18 = 180

3x = 162

x = 54

. a model for the population p(t) in a suburb of a large city is given by the initial-value problem dp dt 5 p(1021 2 1027 p), p(0) 5 5000, where t is measured in months. what is the limiting value of the population? at what time will the population be equal to onehalf of this limiting value?

Answers

The population will be equal to one-half of the limiting value after 4.67 months.

Model for the population p(t) in a suburb of a large city is given by the initial-value problem dp/dt= 5 p(1021−2×1027p), p(0) = 5000. Now we are to find out the limiting value of the population and the time when the population will be equal to one-half of the limiting value.Limiting value of the populationThe limiting value is the population value when the population grows until it levels off. In other words, we can say that it is the maximum population that can be sustained by the resources available.

We can find the limiting value by considering what would happen if the rate of change of the population became zero. This can occur only when p=0 or 1021−2×1027p =0.Solving this equation, we get p = 0 and p = 5.1 × 10⁷/2 = 2.55 × 10⁷Thus, the limiting value of the population is 2.55 × 10⁷.We know that the population is given by p(t) and we have to find the time when the population will be equal to one-half of the limiting value. To find t, we need to solve the differential equation dp/dt= 5 p(1021−2×1027p).

Separating variables, we getdp/p(1021−2×1027p) = 5 dtOn integrating, we get-1/2 ln|1021−2×1027p| = 5t + CWhere C is the constant of integration.Using the initial condition p(0) = 5000, we getC = -1/2 ln|1021−2×1027(5000)|Solving for C, we getC ≈ -2.97Solving for p, we get1021−2×1027p = ±e^(-10t+2.97)Multiplying both sides by -1/2, we get-0.5(1021−2×1027p) = ±0.5e^(-10t+2.97)Taking the negative sign, we getp = 0.5(1021 + 0.5e^(-10t+2.97))/1027Substituting p = 1.275 × 10⁷, we get1.275 × 10⁷ = 0.5(1021 + 0.5e^(-10t+2.97))/1027Multiplying both sides by 1027 and simplifying, we get1.32 × 10^4 = 1021 + 0.5e^(-10t+2.97)Solving for e^(-10t+2.97), we gete^(-10t+2.97) = 2 × (1.32 × 10^4 - 1021)Taking the natural logarithm, we get-10t + 2.97 = ln[2 × (1.32 × 10^4 - 1021)]Solving for t, we gett ≈ 4.67 months.

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Bo and Erica are yoga instructors. Between the two of them, they teach 43 yoga classes each week. If Erica teaches 11 fewer than twice as many as Bo, how many classes does each instructor teach per week?

Answers

Answer:

Erica teaches 32.33 or 32 classes

Bo teaches 10.67 or 10 classes

Step-by-step explanation:

B + E = 43

E - 11 = 2B

B + E = 43

E = 43 - B

E - 11 = 2B

(43 - B) - 11 = 2B

B = 10.67 = 10

B + E = 43

(10.67) + E = 43

E = 32.33 = 32

Suppose that the functions q and r are defined as follows. Find the following

Answers

The value of the function q and r are as follows (q ° r )(7) = 22 and (r ° q)(7) = 8.

What are composite functions?

The process of integrating two or more functions into one function is known as composition of functions. A function is an example of labour. Take making bread as an example. Let x be the flour, let g(x) be the function that the food processor performs to prepare the dough using the flour, and let f(x) be the function that the oven does to bake the bread. The output of g(x) should be sent into the function f(x) to make bread (i.e., the prepared dough should be placed in the oven). The outcome is represented by the symbol f(g(x)), and it is made up of the functions f(x) and g. (x).

The function q and r are as follows:

q(x) = x² + 6

r(x) = √(x + 9)

The value of:

(q ° r )(x) = q(r(x))

Here, substitute the value of x in q(x) with the value of r(x):

q(r(x)) = (√(x + 9))² + 6

q(r(x)) = x + 9 + 6

Substitute x = 7:

q(r(7)) = 7 + 9 + 6 = 22

Now, (r ° q) = r(q(x))

r(q(x)) = √(x² + 6 + 9)

= √(x² + 15)

Substitute x = 7:

r(q(7)) = √(7² + 15) = √(49 + 15) = √64 = 8

Hence, the value of the function q and r are as follows (q ° r )(7) = 22 and (r ° q)(7) = 8.

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what enone product would you expect to obtain from intramolecular aldol condensation of 3-methylheptane dial?

Answers

The expected product from the intramolecular aldol condensation of 3-methylheptane dial is a cyclic α,β-unsaturated ketone with a seven-membered ring.

3-methylheptane dial is a 7-carbon compound with two carbonyl groups, one at each end of the molecule. Intramolecular aldol condensation occurs when one carbonyl group reacts with the other within the same molecule. The carbonyl group acts as an electrophile, while the enolate formed from the other carbonyl group acts as a nucleophile.

In the case of 3-methylheptane dial, intramolecular aldol condensation can occur between the carbonyl group at the 3-position and the enolate formed from the carbonyl group at the 6-position. The resulting intermediate undergoes dehydration to form a cyclic α,β-unsaturated ketone.

The product of the reaction will have a cyclic structure with a double bond between the α and β carbons. The exact structure of the product will depend on the stereochemistry of the starting material and the reaction conditions. However, the product is expected to have a seven-membered ring and to be an α,β-unsaturated ketone.

Therefore, the expected product from the intramolecular aldol condensation of 3-methylheptane dial is a cyclic α,β-unsaturated ketone with a seven-membered ring.

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(-77.92) + (-8.39) + 59.4 - (-91.77)

Answers

Answer:

64.86

Step-by-step explanation:

Given: (-77.92) + (-8.39) + 59.4 - (-91.77)

The + and - will become -, and the - and - will become +:

-77.92 - 8.39 + 59.4 + 91.77

Finally, calculate:

-86.31 + 151.17

= 64.86

is -2/3 less than or greater than -5/2?????????/

Answers

Answer:

Greater than

Step-by-step explanation:

With negative numbers the smaller it is, the more its worth. (If that makes sense) -2 is MUCH bigger than -500

:)

Monique has 4 pencils for every 2 pens in her backpack. If she has 6 pencils, how many pens does she have? If pens are the X variable and pencils are the Y variable, plot this relationship as a point in the coordinate plane.

Answers

Answer: 3 pens

Step-by-step explanation: The ratio of pencils to pens Monique has is 2:1, this means that for every 2 pencils Monique has she will have 1 pen. To plot this on a graph you can put one point at (2,1) and another point at (4,2)

in 2001, the population of a district was 26,100. with a continuous annual growth rate of approximately 4%, what will the population be in 2026 according to the exponential growth function?

Answers

The population in 2026 according to the exponential growth function will be approximately 54,515.

According to the exponential growth function, what will be the population in 2026 if in 2001 the population of a district was 26,100 and with a continuous annual growth rate of approximately 4%?

Given,

The population in 2001 = 26,100

Annual growth rate = 4%

Population growth function can be written as,

[tex]P(t) = P0e^rt[/tex]

Where,P(t) = Population after t years

P0 = Population at time t = 0

r = Annual growth rate (in decimal form)

t = Time (in years)

According to the given question,In the year 2026, the number of years from 2001 is,2026 – 2001 = 25 years

Therefore,t = 25 years

r = 4% = 0.04

Using these values in the population growth function,

[tex]P(t) = P0e^rt[/tex]

Population in 2026 = P(25)

[tex]P(25) = 26,100e^(0.04 x 25)[/tex]

P(25) = 26,100e

P(25) ≈ 54,515

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Write -1.1 as a mixed number.

Answers

Answer:

- 1 1/10

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

A mixed number is the number in the format a b/c, where a - whole number and b/c - the fraction part.

Show the given as a mixed number:

- 1.1 = - (1 and 0.1) = - (1 and 1/10) = - 1 1/10

List down three (3) equations that can be seen in the graph for each type of function and identify their
domamn and range.

constant funtion

Function,Domain,Range=

linear function

function,domain,range=

quadratic function

function,domain,range=

Answers

Three equations that can be seen in the graph for each type of function are x = -6, y = 1.5x  -2.5 and y = x² + 6x + 10

How to calculate the identities and equations of the functions

Function 1: Constant

A constant function is a mathematical function that always returns the same output value regardless of its input.

A constant function with the equation x = -6 exist on the graph with the following features: x = -6 as domain and [0, 4] as the range

Function 2: Linear

A linear function is a type of mathematical function where the output varies linearly with the input.

From the graph, we have the points

(4, 3.5) and (5, 5)

Using a graphing tool, the equation is

y = 1.5x  -2.5

And the identities are [4, 5] as the domain and [3.5, 5] as the range

Function 3: Quadratic

This is a function of the form y = a(x - h)² + k or y = ax² + bx + c

From the graph, we have

(h, k) = (-3, 1) and (x, y) = (-2, 2)

Using a graphing tool, the equation is

y = x² + 6x + 10

And the identities are [-4, -2] as the domain and [1, 2] as the range

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Determine whether the polygons with the given vertices are congruent. Use transformations to explain your reasoning. 7. A(8, -6), B(1, -3), C(1, -9), and D(-7, 1), E(0, -2), F(0, 4) 8. J(-4, 1), K(-10, 3), L(-10, 9), M(-4, 7) and N(4, 2) O(2, -8), P(-4, -8), Q(-2, 2)

Answers

(7)  The two polygons are congruent since we can obtain a congruent image of DEF by applying a translation or a rotation.

(8) The two polygons are congruent since we can obtain a congruent image of JKLM by applying a translation or a rotation.

What is the translation or a rotation of the polygons?

To determine whether the two polygons are congruent, we can apply a series of transformations to one of them to see if it can be mapped onto the other.

(7) Let's first label the polygons: ABCD is the first polygon and DEF is the second polygon.

Translation: We can translate DEF four units to the right and two units down to obtain the image of DEF, which is congruent to ABCD.

Rotation: We can rotate DEF about the point (0, 1) by 180 degrees to obtain the image of DEF, which is congruent to ABCD.

Since we can obtain a congruent image of DEF by applying a translation or a rotation, we can conclude that the two polygons are congruent.

(8) Let's label the two polygons: JKLM is the first polygon and NOPQ is the second polygon.

Translation: We can translate JKLM six units to the right and three units down to obtain the image of JKLM, which is congruent to NOPQ.

Rotation: We can rotate JKLM about the point (-4, 4) by 180 degrees to obtain the image of JKLM, which is congruent to NOPQ.

Since we can obtain a congruent image of JKLM by applying a translation or a rotation, we can conclude that the two polygons are congruent.

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how many extra calories would a person burn if they slowly walked (1.7 miles per hour) rather than sit for one hour?

Answers

On average, a person weighing 150 pounds can burn approximately 80 to 90 extra calories by slowly walking at a pace of 1.7 miles per hour for one hour instead of sitting.

The number of extra calories a person would burn by slowly walking instead of sitting for one hour depends on various factors, such as the person's weight, height, age, and gender. However, on average, a person weighing 150 pounds can burn approximately 80 to 90 calories by walking at a slow pace of 1.7 miles per hour for an hour.

This number may vary slightly based on individual differences and other factors, such as incline or terrain. Walking is a low-impact form of exercise that can help increase calorie burn and improve overall health, making it a great option for those looking to lead a more active lifestyle.

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A weather station on the top of a mountain reports that the temperature is currently oc and has been falling at a constant rate of 3c per hour.if it continues to fall at this rate find each indicated temperature explain or show your reasoning

Answers

Therefore , the solution of the given problem of unitary method comes out to be the temperature will continue to drop at a rate of 3°C per hour, meaning that it will be 3°C colder .

What is a unitary method?

The task may be completed using this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, you may have another opportunity to interact with the item. Otherwise, all significant factors that affect how algorithmic factor proof behaves will be gone.

Here,

=> T = -3t + 0

We need only change the value of t in the equation and simplify to determine the temperature at a particular moment.

For instance:

T equals 1 after one hour:

=> T = -3(1) + 0 T = -3

So, the weather is -3°C after an hour.

T equals 2 after two hours:

=> T = -3(2) + 0 T = -6

Thus, the temperature is -6°C after two hours.

T equals 3 after three hours:

=> T = -3(3) + 0 T = -9

So, the weather is -9°C after three hours.

so forth,

As a result, the temperature will continue to drop at a rate of 3°C per hour, meaning that it will be 3°C colder after each hour than it was the hour before.

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david has real 18 pages more than 1/4 pages of a book. write an expressions to represents the p pages david has read.

Answers

The expression to represent the p pages David has read is: p = 18 + (1/4)x, where x is the total number of pages in the book.

David has read 18 pages more than 1/4 pages of a book. The expression to represent the p pages that David has read would be: p = 18 + (1/4)x, where x is the total number of pages in the book. The reasoning behind this is as follows:

David has already read 18 pages more than 1/4 of the book, so we have to add 18 pages to whatever the pages of the book are. Since we don't know what the actual number of pages are, we'll call that x. Therefore, David read 1/4 of the book (or 1/4 of x) plus 18 pages.

Hence, the expression is: p = 18 + (1/4)x.

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What is the relationship between the central angle and the interior angle?

As the number of sides increases, how do the angles change?

Please use complete sentences. Thanks!

Answers

The relationship between the central angle and interior angle is Central angle = 2 * Interior angle.

What is internal angle and central angle?

The internal angle is the angle created by two adjacent sides of a polygon within the circle, whereas the central angle is the angle formed by two radii of a circle that intersect at its centre. Since one of the sides of the polygon opposing the interior angle is opposite the central angle, the two angles are connected by the following formula:

central angle = 2 * Interior angle.

As the number of sides in a polygon increases, the measure of each interior angle decreases while the measure of each central angle remains constant.

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Please help me, this question is so hard

Answers

The shaded portion of the rectangle is approximately 21.8% of the rectangle, rounded to the nearest 10th.

Describe Rectangle?

In geometry, a rectangle is a four-sided polygon with four right angles (90-degree angles) and opposite sides that are parallel and congruent to each other. It is a special case of a parallelogram in which all angles are right angles.

The properties of a rectangle include:

Opposite sides are parallel and congruent.

All angles are right angles.

Diagonals are congruent and bisect each other.

The area of a rectangle is given by the formula A = lw, where l is the length and w is the width.

The perimeter of a rectangle is given by the formula P = 2l + 2w.

To solve this problem, we first need to find the areas of the shaded regions and the rectangle:

Area of rectangle = l × w = 26 × 16 = 416

Area of circle = (π × (d/2)²)/4 = (π × 4²)/4 = π

Area of pentagon = (5/2) × r² × sin(72°) = (5/2) × 5.5² × sin(72°) = 51.3

Area of right-angled triangle = (1/2) × h × d = (1/2) × 8 × 8 = 32

Total area of shaded region = Area of circle + Area of pentagon + Area of right-angled triangle = π + 51.3 + 32 ≈ 90.8

To find the percentage of the rectangle that is shaded, we divide the area of the shaded region by the area of the rectangle and multiply by 100:

Percentage of shaded region = (90.8/416) × 100 ≈ 21.8%

Therefore, the shaded portion of the rectangle is approximately 21.8% of the rectangle, rounded to the nearest 10th.

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The diagonal of a square is 10 inches long. What is the length, in inches, of each side of the square? Write the answer in simplified radical form.

Answers

The length of each side of the square is 5√2 inches

The diagonal of a square divides it into two 45-45-90 right triangles. In such triangles, the hypotenuse (which is the diagonal of the square) is √2 times as long as each leg. Let x be the length of each side of the square. Then we have

x√2 = 10

Solving for x, we get

x = 10 /√2

To simplify this expression, we can multiply both the numerator and denominator by √2

x = 10 /√2 × √2 /√2

Multiply the numbers

= 10√2 / 2

Divide the numbers

= 5√2 inches

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Please help me! LIKE RNWWW. I HAVE BEEN WAITING AND NO ONE HAS BEEN HELPING. THIS IS DUE AT 2:15 PM!!!! IN TWO MINSSS!!!!! A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency


B 247

I 272

N 238

G 241

O 252


For which letter is the experimental probability closest to the theoretical probability? Explain please.

Answers

The letter O has the experimental probability that is closest to its theoretical probability.

Define the term probability?

Probability is an area of statistics that deals with the study of random events and their likelihood of occurrence.

The theoretical probability of drawing a particular letter is the number of balls of that letter divided by the total number of balls in the game. For each letter, the theoretical probability is:

B: 15/75 = 0.2

I: 15/75 = 0.2

N: 15/75 = 0.2

G: 15/75 = 0.2

O: 15/75 = 0.2

The experimental probability of drawing a particular letter is the number of times that letter was actually drawn divided by the total number of draws. For each letter, the experimental probability is:

B: 247/1250 = 0.1976

I: 272/1250 = 0.2176

N: 238/1250 = 0.1904

G: 241/1250 = 0.1928

O: 252/1250 = 0.2016

Compare the differences between the theoretical and experimental probabilities for each letter. The letter with the smallest difference is the one whose experimental probability is closest to its theoretical probability.

Here, the differences between the theoretical and experimental probabilities for each letter are:

B: 0.2 - 0.1976 = 0.0024

I: 0.2 - 0.2176 = 0.0176

N: 0.2 - 0.1904 = 0.0096

G: 0.2 - 0.1928 = 0.0072

O: 0.2 - 0.2016 = 0.0016

Based on these calculations, we can see that the letter O has the smallest difference between its theoretical and experimental probabilities, with a difference of only 0.0016.

Therefore, the letter O has the experimental probability that is closest to its theoretical probability.

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Last month, the price of one pound of carrots was $2 1/12 and Joe
sold 12 1/12 pounds of carrots. This month, the price has increased
by $1 1/10and Farmer Joe only sold 5 1/8 pounds of carrots. What is
the price of a pound of carrots this month?

Answers

The price of a pound of carrots this month is $3.183.

What is the price of a pound of carrots in the month?

The price of one pound of carrots last month was $2 1/12. To add $1 1/10 to this price, we need to convert both prices to twelfths of a dollar to make the addition easier.

$2 1/12 = 25/12

$1 1/10 = 11/10

Adding these two prices together gives us:

= 25/12 + 11/10

= 3.18333333333

= $3.183.

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Find the surface area of the composite figure. 2 in. 4 in. 10 in. SA 4 in. 2 in. 4 in. 7 in. 4 in. = = [?] in.2 Sea FATEM 37049077 PED If you'd like, you can use a calculator. Enter​

Answers

The surface area of the composite figure is; SA = 224 in.²

How to find the area of a Composite Figure?

From the composite figure attached, we can find the surface area of each of the rectangular/square external face seen as:

[tex]SA= 2(10 \times 2) + 2(4 \times 7) + 2(4 \times 4) + 2(4 \times 2) + (4 \times 7) + (10 \times 4) + (3 \times 4)[/tex]

[tex]SA = 40 + 56 + 32 + 16 + 28 + 40 + 12[/tex]

[tex]SA = 224 \ \text{in}.^2[/tex]

Thus, we can conclude that the surface area of the composite figure is:

[tex]SA = 224 \ \text{in}.^2[/tex]

marketing companies have collected data implying that teenage girls use more ring tones on their cellular phones than teenage boys do. in one particular study of 40 randomly chosen teenage girls and boys (20 of each) with cellular phones, the mean number of ring tones for the girls was 3.3 with a standard deviation of 1.6. the mean for the boys was 1.6 with a standard deviation of 0.7. conduct a hypothesis test at the 5% significance level to determine if the girls' mean is higher than the boys' mean.

Answers

Conducting a hypothesis test at the 5% significance level we can conclude that the girls' mean is higher than the boys' mean.

To conduct a hypothesis test to determine if the girls' mean is higher than the boys' mean, you will need to use a two-tailed hypothesis test with a significance level of 5%. The null hypothesis is that the girls' mean is not higher than the boys' mean, and the alternative hypothesis is that the girls' mean is higher than the boys' mean. The test statistic is calculated using the formula:


Test statistic = (Girls' mean - Boys' mean) / (Standard deviation of the difference / √(sample size))

The test statistic for this study is calculated as: (3.3 - 1.6) / (1.6/√40) = 4.375.


Using a 5% significance level and two-tailed hypothesis test, the critical value for this test is 1.96. Since the test statistic (4.375) is greater than the critical value (1.96), the null hypothesis can be rejected.

Therefore, we can conclude that the girls' mean is higher than the boys' mean.

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The polynomial 3x³-16x² +31x-20 represents the area of a trapezoidal desktop. The length of the bases of the
trapezoid are represented by the expressions x + 5 and x² - 5x. If area of a trapezoid equals 1/2h(b₁ + b2), what is
the height of the trapezoid? Hint: Use long division. (please help i’ve been stuck on it for 45 minutes and i’m crying)

Answers

Therefore, the possible values for x are 1, 4, and 5.

First, let's use long division to factor the polynomial 3x³-16x²+31x-20, which represents the area of the trapezoidal desktop, by x²-5x+x-5:

           ____________________________

[tex]x^{2} -5x+x-5 | 3x^{3} - 16x^{2} + 31x - 20[/tex]

[tex]- (3x^{3} - 15x^{2} + 3x^{2} - 15x)[/tex]

           ____________________________

                  [tex]- x^{2} + 31x - 20[/tex]

                    [tex]-(- x^{2} + 5x - 5)[/tex]

                     ________________

                          [tex]26x - 15[/tex]

The result of the long division is x - 5 with a remainder of 26x - 15.

Therefore, we can rewrite the polynomial as:

[tex]3x^{3} - 16x^{2} + 31x - 20 = (x - 5)(x^{2} - 5x + 4) + (26x - 15)[/tex]

Now, let's use the formula for the area of a trapezoid to set up an equation using the polynomial above:

[tex]area = 1/2h(b_1 + b_2)[/tex]

We know that the bases of the trapezoid are represented by the expressions x + 5 and x² - 5x, so we can substitute them in the formula:

[tex]3x^{3} - 16x^{2} + 31x - 20 = 1/2h((x + 5) + (x^{2} - 5x))[/tex]

Simplifying the expression:

[tex]3x^{3} - 16x^{2} + 31x - 20 = 1/2h(x^{2} - 4x + 5)[/tex]

Multiplying both sides by 2:

[tex]6x^{3} - 32x^{2} + 62x - 40 = h(x^{2} - 4x + 5)[/tex]

Now, we can substitute the remainder of the long division we did earlier (26x - 15) for h:

[tex]6x^{3} - 32x^{2} + 62x - 40 = (x - 5)(x^{2} - 5x + 4) + (26x - 15)[/tex]

[tex]6x^{3} - 32x^{2} + 62x - 40 = (x - 5)(x^{2} - 5x + 4) + h[/tex]

[tex]6x^3 - 32x^2+ 62x - 40 = (x - 5)(x^2 - 5x + 4) + (26x - 15)[/tex]

Simplifying the expression again:

[tex]6x^3 - 32x^2 + 36x - 25 = (x - 5)(x^2 - 5x + 4)[/tex]

Now we have a quadratic equation that we can solve for x:

[tex]x^3 - 5x^2 + 4x + 5x^2 - 25x + 20 = 0[/tex]

[tex]x^3 - 21x + 20 = 0[/tex]

[tex](x - 1)(x - 4)(x - 5) = 0[/tex]

Therefore, the possible values for x are 1, 4, and 5.

Now we can substitute these values in the expression we derived for h:

[tex]h = (6x^3 - 32x^2 + 62x - 40)/(x^2 - 4x + 5)[/tex]

For x = 1:

[tex]h = (6(1)^3 - 32(1)^2 + 62(1) - 40)/2\\h = 6-32+62-40/2\\h = 68-72/2\\h = -4/2\\ h= -2[/tex]

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