Daniel built a wooden, cubic toy box for his daughter. Each edgeof the box measures 2 feet. How many square feet of wood did he use to build the house? A.

The rate at which the water was drained from the tank is 6 gallons of water per minute.

Given:

Draining Time (minutes)      10         30

Water in Tank (gallons)     450        330

According to the question,

Now, we calculating the rate at which water was drained at a constant rate.

Rate of water drained = [tex]\frac{Rate of change of water in Tank}{Rate of change Draining Time }[/tex]

Rate of water drained = [tex]\frac{450 - 330}{30 - 10} = \frac{120}{20} = 6[/tex]

The gallon is an important unit of measurement that continues to be used widely today. Specifically, it refers to the amount of space occupied by one US liquid gallon of water, which is equivalent to approximately 3.785 liters. The gallon is commonly used to measure liquids such as gasoline, milk, and water.

The term "gallon" has a long history, dating back to medieval England, where it was used to measure wine and beer. Over time, different countries and regions developed their own variations of the gallon, with the US liquid gallon being slightly larger than the UK imperial gallon. In addition to its use in everyday life, gallons are also used in various industries, including agriculture, manufacturing, and transportation.

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Complete Question:

A tank of water was drained at a constant rate. The table shows the number of gallons of water left in the tank after being drained for two amounts of time. Draining Time (minutes) Water in Tank (gallons) 10 450 30 330

Answer:

9

Step-by-step explanation:

since 16 is a positive number and the 7 is negative, it would basically be 16 - 7.

It is 8! x 5! or 483840 different arrangements.

To calculate the number of ways to arrange the letters in your first name, Joseph, there are 8! or 40320 different arrangements.

To calculate the number of ways to arrange the letters in your last name, Burke, there are 5! or 120 different arrangements.

Lastly, to calculate the number of ways to arrange the letters in both your first name and last name, it is 8! x 5! or 483840 different arrangements.

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A graph that represents the following ellipse (x + 1)²/16 + (y - 3)²/36 = 1 is: C. graph C.

Mathematically, the standard form of the equation of an ellipse is given by mathematical expression:

x²/a² + y²/b² = 1  

Where;

This ultimately implies that, the major axis of this ellipse is the x-axis. By critically observing the graph (see attachment), we can logically deduce the following values:

a = √16 = 4.

b = √36 = 6.

In conclusion, the standard form of the equation of this ellipse is given by (x + 1)²/16 + (y - 3)²/36 = 1.

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The limiting probabilities are π0 = 7/12 and π1 = 5/12.

Verify that this is an irreducible ergodic Markov chain.

An irreducible Markov chain is one in which it is possible to move from any state to any other state in a finite number of steps. In this case, the probability transition matrix P is:

P = [0.4 0.6]

   [0.7 0.3]

Since there are non-zero probabilities in every row and column, it is possible to move from any state to any other state in a finite number of steps. Therefore, this is an irreducible Markov chain.

An ergodic Markov chain is one in which every state is positive recurrent and aperiodic. Since this is an irreducible Markov chain, every state is positive recurrent. Additionally, there are no cycles in the transition matrix, so every state is aperiodic. Therefore, this is an ergodic Markov chain.

Compute the two step transition probability matrix P(2).

The two step transition probability matrix P(2) is obtained by multiplying the matrix P by itself:

P(2) = P * P = [0.4 0.6] * [0.4 0.6]

                  [0.7 0.3]                    [0.7 0.3]

         = [0.4*0.4 + 0.6*0.7  0.4*0.6 + 0.6*0.3]

              [0.7*0.4 + 0.3*0.7  0.7*0.6 + 0.3*0.3]

         = [0.58  0.42]

              [0.49  0.51]

Find the limiting probability π0 and π1.

The limiting probabilities are the stationary probabilities of the Markov chain, which are obtained by solving the following system of equations:

π0 = 0.4*π0 + 0.7*π1

π1 = 0.6*π0 + 0.3*π1

π0 + π1 = 1

Solving this system of equations gives:

π0 = 7/12

π1 = 5/12

Therefore, the limiting probabilities are π0 = 7/12 and π1 = 5/12.

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The answer to the question "What is (fog)(x)?" is:
(fog)(x) = x

The first step in solving this problem is to find the composition of f and g, or (fog)(x). This is done by substituting the expression for g(x) into the expression for f(x):
(fog)(x) = f(g(x)) = f(1/11x) = 11(1/11x) = x
Similarly, we can find the composition of g and f, or (gof)(x), by substituting the expression for f(x) into the expression for g(x):
(gof)(x) = g(f(x)) = g(11x) = 1/11(11x) = x
Now, we can determine whether (fog)(x) = (gof)(x) by comparing the two expressions. Since both (fog)(x) and (gof)(x) are equal to x, we can conclude that (fog)(x) = (gof)(x).
Therefore, the answer to the question "What is (fog)(x)?" is:
(fog)(x) = x

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Answer:

answer is D

Step-by-step explanation:

if you replace X with 4 the equation should give you a 0.

after the long division method, you will obtain a quadratic equation.

to solve the quadratic equation you can use either of the known methods like factorisation or graphical methods or the quadratic formula.

t

(1)

21m^2 ÷ 7m = 3m

The quotient is 3m and there is no remainder.

(3)

(-48p^4) ÷ (-9p^2) = 5p^2 + (3p^2/(-9p^2)) = 5p^2 - (1/3)

The quotient is 5p^2 - (1/3) and the remainder is -(1/3).

(5)

(5x^3 - 3x^2) ÷ x^2 = 5x - 3

The quotient is 5x - 3 and there is no remainder.

(7)

(2y^3 + 4y^2 + 3) ÷ 2y^2 = y + (y+3)/(2y^2) = y + (3)

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Using Compound Interest, The largest balance is $7802.55, so the option A will give them the largest balance after 5 years.

Even though there are several ways to define an investor, compound interest helps investors. When banks lend money and utilize the income they earn to finance other loans, for instance, they profit from compound interest. When depositors earn interest on their bank accounts, bonds, or other investments, compound interest benefits them.

here, we have,

It's crucial to remember that although while "compound interest" includes the word "interest," the idea extends beyond the contexts in which the expression is typically employed, such as bank accounts and loans.

We will calculate compound interest in every case:

Using formula

amount = P(1+r/m)^t

option A: balance after 5 years:

7802.55

option B:

balance after 5 years:

7789.84

option C:

balance after 5 years:

7768.85

The largest balance is $7802.55, so the option A will give them the largest balance after 5 years.

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Answer:

Step-by-step explanation:

to the rieft

The simplified form of the expression ( -3 )² + ( -2 )² is 13.

Given the expression in the question;

( -3 )² + ( -2 )²

To solve the expression (-3)² + (-2)², we first need to simplify each term inside the parentheses by multiplying each term by itself.

It involves squaring the values of -3 and -2, and then adding them together.

First, we can simplify;

(-3)² as (-3) x (-3), which gives us 9.

Similarly,

(-2)² can be simplified as (-2) x (-2), which gives us 4.

So, substituting these values back into our original expression, we get:

(-3)² + (-2)² = 9 + 4 = 13

(-3)² + (-2)² = 12

Therefore, (-3)² + (-2)² simplifies to 13.

Option C) 13 is the correct answer.

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Answer:

Step-by-step explanation:

No, Selena is incorrect.

answer: Even though there are six

more people than pizzas at the large table and only five more people

than pizzas at the small table, each person at the large table will get

a greater share of pizza than each person at the small table.

The answer is (5h+18)/(14).

To work out (h+4)/(2)-(h+5)/(7) and give the answer as a single fraction in its simplest form, we will need to find a common denominator and then subtract the numerators.

Step 1: Find a common denominator. The common denominator of 2 and 7 is 14.
Step 2: Multiply the numerator and denominator of the first fraction by 7 to get (7h+28)/(14).
Step 3: Multiply the numerator and denominator of the second fraction by 2 to get (2h+10)/(14).
Step 4: Subtract the numerators: (7h+28)-(2h+10) = 5h+18.
Step 5: Place the difference over the common denominator: (5h+18)/(14).
Step 6: Simplify the fraction if possible. In this case, the fraction cannot be simplified further.

Therefore, the answer is (5h+18)/(14).

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Each student gets 1/3 of the juice.

What is Division?

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.

When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.

Each student gets 1/3 of the juice.

Equation: 1/3 x 5 = 5/3 or 1 2/3 liters per student.

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The reflection of the shape over the line p is drawn and added as an attachment

When a shape is reflected over a line, it is flipped across that line. The reflected image of the shape is a mirror image of the original shape, and appears to be a mirror image of the original shape.

This means that we simply flip the shape over the line of reflection

The line over which the shape is reflected is called the line of reflection, and it acts as a mirror. In this case, it is the line p. The shape and its reflected image are symmetric with respect to the line of reflection.

Flipping the shape would result in any point on the original shape and its corresponding point on the reflected image are equidistant from the line of reflection, as the distance between a point and its reflected image is equal to twice the perpendicular distance from the point to the line of reflection.

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Answer:

The polynomial is:

[tex]15h^2+42h+24[/tex]

Step-by-step explanation:

We have to simplify the expression which is given as:

[tex](5h + 4)(3h + 6)[/tex]

We have to simplify with the use of a table as:

            3h              6

5h          [tex]15h^2[/tex]         [tex]30h[/tex]

4            [tex]12h[/tex]              [tex]24[/tex]      

Hence, the polynomial that is formed using this table form simplification is addition of all the entries in the table i.e.:

[tex](5h + 4)(3h + 6)=15h^2+30h+12h+24[/tex]

[tex](5h + 4)(3h + 6)=15h^2+42h+24[/tex]

Hence, the polynomial is:

[tex]15h^2+42h+24[/tex]

Carl's cable company is cheaper than Teleview. For 14 or more movies, teleview is cheaper than Carl's cable company.  

by the question.

Let's represent the number of movies by the variable "x".

The cost of Carl's cable company is given by:

C(x) = 55 + 4x

The cost of Teleview cable company is given by:

T(x) = 110

We want to find the number of movies for which Carl's cable company is cheaper than teleview. In other words, we want to find x such that:

C(x) < T(x)

Substituting the expressions for C(x) and T(x), we get:

55 + 4x < 110

Subtracting 55 from both sides, we get:

4x < 55

Dividing both sides by 4, we get:

x < 13.75

Since the number of movies has to be a whole number, the largest number of movies for which Carl's cable company is cheaper than teleview is 13.

For 13 or fewer movies,

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When t = 5, the value οf the expοnential functiοn[tex]y = 25(1.2)^t[/tex] is apprοximately 36.7.

An expοnential functiοn is a mathematical functiοn οf the fοrm[tex]f(x) = ab^x[/tex] where a and b are cοnstants, and x is the independent variable. The base b is a pοsitive cοnstant greater than 0 and nοt equal tο 1.

In the expοnential functiοn [tex]y = 25(1.2)^t[/tex], the initial amοunt is 25, which is the value οf the functiοn when t = 0.

The rate οf grοwth is 20%, which is the value οf the base οf the expοnential functiοn minus 1, expressed as a percentage. In this case, the base is 1.2, which is 20% greater than 1.

Tο evaluate the functiοn when t = 5, we substitute t = 5 intο the functiοn and simplify:

[tex]y = 25(1.2)^t[/tex]

[tex]y = 25(1.2)^5[/tex]

[tex]y = 25(1.469)[/tex]

[tex]y = 36.73[/tex]

Rοunding tο the nearest tenth, we get y ≈ 36.7.

Therefοre, when t = 5, the value οf the expοnential functiοn [tex]y = 25(1.2)^t[/tex]is apprοximately 36.7.

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Answer:

x=63

Step-by-step explanation:

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

The ANOVA will depend on the total sample size.

a. False. The psychologist's reasoning is incorrect, as the critical value for evaluating the ratio of between-group mean squares to within-group mean squares for the ANOVA does not depend solely on the total sample size, but also on the number of groups being compared and the level of significance. Furthermore, a Bonferroni adjusted post-hoc test does not require the p-value for each pairwise comparison to be no more than .0083 to be considered as statistically significant.

b. True. The critical value for evaluating the ratio of between-group mean squares to within-group mean squares for the ANOVA will depend on the total sample size, as well as on the number of groups being compared and the level of significance. Therefore, if the observed means across the three conditions differ entirely due to sampling errors, the critical value for evaluating the ratio of between-group mean squares to within-group mean squares for the ANOVA will depend on the total sample size.

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Answer:

See below.

Step-by-step explanation:

We are asked to find the value of x.

We should know that these angles are Same-Side Interior Angles.

Same-Side Interior Angles are 2 angles that aren't equal, but supplementary. They're formed inside 2 parallel lines.

Supplementary angles are 2 angles that add up to 180°.

Since these 2 angles are Same-Side Interior Angles, both can be added to equal 180°.

[tex]4x+2x+12=180[/tex]

Combine Like Terms:

[tex]6x=168\\x = 28[/tex]

The value of x is 28.

Answer: 1

Step-by-step explanation:

(6) + (8) ÷ 8 - 6
divide first then do left to right
6 + 1 - 6
7 - 6
1

Answer:

1

Step-by-step explanation:

t = 6 and d = 8

t + d ÷ 8 - 6 = 6 + 8 ÷ 8 - 6

6 + 1 - 6

6 + 1 - 6 = 1

Julia will finish the upcoming 6.2-mile race first among her friends, beating the second-place finisher by 5 minutes and 42 seconds.  

Distance is the measure of how far apart two objects or points are. It is expressed in terms of length, area, volume, or time. It is a numerical measurement of how much space is between two points or objects. Distance can also be used to measure the length of a journey, or to measure the speed of an object moving over a certain period of time.

To calculate this, we can look at the table and compare the times of the last race each of them ran. Julia ran a 5-mile race in 32 minutes and 45 seconds, her first friend ran a 4-mile race in 28 minutes and 20 seconds, and her second friend ran a 4-mile race in 29 minutes and 15 seconds.

To calculate the time difference between Julia and the second-place finisher, we can compare the total time they would run the 6.2-mile race. Julia would run the 6.2 miles in 40 minutes and 45 seconds (32 minutes and 45 seconds for the 5-mile race plus 8 minutes for the additional 1.2 miles) and the second-place finisher would run the 6.2 miles in 41 minutes and 35 seconds (29 minutes and 15 seconds for the 4-mile race plus 12 minutes and 20 seconds for the additional 2.2 miles). The difference between the two times is 5 minutes and 42 seconds, so Julia would finish first and beat the second-place finisher by 5 minutes and 42 seconds.

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The area of the composite figure given is 39 cm²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure.

Given is a figure with dimensions, 3 cm 4 cm 6 cm 5 cm we need to find the area of the figure,

Since, we can see that the figure is a composite figure, we will first split the figure and find the area of each part separately then, add all of them,

The figure is consisting of two rectangles, with dimensions, 4 cm and 6 cm and the second one with dimensions, 5 cm and 3 cm,

so, the area of the rectangle with dimensions, 4 cm and 6 cm = 4 x 6 = 24 cm²

And,

The area of the rectangle with dimensions, 5 cm and 3 cm = 5 x 3 = 15 cm²

The area of the figure = 15 + 24 = 39 cm²

Hence, the area of the composite figure given is 39 cm²

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The complete question is attached

Clara should use the 50% off coupon to save the most money on a tent originally priced at $46.


To determine which coupon will save Clara the most money, we need to calculate the final price of the tent with each coupon.

For the $24 off coupon:
Final price = Original price - Coupon amount
Final price = $46 - $24
Final price = $22

For the 50% off coupon:
Final price = Original price - (Original price x Coupon percentage)
Final price = $46 - ($46 x 0.50)
Final price = $46 - $23
Final price = $23

As we can see, the final price of the tent with the $24 off coupon is $22, while the final price with the 50% off coupon is $23. Therefore, Clara should use the $24 off coupon to save the most money.

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(a) The area of a triangle can be found using the formula A = (1/2)bh, where b is the base and h is the height. In this case, the base is one of the sides with length 13 or 15, and the height is the altitude with length 12. Using the formula, the area is A = (1/2)(13)(12) = 78 square units.

(b) The area of a triangle can also be found using Heron's formula, which is A = √[s(s-a)(s-b)(s-c)], where s is the semiperimeter of the triangle, and a, b, and c are the lengths of the sides. In this case, s = (10+10+16)/2 = 18, so the area is A = √[18(18-10)(18-10)(18-16)] = 80 square units.

(c) Using Heron's formula again, s = (5+12+13)/2 = 15, so the area is A = √[15(15-5)(15-12)(15-13)] = 30 square units.

(d) The area of an isosceles triangle can be found using the formula A = (1/2)bh, where b is the base and h is the height. In this case, the base is 30 and the height can be found using the Pythagorean theorem, h = √(17^2 - (30/2)^2) = 8. So the area is A = (1/2)(30)(8) = 120 square units.

(e) The area of an isosceles triangle can also be found using the formula A = (1/2)ab sin C, where a and b are the lengths of the two equal sides and C is the vertex angle. In this case, a = b = 20 and C = 68°, so the area is A = (1/2)(20)(20) sin 68° = 190.4 square units.

(f) Using the same formula as in (e), but with a = b = 30 and C = 62°, the area is A = (1/2)(30)(30) sin 62° = 675 square units.

(g) The area of a triangle inscribed in a circle can be found using the formula A = (1/2)ab sin C, where a and b are the lengths of the two sides and C is the angle between them. In this case, one side is a diameter with length 8 (2 times the radius of 4), another side has an unknown length, and the angle between them is 30°. The area is A = (1/2)(8)(b) sin 30° = 2b square units.

(h) The area of a triangle cut off by a line parallel to the base can be found using the formula A = (1/2)bh, where b is the length of the base and h is the height. In this case, the base is 10 and the height is 5 - 6 = -1, so the area is A = (1/2)(10)(-1) = -5 square units.

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The value of x and y are 40° and 40° respectively

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

These are the few theorems of circle geometry

1. The angle at the centre is twice the angle at the circumference.

2. The angle in a semicircle is a right angle.

Angles in the same segment are equal.

3. Opposite angles in a cyclic quadrilateral sum to 180°

4. The angle between the chord and the tangent is equal to the angle in the alternate segment.

from triangle AOB,

angle 0 = 60° (opposite angles)

x = 180-( 80+60)

x = 180-140

x = 40°

x= y ( angle in the same segment are equal)

y = 40°

therefore the value of x and y are 40°

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Answer: 38.465 feet

Step-by-step explanation: The diameter (7 feet) divided by 2, equals 3.5. multiply 3.5 squared (12.25 feet) by pi (3.14) equals your answer of 38.465 feet.

Each interior angle is 720°/6 = 120°.

The sum of the interior angles of a regular hexagon can be found using the formula 180(n-2), where n is the number of sides of the hexagon. In this case, n = 6, so the sum of the interior angles is 180(6-2) = 180(4) = 720°. Since the hexagon is regular, all of its interior angles are of equal size. Therefore, each interior angle is 720°/6 = 120°.

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The total volume is 5760cm^3

Here we have a composite figure that can be decomposed into two simpler ones, such that the simpler ones are rectangular prisms of:

12 cm by 20 cm by 8 cm

12 cm by 40  cm by 8cm

We know that the volume is equal to the product between the dimensions, then the volumes are:

v1 = 12cm*20cm*8cm = 1,920 cm^3

v2 = 12cm*40cm*8cm = 3,840cm^3

The total volume is the sum of these two:

V = 1920cm^3 + 3840cm^3 = 5760cm^3

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