A microwave is placed on top of two boxes. One box is 2 feet 10 inches tall, the other box is 4 feet 7 inches tall, and the microwave is 3 feet 4 inches tall. How tall are they combined? Write your answer in feet and inches. Use a number less than 12 for inches.

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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The two possible locations of point B on the number line are 0.1 and 1.1.

A number line is a graphic depiction of numbers organized in a straight line in mathematics. Positive numbers appear to the right of zero and negative numbers to the left of zero when it is displayed horizontally. At the line's intersection, the number zero serves as a standard against which other numbers' magnitudes can be measured.

Many forms of numbers, including whole numbers, integers, fractions, decimals, and even irrational numbers, can be represented on a number line. The distance between any two points on the number line, which stands for the difference between any two matching numbers, corresponds to a distinct number.

Number lines are frequently used to graph functions and equations as well as to execute basic arithmetic operations including addition, subtraction, multiplication, and division. They are also helpful for comprehending ideas like magnitude, distance, and absolute value.

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As a car dealer lowers a vehicle that was worth 18300 to 16000 by applying the formula of change in percentage we get that by 12.569 percentage (approximately) the price gets lowered .

The initial price of the car is set at P = 18300 (units)

The price after lowering drom P becomes A= 16000 (units)

Hence the change in price (or value) of the car, that is the price of the car is lowered by, C = (initial price - lowered price) = (P - A) = (18300 - 16000) units = 2300 units.

The formula for calculating percentage change is given as follows,

Change in percentage = [(Change in value)/ ( Initial value) ]*100

⇒Change in percentage = (C/ P)*100

⇒ Change in percentage =( 2300/ 18300)*100 = 12.569% (approximately)

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Answer:

................

Step-by-step explanation:

.................

The factorization of of −12x+6 is 6(-2x + 1).

Factorization simply means writing if a number as a product of several factors. It is also the breaking or the decomposition of an entity.

In this case, -12x + 6 will be illustrated thus. It should be noted that the common factor between the numbers is 6. This will be:

= -12x + 6

= 6(-2x + 1)

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Answer:

The answer will be -300

Step-by-step explanation:

Doing this in a calculator, it will give you -300

Answer:

24... I hoped dis helped.

The solution to the equation is -1.5 or -3/2.

We have the equation:

x² + 3-2x= 1+ x² +5

Combine Terms and subtract x² from both sides:

x² - x² + 3 -2x = 1 + 5 + x² - x²

3 -2x = 1 + 5

Add:

3 -2x = 6

Combine Terms and subtract 3 from both sides:

-2x + 3 -3 = 6 - 3

-2x = 3

Dividing by -2 we get:

x = 3/(-2)

x = -3/2

x = -1.5

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Project #2 involves collecting your own sample of data and analyzing the relationship between a quantitative variable and a categorical variable with only two categories

In Project #2, you will be collecting your own sample of data in order to study the relationship between a quantitative variable and a categorical variable with only two categories.

The main variable must be a quantitative variable, such as weight, height, or length, since we will be asking questions about the mean.

The second variable must be a categorical variable with only two categories, such as color or material, in order to divide the population into two subpopulations.

To collect your data, you will need to choose a sample of at least 30 non-human objects. It is important to choose a sample that is representative of the population you are studying, so you may want to use a random sampling method to ensure that your sample is unbiased.

Once you have collected your data, you can calculate the mean for each subpopulation and compare them to see if there is a significant difference between the two groups.

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Answer:

The price of rice per gram is 4.50 / 750 = 0.006 dollars per gram.

Step-by-step explanation:

David wants to make 10 servings, where each serving has 75 grams of rice. So, he needs a total of 10 * 75 = 750 grams of rice. the price of rice per gram is 4.50 / 750 = 0.006 dollars per gram.

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

To solve the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0, we need to simplify and rearrange the equation to its standard form and then solve for p.

Combining like terms, the equation becomes:

3p^2 - 10p + 5 = 0

Now, we can use the quadratic formula to solve for p. The quadratic formula states:

p = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -10, and c = 5. Substituting these values into the quadratic formula, we have:

p = (-(-10) ± √((-10)^2 - 4 * 3 * 5)) / (2 * 3)

Simplifying further:

p = (10 ± √(100 - 60)) / 6

p = (10 ± √40) / 6

p = (10 ± 2√10) / 6

Now, we can simplify and find the two possible values of p:

p₁ = (10 + 2√10) / 6

p₂ = (10 - 2√10) / 6

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

In simplified form, the solutions are:

p₁ = (5 + √10) / 3

p₂ = (5 - √10) / 3

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Answer:

C. p -> q

Step-by-step explanation:

Just did this on Edge2020. Hope this helps :)

The rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station is approximately 322.8 miles per hour.

Ware required to find the rate at which the distance from the plane to the station is increasing.

Let's use the Pythagorean theorem to find PR:PR² = QR² + PQ²

Where,

PQ = speed of the plane * time

To find time,Let t be the time taken by the plane to travel from Q to P. Then, the time taken by the plane to travel from R to Q is also t.

Distance = Speed × Time

Therefore

,QR = 500t

PR² = QR² + PQ²

PR² = (500t)² + 1²

Differentiate both sides of the above equation w.r.t time t, we get:

2PR * dPR/dt = 2(500t)(500) + 2(1)(dPQ/dt)

Rearrange the above equation to find dPR/dt:

dPR/dt = [(500t)(500) + PQ(dPQ/dt)] / PR

Substitute PQ = 500t and PR = √(500t)² + 1²), we get:

dPR/dt = [(500t)(500) + 500t(dPQ/dt)] / √(500t)² + 1²)

We know that PQ = 500t, therefore,

dPQ/dt = 500

So,dPR/dt = [(500t)(500) + 500t(500)] / √(500t)² + 1²)

Putting t = 2, we get:

dPR/dt = [(500 × 2)(500) + (500)(500)] / √(500 × 2)² + 1²)

dPR/dt = 322.8

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The perimeter and area of the given composite figure are:

Area = 50 cm²

Perimeter = 42 cm

To find the total surface area of the composite figure, we will find the area of each individual surfaces and then add them together.

Formula for area of a triangle is:

Area = ¹/₂ * base * height

Formula for area of a rectangle is:

Area = Length * Width

Thus:

T.S.A = 2(¹/₂ * 4 * 5) + (10 * 3)

T.S.A = 20 + 30

T.S.A = 50 cm²

The perimeter will be the sum of the entire boundary length. Thus:

Perimeter = 3 + 10 + 10 + 3 + 3 + 3 + 5 + 5

Perimeter = 42 cm

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Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

The length of the triangle is given by the equation L = 7.7 units

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the length of the triangle be represented as L

Now , the area of the triangle A = 19 1/4 units

Area of the triangle A = ( 77/4 ) units

And , the base of the triangle B = 5 units

From the triangle theorem ,

The area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

77/4 = ( 1/2 ) x  L x 5

Divide both sides of the equation by 5 , we get

L/2 = ( 19.25 ) / 5

L / 2 = 3.85

Multiply both sides of the equation by 2 , we get

Length of the triangle L = 7.7 units

Hence , each side length represents 1 unit , so the area of the triangle whose length is 7.7 units and base 5 units will be 19 1/4 units

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Answer:

Answer: x is -9

Step-by-step explanation:

If it's a line AC with a point B between;

AC = AB + BC

substitute in terms of x :

\(8 = (2x + 20) + (2x + 24)\)

group x terms in a same bracket, and constants in their bracket

\(8 = (2x + 2x) + (20 + 24) \)

operate the brackets:

\(8 = 4x + 44\)

subtract 44 from both sides:

\(8 - 44 = (4x + 44) - 44 \)

simplify:

\( - 36 = 4x\)

divide all sides by 4:

\( \frac{ - 36}{4} = \frac{4x}{4} \\ \\ x = - 9\)

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

110 Degrees and 80 Degrees.

Sorry no step by step in a hurry :)

Answer:

Step-by-step explanation:

Isosceles Obtuse.

It is obtuse because the largest angle is over 90.

It is Isosceles because the two base angles are equal.

If you get it wrong, it is because the question assumes that the two base angles are acute (which they are) but for this question I think you are referring to the lone angle at the top.

Answer:

Step-by-step explanation:

\(2 {x}^{2} - 4 {y}^{2} \)

By putting the value of x = 2 and y = -3 then,

\( = ( 2 \times {2}^{2}) - (4 \times {( - 3)}^{2} )\)

\( = (2 \times 4) - (4 \times 9)\)

\( = 8 - 36\)

= - 28 (Ans)

4x - 6 = x + 9

4x - x = 9 + 6

3x = 15

\(x = \frac{15}{3} \\ \)

x = 5 ...

Answer:

\(x =5\)

Step-by-step explanation:

\(4x - 6=x+9\)

Subtract x from both sides

\(4x -6-x=x+9-x\)

\(3x-6=9\)

Add 6 to both sides

\(3x-6+6=9+6\)

\(3x=15\)

Divide both sides by 3

\(\frac{3x}{3} = \frac{15}{3}\)

\(x = 5\)

The perimeter of the shape is approximately 20.57 inches.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

The shape consists of two shapes; a square and 2 semi-circles

Perimeter of square = 4L

where L = 2 inches

Perimeter = 4(2)

Perimeter = 8 inches

Perimeter of Semi-circle = \(\pi r}\)

where \(\pi = 3.142\)

r = 2 inches

Perimeter of Semi-circle = 3.142 x 2

Perimeter of Semi-circle = 6.284 inches

Perimeter of shape = Perimeter of square + 2 x Perimeter of Semi-circle

Perimeter of shape = 8 inches + 2 x  6.284 inches

Perimeter of shape = 8 inches + 12.568 inches

Perimeter of shape = 20.568 inches

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If there is a 0.41% chance that an American citizen will die from falling, then the probability  that you will not die from a fall is 99.59%

The chances of an American citizen will die from falling = 0.41%

The probability is the ratio of number of favorable outcomes to the total number of outcomes

The equation will be

The probability = Number of favorable outcomes / Total number of outcomes

The probability  that you will not die from a fall = 1 -  The chances of an American citizen will die from falling

Substitute the values in the equation

The probability  that you will not die from a fall = 1 - 0.41

= 99.59%

Therefore, the probability  that you will not die from a fall is 99.59%

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Answer:

5:4

Step-by-step explanation:

In Mrs. Nathan's class,  the ratio of girls to boys is 5:4.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, In Mrs. Nathan's class, there are 16 boys and 20 girls.

the ratio of girls to boys = 20/16

the ratio of girls to boys = 5/4

Therefore, the ratio of girls to boys in Mrs. Nathan's class is 5: 4.

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The two ways that sequences can be defined include the following: Arithmetic Sequences and Geometric Sequences.

A sequence is defined as the collection of items in such a way that repetitions can be observed.

There are two major ways the sequence can be defined in arithmetics and this includes the following:

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The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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Answer:

2

(

4

+

3

)

Step-by-step explanation: