Subtract mixed numbers problem help

9 1/4-12 7/8

Answer:

Step-by-step explanation:

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, to find the interval of hours that represents the lifespan of the middle 68% of light bulbs, we need to find the interval that is one standard deviation away from the mean in either direction.

Since the mean is 1400 hours and the standard deviation is 50 hours, we can use the following formula to find the interval:

(mean - standard deviation, mean + standard deviation)

Plugging in the values, we get:

(1400 - 50, 1400 + 50)

Simplifying, we get:

(1350, 1450)

Therefore, the interval of hours that represents the lifespan of the middle 68% of light bulbs is from 1350 hours to 1450 hours.

Answer:

(1350,1450)

Step-by-step explanation:

The Empirical Rule states that 68% of data points fall within one standard deviation of the mean. So, subtract 50 from the mean and add 50 to the mean to find the lifespan of the middle 68% of bulbs.

The vertices of the image of the triangle BCD are B'(x, y) = (- 3, 13), C'(x, y) = (0, 19) and D'(x, y) = (18, 10). The representation of the resulting figure is in the image attached below.

Herein we find the representation of a triangle on Cartesian plane, whose image, that is, the result of a dilation, must be found. The formula to be used is introduced below:

P'(x, y) = P(x, y) + k · [P(x, y) - O(x, y)]

Where:

If we know that B(x, y) = (- 3, 7), C(x, y) = (- 2, 9), D(x, y) = (4, 6), O(x, y) = (- 3, 4) and k = 2, then the coordinates of the vertices of the image are listed below:

B'(x, y) = (- 3, 7) + 2 · [(- 3, 7) - (- 3, 4)]

B'(x, y) = (- 3, 7) + 2 · (0, 3)

B'(x, y) = (- 3, 7) + (0, 6)

B'(x, y) = (- 3, 13)

C'(x, y) = (- 2, 9) + 2 · [(- 2, 9) - (- 3, 4)]

C'(x, y) = (- 2, 9) + 2 · (1, 5)

C'(x, y) = (- 2, 9) + (2, 10)

C'(x, y) = (0, 19)

D'(x, y) = (4, 6) + 2 · [(4, 6) - (- 3, 4)]

D'(x, y) = (4, 6) + 2 · (7, 2)

D'(x, y) = (4, 6) + (14, 4)

D'(x, y) = (18, 10)

Now we proceed to plot the image by means of a graphing tool.

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The statement that 35 percent of 150 is about 50  is completely false and hence unreasonable as 35 percent of 150 is exactly equal to 52.50.

In the given problem which is related to percentage of some specific number, the value is obtained by direct multiplication of percentage with the given number to get the answer. Percentage is defined as the ratio which is given with respect to number 100 or 100 units as a whole. Its symbol is %. It is a dimensionless quantity and hence has no units as ratios does not have units.

The given equation can be represented as follows to obtain the answer:

(35/100) × 150 = 52.50

Since 52.50 cannot be considered close to 50, hence the statement is u reasonable. Though 52.5 can be considered as about 52 or 53.

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The quadratic equation (c+5)²=36 will give c = 1,-11.

A quadratic equation is a type of equation in algebra that involves a variable (usually denoted as "x") raised to the power of 2, or squared. The standard form of a quadratic equation is:

ax² + bx + c = 0

where a, b, and c are constants, with a≠0. The goal is to solve for the variable x, which may have one or two possible solutions depending on the coefficients of the equation.

Now,

To solve the equation (c + 5)² = 36:

Taking the square root of both sides of the equation

√(c + 5)² = ±√36

Simplify the left-hand side using the rule that √a² = |a|:

|c + 5| = ±6

Solve for c in each case by subtracting 5 from both sides of the equation:

c + 5 = 6 or c + 5 = -6

Solve for c in each equation:

c = 1 or c = -11

Therefore, the solutions to the equation (c + 5)² = 36 are c = 1 and c = -11.

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The given system of equations is:

3x + 2y + 4z - w = 13

-2x + y + 5z = 5

We can write this system in the form of an augmented matrix as:

| 3 2 4 -1 | 13 |

| -2 1 5 0 | 5 |

To transform this matrix to echelon form, we perform the following elementary row operations:

Add 2 times the first row to the second row:

| 3 2 4 -1 | 13 |

| 0 5 13 -2 | 31 |

Divide the second row by 5 to obtain a leading 1:

| 3 2 4 -1 | 13 |

| 0 1 13/5 -2/5 | 31/5 |

Subtract 4 times the second row from the first row:

| 3 0 -6/5 3/5 | 9/5 |

| 0 1 13/5 -2/5 | 31/5 |

Multiply the second row by 6/5 and add it to the first row:

| 3 0 0 16/5 | 57/5 |

| 0 1 13/5 -2/5 | 31/5 |

The matrix is now in echelon form. Using back substitution, we can solve for the variables:

From the second row, we have:

y + (13/5)z - (2/5)w = 31/5

y = (2/5)w - (13/5)z + 31/5

Substituting y in the first row, we have:

3x + 2[(2/5)w - (13/5)z + 31/5] + 4z - w = 57/5

3x + (4/5)w - (26/5)z = 2/5

Solving for x, we have:

x = (2/15)w + (26/15)z - 2/15

So the solution is:

x = (2/15)w + (26/15)z - 2/15

y = (2/5)w - (13/5)z + 31/5

z = z

w = w

This is a parametric solution, as we have one free variable (z) and can express the other variables in terms of it. Therefore, the system has infinitely many solutions.

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Match the description with the step accordingly:

How many times larger is 2 × 10⁻² then 3 × 10⁻⁶: Divide the larger Scientific Notation by the smaller Scientific Notation - divide coefficients and subtract exponents.

Difference between 2 × 10⁻² and 3× 10⁻⁶: Subtract by getting the same exponent to be like terms.

400 times 2 × 10³: Multiply by changing the number to Scientific Notation - multiply coefficients and add exponents.

Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form.

To find How many times larger is 2 × 10⁻² then 3 × 10⁻⁶. Divide the larger Scientific Notation by the smaller Scientific Notation - divide coefficients and subtract exponents. That is:

(3 × 10⁻⁶)/(2 × 10⁻²) = 3/2 × 10⁻⁶⁻⁽⁻²⁾ = 1.5×10⁻⁴

To find the difference between 2 × 10⁻² and 3× 10⁻⁶. Subtract by getting the same exponent to be like terms. That is:

2×10⁻² - 3×10⁻⁶ = (2 × 10⁻²) - (0.0003× 10⁻²)

                           = (2 - 0.0003) × 10⁻²

                           = (2 - 0.0003) × 10⁻²

                           = 1.9997× 10⁻²

For 400 times 2 × 10³. Multiply by changing the number to Scientific Notation - multiply coefficients and add exponents. That is:

400 × 2 × 10³ = 4 × 10² × 2 × 10³

                     = 4 × 2 × 10³ × 10²

                     = 4 × 2 × 10³⁺²

                     = 8 × 10⁵

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In his bookshelf, Luke can arrange his textbooks in a total of six different ways.

Luke can line up his textbooks in 3! = 321 = 6 different ways. This is because for the first book, he has three choices, for the second book, he has two choices left, and for the third book, he has only one choice left.

Therefore, the number of different ways Luke can line up his textbooks on his bookshelf is 6.

The six possible ways are:

English, biology, history

English, history, biology

Biology, English, history

Biology, history, English

History, English, biology

History, biology, English

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The three points that are not collinear are J, K and L

In geometry, points that are not collinear are points that do not lie on the same straight line. i.e. points that are not collinear are points that are not on the same line

Using the above as a guide, the non-collinear points are points J, K and L

Opposite rays are two rays that have the same endpoint and extend indefinitely in opposite directions.

Using the above definition, we have

Opposite rays = HG and HI

The line JH can be named based on its endpoints

So, another name for JH is HJ

Three points are required to form a plane

This means that the planes that contain HL can be named as GHL and JHL

There are other planes that contained HL too

See attachment for the sketch

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Answer:

Step-by-step explanation:

[tex]f(9)[/tex] means we need to find the value of [tex]f(x)[/tex] when [tex]x=9[/tex], so

[tex]f(9)=2[/tex]×[tex]9=18[/tex]

[tex] \frac{ {38}^{2} - {22}^{2} }{16} \\ [/tex]

The identity which can be used in this case is :

[tex] \boxed{ {a}^{2} - {b}^{2} = (a - b)(a + b)}[/tex]

Applying the above identity to the given equation , we get

[tex] \frac{ {38}^{2} - {22}^{2} }{16} \\ \\ \implies \: \frac{(38 - 22)(38 + 22)}{16} \\ \\ \implies \: \frac{(\cancel{16})(60)}{\cancel{16} } \\ \\ \implies \: \underline{\underline{60}}[/tex]

hope helpful! :)

Step-by-step \frac{1}{2} x^{5} - 15x

Answer:

1 mile is equal to 1,760 yards. Therefore, 3 miles is equal to 3 x 1,760 = 5,280 yards.

Comparing 5,280 yards to 1,000 yards, we can see that 5,280 yards is greater than 1,000 yards.

To determine how much greater, we can subtract 1,000 from 5,280:

5,280 - 1,000 = 4,280

Therefore, 3 miles is 4,280 yards greater than 1,000 yards.

Answer: Add.

Step-by-step explanation: When you multiply two numbers, all you have to do is simply add the exponents!

Example: 3^4 × 3^2 = 3^(4 + 2) = 3^6

Hope this helps!!

Mohal would expect to earn $265 in a day when he waits on 16 tables, and he would expect to earn $15tt + $25 in a day when he waits on tt tables

Earnings or wages refer to the amount of money an individual receives in exchange for their work or services. This can include a regular salary or hourly wage, as well as bonuses, commissions, and other forms of compensation.

Earnings or wages are typically determined by a variety of factors, including the type of work being performed, the level of skill and experience required, the local job market, and the employer's policies and practices. In some cases, earnings may be negotiated between the employer and the employee, while in other cases they may be set by industry standards or government regulations.

To calculate Mohal's expected earnings in a day when he waits on 16 tables, we can use the formula:

Total earnings = Guaranteed wage + Tips

Guaranteed wage = $25

Tips = $15 x Number of tables

Number of tables = 16

So, Total earnings with 16 tables = $25 + ($15 x 16) = $265

To calculate Mohal's expected earnings in a day when he waits on tt tables, we can use the same formula:

Total earnings = Guaranteed wage + Tips

Guaranteed wage = $25

Tips = $15 x Number of tables

Number of tables = tt

So, Total earnings with tt tables = $25 + ($15 x tt) = $15tt + $25

Therefore, Mohal would expect to earn $265 in a day when he waits on 16 tables, and he would expect to earn $15tt + $25 in a day when he waits on tt tables.

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Answer:

Total earnings with 16 tables: 265

Total Earnings with t tables: 15t+25

Step-by-step explanation:

Answer: There are 10 candidates for each position, and since a candidate can only hold one leadership position, the number of ways to fill the president position is 10. After the president position is filled, there are 9 candidates remaining for the vice president position. Finally, there are 8 candidates remaining for the secretary position.

The total number of ways to fill the three positions is the product of the number of ways to fill each position. Therefore, the number of ways to fill the three positions is:

10 x 9 x 8 = 720

So there are 720 different ways to fill the three leadership positions using the 10 possible candidates.

Step-by-step explanation:

Answer:It is given that

In △ABC,

DE∥AC

What is similarity of triangles?

Two triangles are similar if corresponding angles are equal and corresponding sides are in proportion.

Let us consider △BDE and △ABC,

∠B=∠B.....common angles

∠BDE =∠BAC....corresponding angles

so, △BDE∼△ABC

Since △BDE and △ABC are similar so, corresponding sides will be in proportion,

Subtract 1 from both sides,

Thus, we proved   using the similarity of triangles.

Step-by-step explanation:

The cost Analysis for the two proposed plans for building a low ultra-light bicycle concluded on the recommendation that d that Bici Bicycle Company follow the first plan.

The first plan involves a cost of $125,000 to design and build a prototype bicycle. The combined materials and labor costs for each bike made under the first plan will be $225. This means that for every bike Bici Bicycle Company produces under the first plan, it will incur a total cost of $350 ($125,000 + $225).

On the other hand, the second plan involves a cost of $100,000 to design and build the prototype. The combined materials and labor costs for each bike made under the second plan will be $275. This means that for every bike Bici Bicycle Company produces under the second plan, it will incur a total cost of $375 ($100,000 + $275).

Therefore, while the second plan has a lower initial cost of prototype development, it will ultimately result in a higher cost per unit produced. The first plan, although it has a higher initial prototype development cost, will ultimately result in a lower cost per unit produced.

To determine the break-even point, we can set the total cost of producing a bike under each plan equal to each other and solve for the number of bikes produced.

For the first plan:

Total cost = $125,000 + ($225 x n)

For the second plan:

Total cost = $100,000 + ($275 x n)

Setting these equal to each other, we get:

$125,000 + ($225 x n) = $100,000 + ($275 x n)

$25,000 = $50 x n

n = 500

Therefore, Bici Bicycle Company would need to produce at least 500 bicycles for the cost per unit of the first plan to be less than that of the second plan.

In conclusion, based on my analysis, I would recommend that Bici Bicycle Company follow the first plan, as it will ultimately result in a lower cost per unit produced. However, if the company anticipates producing fewer than 500 bicycles, the second plan may be more cost-effective.

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Answer: 16π

Step-by-step explanation:

The area of a full circle is πr^2. We only need a quarter so we'll use, A = 1/4(πr^2)

Area = 1/4(π(8)^2)

Area = 1/4(64π)

Area = 16π

Hope this helps

Answer:

I thing it 16 pi if u get it wrong I'm sry but since I just learned this pi stuff this is what I came up with

The cost per square foot of the remaining sheet metal is $4.10.

To find the cost per square foot of the remaining sheet metal, we can first calculate how much sheet metal is remaining by solving the equation:

7.6X - 3.5X = 65.6

where X is the amount of sheet metal remaining in square feet.

Simplifying the left side of the equation gives:

4.1X = 65.6

Dividing both sides by 4.1 gives:

X = 16

Therefore, the amount of sheet metal remaining is 16 square feet.

To find the cost per square foot, we can divide the cost of the remaining sheet metal by the amount of sheet metal remaining:

$65.60 / 16 sq. ft. = $4.10 per square foot.

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Answer:

3/4 x 2/5 => NO

2/5 x 5/6 => NO

1/10 x 1/5 => NO

1/2 x 3/5 => YES

Step-by-step explanation:

3/4 x 2/5 = 6/20 => NO

2/5 x 5/6 = 10/30 => NO

1/10 x 1/5 = 1/50 => NO

1/2 x 3/5 = 3/10 -> YES

The true statements are:

A sort of transformation comprehended a translation involves moving each point in a figure the same distance in the same direction.

Reworking text from one language into another while preserving the original message and communication is called translation. But, there are various approaches to translation, and they range in both form and purpose, just like anything else.

An operation is a transformation if it moves, flips, or otherwise alters a figure to produce a new figure. Rigid transformations sometimes referred to as isometry or congruence transformations, do not alter the size or shape of a figure.

therefore, the true statements are:

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Best describes the translation of the figure moves Left and down.

A translation is a transformation that moves every point of a figure or object by the same distance and in the same direction without changing its shape, size, or orientation. It is a type of rigid transformation that preserves the distance between points and angles between lines.

A translation can be described using the horizontal and vertical shift or displacement of the object. If a point (x, y) is translated by a distance of 'a' units to the right and 'b' units upwards, the new location of the point would be (x + a, y + b).

Question says that a figure is translated using the mapping (x, y) → (x + a, y + b).

If the value of 'a' is negative and the value of 'b' is negative in the mapping (x, y) → (x + a, y + b), it means that the figure is being translated to the left and downwards.

The x-coordinates are being decreased by the absolute value of 'a', which means that the figure is moving left. Similarly, the y-coordinates are being decreased by the absolute value of 'b', which means that the figure is moving downwards.

Therefore, the best description of the translation is "the figure moves left and down"

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The degree and terms of the polynomial are explained and an example is also discussed.

What are polynomials?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. It is a mathematical expression made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division (No division operation by a variable).

The expression's components that are divided up by the operators "+" or "-" are referred to as polynomial terms. In polynomials, like terms are ones that share the same variable and power. Unlike terms are those that have dissimilar variables and/or dissimilar powers.

The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial. A polynomial equation's maximum number of solutions can be calculated using the degree.

The different types of polynomials based on terms are:

The different types of polynomials based on the degree are:

Example,

Consider a polynomial 3x² + 5x + 4

Number of terms = 3 (Trinomial)

Degree = 2 (Quadratic polynomial)

Therefore the degree and terms of the polynomial are explained and an example is also discussed.

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The answer is:

Work/explanation:

Here's how we classify polynomials based on the number of terms:

monomial - has only one term

binomial - has two terms

trinomial - has three terms

polynomial - has four terms or more

As for degrees, those are the highest exponents the polynomial.

Example: Classify [tex]\bf{2p^2+p}[/tex].

It has 2 terms so it's a binomial.

Its highest exponent is 2 so it's a second degree binomial.

The given relation that is a function is the fourth graph which shows a U- shaped curve.

The graph of a quadratic function is a U-shaped curve called a parabola, which can either face upwards or downwards depending on the value of "a". If "a" is positive, the parabola faces upwards, and if "a" is negative, the parabola faces downwards.

The coefficient "a" determines the width and direction of the parabola, while the constants "b" and "c" determine its position on the coordinate plane. This therefore shows that the fourth graph is a function.

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Rotate point A 180 counterclockwise about the origin to get point A'. -2,-3 coordinate is A'

What is counterclockwise rotation?

Rotations that are counterclockwise (CCW) travel in the opposite direction from how a clock's hands move. Positive numerals are used to indicate these rotations.

Rotation in either a clockwise or anticlockwise direction refers to a change in the electrical activity flowing through the heart in a horizontal plane. Consider the observer as being at the bedside of the sufferer. It is known as anticlockwise rotation if the patient's heart's electrical activity has shifted more to their right side. It is known as clockwise rotation if the patient's heart's electrical activity has shifted more to the left.

Our point A(x,y) rotates 180 degrees anticlockwise around the origin to become A' (-x,-y). Making both x and y negative is all we do as a result.

Here we can see in the graph ‘A’ is present on (2,3)

So the -2,-3 coordinate is A’.

Hence the correct answer is c, -2,-3

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Answer: The square root of 45 is a like radical to 3 x √5.

To see why, we can simplify each radical using the product rule of radicals:

3 x √5 = √(3^2 x 5) = √45

Similarly, we can simplify the square root of 45 using the prime factorization of 45:

√45 = √(3 x 3 x 5) = 3√5

Therefore, 3 x √5 is a like radical to √45, and vice versa.

Step-by-step explanation:

Answer:

its D

Step-by-step explanation:

TRUST ME BRO

The slope of the line passing through the points (-5,5) and (5,8) is 0.3.

The slope of a line is the rate at which it rises or falls as it moves from left to right. It is defined as the change in the vertical distance divided by the change in the horizontal distance between any two points on the line.

The slope of a line passing through two points (x₁,y₁) and (x₂,y₂) can be calculated using the slope formula:

slope = (y₂-y₁)/(x₂-x₁)

Using the coordinates (-5,5) and (5,8), we can plug in the values to get:

slope = [tex]\frac{(8-5)}{(5-(-5))}[/tex]

slope = [tex]\frac{3}{10}[/tex]

slope = 0.3

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The statement of the solution to the system is the system has one solution

From the question, we have the following parameters that can be used in our computation:

5x + 4y = -3

y = -3x + 5

Substitiute the second equation in the first equation

Using the above as a guide, we have the following:

5x + 4(-3x + 5) = -3

So, we have

5x - 12x + 20 = -3

Evaluate the like terms

-7x = -23

So, we have

x = 23/7

The above means that the equation has a solution

Hence, the number of solutions in the equation is 1

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the unlock code is: 54-575-26-12-7.5-36.

How to determine?

To find the area of each polygon, we need to use the formula for the area of each respective shape.

Assuming the polygons are rectangles, triangles, and trapezoids, we can find their areas as follows:

The area of the rectangle with length 9 ft and width 6 ft is A = length × width = 9 ft × 6 ft = 54 ft².

The area of the triangle with base 10 cm and height 115 cm is A = (1/2) × base × height = (1/2) × 10 cm × 115 cm = 575 cm².

The area of the trapezoid with bases 5 m and 8 m, and height 4 m is A = (1/2) × (base1 + base2) × height = (1/2) × (5 m + 8 m) × 4 m = 26 m².

The area of the triangle with base 3 cm and height 8 cm is A = (1/2) × base × height = (1/2) × 3 cm × 8 cm = 12 cm².

The area of the rectangle with length 1.5 m and width 5 m is A = length × width = 1.5 m × 5 m = 7.5 m².

The area of the trapezoid with bases 6 ft and 3 ft, and height 4 m is A = (1/2) × (base1 + base2) × height = (1/2) × (6 ft + 3 ft) × 4 m = 9 ft × 4 m = 36 ft².

Therefore, the unlock code is: 54-575-26-12-7.5-36.

Note that the areas are listed from left to right based on the order of the shapes in the original question. Also, the areas are separated by hyphens as requested.

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