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a. 5 thirds + 2 ninths _____ 1 9/8

So Lisa and Linda planted 9/6 of the garden altogether. In simplest form, this fraction can be reduced to 3/2, which means that they planted 3/2 of the total garden area.

To find out the total area of the garden that Lisa and Linda planted, we need to add the fraction of the garden that Lisa planted to the fraction of the garden that Linda planted.

Lisa planted 4/7 of the garden, so we can write this as 4/7 of the total area.

Linda planted 1/6 of the garden, so we can write this as 1/6 of the total area.

To add these two fractions, we need to find a common denominator, which is the smallest number that both 7 and 6 can divide into evenly. The smallest common denominator is 6, so we can convert both fractions to have a denominator of 6:

Lisa planted 4/7 of the garden, which can be converted to 8/14 (by multiplying both the numerator and denominator by 2).

Linda planted 1/6 of the garden, which stays the same, since 6 is already the denominator.

Now that both fractions have a denominator of 6, we can add the numerators together to find the total amount of the garden that they planted:

8/14 + 1/6 = (8 + 1)/6 = 9/6

So Lisa and Linda planted 9/6 of the garden altogether.

In simplest form, this fraction can be reduced to 3/2, which means that they planted 3/2 of the total garden area.

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Kimi's weekly total savings would be $17.

Kimi's total earnings from her job in a week would be $9 × 1 = $9.

Her total allowance and earnings from her job would be $9 + $8 = $17.

Kimi earns $9 an hour at her job, and her allowance is $8 per week, so her total weekly income is $9 + $8 = $17.

Jordan earns $7 an hour, and his allowance is $16 per week, so his total weekly income is $7 + $16 = $23.

So, Kimi's weekly total savings would be $17.

Hence, the answer to the given problem is $17.

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--The given question is incomplete; the complete question is

"Komi and Jordan are each working during the summer to earn money in addition to their weekly allowance, and they are saving all their money. Kimi earns $9 an hour at her job, and her allowance is $8 per week; Jordan earns $7 an hour, and his allowance is $16 per week. If the number of hours worked in a week is one, what are Kimi’s weekly total savings?"--

Answer:

The solution is B. (6x+8y)(6x-8y)

Step-by-step explanation:

(6x+8y)(6x-8y)

= 36x²-48xy+48xy-64y²

= 36x²-64y²

Or, we can use the formula (a-b)(a+b) = a²-b²

(6x+8y)(6x-8y)

= (6x)²-(8y)²

= 36x²-64y²

So, the answer is B

The solution of the expression 36x² - 64y² will be (6x - 8y)(6x + 8y).

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is 36x² - 64y². The expression will be solved as below,

E = 36x² - 64y²

E = (6x)² - (8y)²

E = ( 6x + 8y )( 6x - 8y)

The solution of the expression is E = ( 6x + 8y )( 6x - 8y).

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Answer:

-x + y = 2

Step-by-step explanation:

Graphing a shape means all the points in the shape will give you a true answer when you put the x and y back in the equation used to graph that shape.

Let's pick a point (0,2)

x = 1

0 = 1

This is not true, so the first option is wrong.

-x + y = 2

0 + 2 = 2

2 = 2

The second option is true.

x - y = 2

0 - 2 = 2

-2 = 2

This is not true, so the thrid option is wrong.

2x + y = 3

2(0) + 2 = 3

2 = 3

This is no true, so the fourth option is wrong.

Answer:

Last option:

x ≤ 217

Step-by-step explanation:

Mean time = Total Time/Number of observations

Mean time = (192 + 206 + 194 + 191 + x)/5 = (783 + x)/5

We want this mean time to be no greater than 200 seconds.

In other words we want mean time ≤ 200 s

We therefore get the inequality:
(783 + x)/5 ≤ 200

Multiplying both sides by 5
=> (783 + x) · 5  ≤ 200 · 5

=> 783 + x ≤ 1000

=> x ≤ 1000 - 783

=> x ≤ 217

Answer:

3.) 3:7

Step-by-step explanation:

We know

Of the 300 television sets sold at an electronics store last month, 90 were flat-screen TVs.

300 - 90 = 210

So, we know the store sold 90 flat-screen TVs and 210 other TVs

What was the ratio of flat-screen TVs to other TVs sold last month?

The ratio is

90:210

3:7

So, the answer is 3.) 3:7

Answer:

3.) 3:7

Step-by-step explanation:

The unsimplified ratio would be 90:210 since flat-screen TVs are excluded, but if you simplify this you get 3:7.

90:210

9:21

3:7

The transformation rule (x, y) → (-y, x) describes a 270* rotation about the origin for a triangle on the coordinate grid.

A transformation in mathematics is a process of mapping or changing one figure into another while preserving its shape, size and orientation. The coordinate grid is a tool used to plot points and study transformations in a two-dimensional plane.

The transformation rule that describes this rotation is (x, y) → (-y, x). This rule means that for every point (x, y) in the triangle STU, the new point (x', y') in the triangle S'T'U' is obtained by swapping the x and y coordinates and negating the y-coordinate. In other words, the x-coordinate remains unchanged, while the y-coordinate is negated.

For example, if the point (3, 4) is in the triangle STU, the new point (x', y') in the triangle S'T'U' would be (4, -3).

This rule applies to all points in the triangle, and the result is a rotation of the original triangle by 270* in a counterclockwise direction about the origin.

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Finally, to find the number of hours Geoff worked, we can divide both sides of the equation by 17.50:

h = 25

So Geoff worked 25 hours in his first week.

Let's call the number of hours Geoff worked in his first week "h". We can write an equation to find the value of h by using the information given.

Geoff's pay per hour is $17.50, so his pay for h hours would be 17.50h.

Including the $200 one-time hiring bonus, Geoff's total pay for the first week was $637.50, so we can write the equation:

17.50h + 200 = 637.50

To find the number of hours Geoff worked, we need to isolate the h term. To do this, we can subtract 200 from both sides:

17.50h = 437.50

Finally, to find the number of hours Geoff worked, we can divide both sides of the equation by 17.50:

h = 25

So Geoff worked 25 hours in his first week.

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With Mo and Beth splitting £48 in the ratio 3.5 , Beth would get £10.67 with the total ratio of 4.5.

When two people split a sum of money in a certain ratio, it means that they divide the total amount into parts that are proportional to the ratio. In this case, Mo and Beth are splitting £48 in the ratio 3.5. This means that Mo gets 3.5 parts of the total amount, while Beth gets 1 part of the total amount.

To calculate the total ratio, you add up the individual parts of the ratio. In this case, the total ratio is 3.5 + 1 = 4.5. This means that the £48 has to be divided into 4.5 equal parts.

Next, to find the amount that Beth gets, you need to find what portion of the 4.5 parts of the total amount corresponds to her 1 part of the ratio. You do this by dividing £48 by the total ratio, which gives you £48 / 4.5 = £10.67.

Finally, you multiply this amount by 1, which represents Beth's share of the ratio. So, £10.67 * 1 = £10.67. Therefore, Beth would get £10.67.

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the value of  1 mile divided by 2 laps is 0.5 mi/lap.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, 1 mile divided by 2 lap

Simplifying the equation in numerical form

=> 1 mile divided by 2 lap

=> 1/ 2  mil/ laps

=> 0.5 mil/lap

Therefore, the value of  1 mile divided by 2 laps is 0.5 mi/lap.

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The image vertices of K′L′M′N′ if the preimage is rotated 90° clockwise are K′(0, 0), L′(2, −5), M′(−5, −5), N′(−3, 0). Therefore, option B is the correct answer.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3).

After rotated 90° clockwise, we get

K(0, 0)→K'(0, 0)

L(5, 2)→L'(2, -5)

M(5, −5)→M'(-5, -5)

N(0, −3)→N'(-3, 0)

Therefore, option B is the correct answer.

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The value of the equation is  A = 81

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 4 ^ ( log₂ ( 9 ) )   be equation (1)

On simplifying the equation , we get

log₂ ( 9 ) = 2 log₂ ( 3 )

So , on further simplification , we get

A = 2² ^ ( 2 log₂ ( 3 ) )

A = ( 2⁴ )^log₂ ( 3 )

From the logarithmic rule , a^logₐ ( b ) = b

Substituting the values in the equation , we get

A = 2 ^ ( log₂(3) )4

A = 3⁴

A = 81

Hence , the equation is A = 81

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The trigonometric ratio for sin Z is 3/5 in the given right triangle.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The right triangle is given in the question, as shown.

As we know the cosine ratio, is as follows:

cos Z = base/hypotenuse

cos Z = YZ/XZ

cos Z = 32/40

cos Z = 4/5

Now, as we know the sine ratio, is as follows:

sin Z = √(1 - cos² Z)

sin Z = √(1 - (4/5)²)

sin Z = √(1 - 16/25)

sin Z = √(9/25)

sin Z = 3/5

Thus, the trigonometric ratio for sin Z is 3/5.

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The expected value of the sum of the two dice is 72

It is calculated by finding the weighted average of all possible sums, where each possible sum is weighted by its probability of occurring.

Let's call the 8-sided die "A" and the 9-sided die "B". Then, the possible sums are:

2 (A: 1, B: 1), 3 (A: 1, B: 2), 4 (A: 1, B: 3), ..., 16 (A: 8, B: 8)

The probability of each sum is the product of the probabilities of the individual dice outcomes:

P(2) = (1/8) * (1/9)

P(3) = (1/8) * (2/9)

...P(16) = (8/8) * (8/9)

The formula gives the expected value of the sum:

E = ∑P(x) * x

where x is each possible sum and P(x) is its probability.

Plugging in the values, we get:

E = (1/8) * (1/9) * 2 + (1/8) * (2/9) * 3 + ... + (8/8) * (8/9) * 16

E = (1/72) * (2 + 3 + ... + 16) + ... + (8/72) * (16)

E = (1/72) * [2 + 3 + ... + 16] * 8 + ... + (8/72) * 8 * 8

E = (1/9) * [2 + 3 + ... + 16]

We can now use the formula for the sum of an arithmetic series:

S = n/2 * (a + b)

where n is the number of terms, a is the first term, and b is the last term.

Applying this formula to the series [2, 3, ..., 16], we get:

S = 8/2 * (2 + 16) = 8 * (9) = 72

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The slope of the line is given as the change in y divided by the change in x.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. In contrast to the net change in the x coordinate, the net change in the y coordinate is y.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.

Hence, the slope of the line is given as the change in y divided by the change in x.

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The lateral surface area of the rectangular prism is 72 square inches.

All of the sides of the object are the lateral surface of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.

Given that, length =7 inches, breadth =5 inches and height =3 inches.

We know that, the lateral surface area of the rectangular prism is 2(l+b)h

Now, the lateral surface area = 2(7+5)×3

= 2×12×3

= 72 square inches

Therefore, the lateral surface area of the rectangular prism is 72 square inches.

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So Reena has ran a distance of 5 kilometers while only covering one-sixth of the distance.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

If Reena has completed one sixth of the 30 km run,

30 km / 6 = 5 km.

So, Reena has run a distance of 5 km so far when she had run one sixth of the distance.

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The area of quadrilateral EFGH is closest to 29 square units.

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

Based on the values or the sides, and the slopes given, the area will be:

= 1 + 4 + 8 + 8 + 2 + 4 + 2

= 29 units.

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Answer:

the answer is 60990

Step-by-step explanation:

114×535

=60990

Answer:

Option D. 30 units

Step-by-step explanation:

The two sides of the right triangle will be 5 and 12 units as we can see from the diagram

Now to find the hypotenuse, we will use the Pythagoras Theorem

5² + 12² = Hypotenuse²

25 + 144 = Hypotenuse²

169 = Hypotenuse²

So,

Hypotenuse = root169 = 13

Perimeter of Right triangle = sum of all sides

Perimeter of Right triangle = 5 + 12 + 13

Perimeter Of Right triangle = 5 + 12 + 13 = 30

Option D. 30 units is the correct answer

Answer:

30

Step-by-step explanation:

See the attached worksheet.  The perimeter of the triangle is the sum of its three sides, labelled a, b, and c.

a and b can be calculated from the graph, as shown on the worksheet.

Once a and b are know, use the ZPythagorean Theorem to find c, which is 13.

Finially, add the sides a, b, and c:  5 + 12 + 13 = 30, the perimeter.

The  number of self-propelled mowers and riding mowers who paid total fee of $900 with $20 and $40 each are equal to 5 and 20 respectively.

Let 'x' be the number of self-propelled mowers and 'y' be the number of riding mowers.

Total number of self-propelled and riding mowers = 25

⇒ x + y = 25

⇒ x = 25 - y __(1)

Total fees paid = $900

Rental cost for each  self-propelled mower = $20

Rental cost for each riding mower = $40

20x + 40y = 900

⇒ x + 2y = 45___(2)

Substitute the value x in from (1) in  (2) we get,

⇒ 25 - y + 2y = 45

⇒ y = 20

⇒ x = 5

Therefore, the number of self-propelled mowers and riding mowers as per given total fee are 5 and 20 respectively.

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The ratio of cleaning product to water for the condition is 1/5

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.

Given it is recommended that 4 ounces of the product are diluted using 20 ounces of water.

to find the ratio of cleaning products to water

ratio = cleaning product/water

cleaning product = 4 ounce

water = 20 ounces

ratio = 4/20

4/20 is equivalent to 1/5

ratio = 1/5

Hence option A is correct.

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C. When there is no outlier, the mean is the appropriate measure of center.

When there are no outliers in a dataset, the mean is a good measure of center because it takes into account the values of all the data points. The median is also a good measure of center, but it may not be the best choice if there are extreme values or outliers in the dataset, as it can be influenced by those values. However, when there are no outliers, both the mean and the median are appropriate measures of center.

Option A is not true because the mean is not skewed in one direction when there is no outlier. Skewness refers to the shape of the distribution, and it can be affected by outliers, but not by the absence of outliers.

Option B is not true because the median is not skewed in one direction when there is no outlier. Skewness refers to the shape of the distribution, and the median is not affected by the shape of the distribution, but by the position of the values.

Option D is not true because the median can be used as the measure of center even when there is no outlier. It is a robust measure of center that is not influenced by extreme values.

Based on the given pictures:

Angle ∠1 has a more than 90° angle, means that it is classified as obtuse angle.

Angle ∠2 has a less than 90° angle, means that it is classified as an acute angle.

∠ABC is a straight angle because it creates a straight line with 180°.

Angle ∠2 can be named as ∠EBD because it was created by lines EB and ED.

∠WXY = 88°

∠WXZ = 4x - 3

∠ZXY = 2x + 1

∠WXY = ∠WXZ + ∠ZXY

88 = (4x - 3) + (2x + 1)

88 = 6x - 2

6x = 90

x = 15

∠HIJ = 108°

IK bisects ∠HIJ

∠HIK = 4x + 2

∠HIJ = 2∠HIK

108 = 2(4x + 2)

108 = 8x + 4

8x = 104

x = 13

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Answer:

21

Step-by-step explanation:

The median is the value separating the higher half of the data from the lower half.

10,11,13,18,19,  21   ,22,25,27,30,32

We see the middle number in this set is 21, so the median is 21

Answer: 3x + 7

Step-by-step explanation: ??? I think you mean 3x + 7, yes? If I'm mistaken, please correct me :)))))

In the triangles ABC and ADC the measure of ∠DAC = 25° and the length of AB is 12 cm.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

The triangle ABC and ADC follow the AAS theorem.

Here ∠C = ∠C, ∠A = ∠A and CD = CB

The line segment AC is the bisection of angle A, hence -

The missing angle is ∠A = ∠A.

Therefore, the missing angle measure is of 25°.

The missing side length is AB = AD.

Therefore, the missing side length is of 12 cm.

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Answer:

Moore's Law states that the number of transistors on a microchip will double approximately every two years. So, if a microchip in a given year could hold 922,200 transistors, 19 years later, it could hold approximately 922,200 * 2^(19/2) = 922,200 * 2^9.5 = 922,200 * 15,564,224 = 14,225,067,008,000 transistors.