10) A rectangle has a width of 2m+3. The length
is twice as long as the width. What is the length
of the rectangle?

Answer: The answer for the first question goes as follows: Which one(s) have both pairs of opposite sides that are parallel? Rectangle, Rhombus, and square. Which one(s) have both pairs of opposite sides that are congruent? Rectangle, square, and rhombus. Which one(s) have all four sides congruent? Square and rhombus.

The answers to the second question are:

Step-by-step explanation:

Essentially, all of these parallelograms have different properties and properties that they share. For example, a property they share by the definition of a parallelogram is that all of them have two pairs of opposing sides that are parallel. Another property they share from the definition of a parallelogram is that opposite sides are congruent.

As such, rectangles, squares, and rhombuses have the properties that all parallelograms have because they are all parallelograms. However, they also have their own properties.

Second Question Explanation:

1. The question is describing a theater that has a circular base. Therefore, you can use the formula for the circumference of a circle, pi * diameter, to find the circumference (or distance around) the theater. The diameter is given to you: 100 ft. So just multiply that by pi.

2. The question is asking for the area of the theater. This means that you can use the formula for the area of a circle, A = pi * r^2. Note that it is asking you for the area, not the volume, so you would find the area of the circle, not the volume of the hemisphere. r represents the radius of the circle/theater. The diameter is given as 100 ft, and the radius is half of the diameter, so it is 50 ft. Now just plug the radius into the equation and you get the answer I showed.

The vector u2 is (0, √3/3, 2/3). It is a unit vector that is orthogonal to both 8,-8,8 and 0,5,5.

Given two vectors 8,-8,8 and 0,5,5, we need to find another unit vector that is orthogonal to both the given vectors. Let's call this vector u1.The vector u1 can be obtained by taking the cross product of the two given vectors:u1 = (8,-8,8) × (0,5,5)u1 = (-40,-40,40)

To get a unit vector, we need to normalize u1 by dividing it by its magnitude:|u1| = √((-40)² + (-40)² + 40²) = 60u1 = (-40/60, -40/60, 40/60) = (-2/3, -2/3, 1/3)Now we need to find another unit vector that is orthogonal to u1.

One way to do this is to take the cross product of u1 with another vector, and then normalize the result. We can choose any vector that is not parallel to u1. For example, we can choose the vector (1,0,0).u2 = u1 × (1,0,0)u2 = (-2/3, -2/3, 1/3) × (1,0,0)u2 = (0,1/3,2/3)

To get a unit vector, we need to normalize u2 by dividing it by its magnitude:|u2| = √(0² + (1/3)² + (2/3)²) = 1/√3u2 = (0, √3/3, 2/3)

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Step-by-step explanation:volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length

The position of C on the number line is 1/8th position.

A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.

From the given number line, there are total 8 points between 0 to 1

That means, it's fractions of 8.

Location of point C is on the 1st point,

So, position of C on this number line = (1/8) ÷ (1-0) = 1/8

Therefore, In the number line, C is located in the 1/8th place.

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Answer:

x = 45.

Step-by-step explanation:

Given a straight line with the equation.

First collect like terms:

2x + x = 180 - 45

Then calculate:

3x = 135

Finally after dividing both sides by 3:

x = 45

Answer:

36 × 10^6 m²

Step-by-step explanation:

Given the side length of a square = 6 × 10³m,

To solve for the area of a square, use the following formula:

A = S² where:

S = side of the square

Substitute the given value for the side into the formula:

A = S²

A = (6 × 10³)²

A = 36000000 or 36 × 10^6 m²

NOTE:

6 × 10³ is also the same as 6 × 1000 = 6000,

(6 × 10³)² is essentially 6,000² = 36,000,000

Therefore, its area in square meters is 36 × 10^6

The distance from points A(-2, 2) to B (4, -2)​ is equal to √52 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-2))² + (-2 - 2)²]

Distance = √[(6)² + (-4)²]

Distance = √(36 + 16)

Distance = √52 units.

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Answer:

83.6%

Step-by-step explanation:

Let's say the original price is x

x decreased by 12% means 88% of x is left.

0.88x decreased by 5% means 95% of 0.88x is left.

This means the answer is: 0.88x * 0.95 = 0.836

The percent of the total decrease is 83.6%

Hope this helps :)

Have a great day!

a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:

Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day

Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.

b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:

1 machine : 2.5 crates/day = 70 machines : x crates/day

Solving for x, we get:

x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day

Therefore, 70 of these machines would pack 175 crates of limes per day.

Step-by-step explanation:

a) The ratio of the number of machines to the number of crates packed per day can be written as:

60 : 150

To simplify this ratio, we can divide both sides by 10:

6 : 15

Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:

1 : 2.5

Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.

b) If 60 machines can pack 150 crates per day, then one machine can pack:

150/60 = 2.5 crates per day

So, 70 machines can pack:

70 × 2.5 = 175 crates per day

Therefore, 70 machines can pack 175 crates of limes per day.

a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.

a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

They cover almost equal distances from their starting points:

24 miles ≈ √12²+21² miles

b) They encounter each other.

c) The angle at one vertex measures 30 degrees.

d) e) As shown in the attached picture, it is an almost right triangle.

f) Together, they cover a total distance of 57 miles (12+21+24).

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Answer:

Step-by-step explanation:

Using the property of a kite: the angles formed by two unequal sides of a kite are equal. The value of ∠BCD∠BCD is

∠BCD = ∠BAD ⇒ ∠BCD = 106°  

In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.

According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.

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Answer:

Length = 53 feet

Width = 22 feet

Step-by-step explanation:

Perimeter = 2(length + width)

Then:

a = 2w + 9            Ec. 1

150 = 2(a + w)       Ec. 2

a = length

w = width

From Eq. 1:

a - 9 = 2w            Eq. 3

From Eq. 2:

150 = 2*a + 2*w

150 = 2a + 2w

150 - 2a = 2w        Eq. 4

Equalizing Eq. 3 and Eq. 4

a - 9 = 150 - 2a

a + 2a = 150 + 9

3a = 159

a = 159/3

a = 53

From Eq. 1:

a = 2w + 9

53 = 2w + 9

53 - 9 = 2w

44 = 2w

44/2 = w

w = 22

Check:

From Eq. 2

150 = 2(a+w)

150 = 2(53+22)

150 = 2*75

Answer:

10 sides

Step-by-step explanation:

We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:

S = (n - 2) x 180 degrees

If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:

1440 = (n - 2) x 180

Dividing both sides by 180, we get:

8 = n - 2

Adding 2 to both sides, we get:

n = 10

Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.

Answer: 54 square in

Step-by-step explanation:

I don't know if this is the same person but I answered this same question just now please check my profile or comment if you want the explanation

The probability of drawing a diamond, then a black card, and then a face card from a standard deck of 52 cards with replacement is 3/104 or 0.028846 .

The probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card is given by the expression, `(13/52) × (26/52) × (12/52)`.

In a standard deck of 52 cards, there are 13 diamonds, 26 black cards (13 clubs and 13 spades), and 12 face cards (4 Jacks, 4 Queens, and 4 Kings).

To calculate the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card, we use the formula of probability:

`P(E) = n(E) / n(S)`

where, P(E) = Probability of an event

n(E) = Number of favorable outcomes

n(S) = Total number of outcomes

Total number of outcomes = 52

First card will be a diamond

Number of diamonds in a deck of 52 cards = 13

Total number of outcomes after drawing the first card = 52

Probability of drawing a diamond in the first attempt = P(diamond)`= 13/52

Probability of drawing a black card in the second attempt, given that the first card is a diamond= `P(black/diamond)`= (26/52) = `(1/2)`

Probability of drawing a face card in the third attempt, given that the first card is a diamond and second card is a black card= `P(face/diamond and black)`= `(12/52)` = `(3/13)`

Therefore, probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card`= P(diamond) × P(black/diamond) × P(face/diamond and black) = (13/52) × (1/2) × (3/13)= 3/104`

Therefore, the required probability is 3/104 or 0.028846 rounded to the nearest millionth.

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Answer:

m = -9/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (4, -6) (2, 3)

We see the y increase by 9, and the x decrease by 2, so the slope is

m = -9/2

The expression 4 triangles to 16 squares when simplified is 1 triangle to 4 squares

Given that

4 triangles to 16 squares

When expressed as ratio, we have

Triangle : Square = 4 : 16

To simplify the ratio Triangle : Square = 4 : 16, we can divide both the numerator and denominator by their greatest common factor, which is 4.

So, we have

Triangle : Square = 4 : 16

Divide both sides by 4:

Triangle/4 : Square/4 = 1 : 4

So the simplified ratio is 1 : 4, which means for every one triangle, there are four squares.

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Yes, she can definitely use her van safety in one journey. The total weight is the weight of potatoes plus the weight of carots.

Given,

Number of sacks of potatoes = 30

Mass of each potato = 25

Total weight of Potatoes = 30 * 25

= 750

Number of sacks of carrots = 20

Mass of each Carot = 7.5

Total weight of Carrot = 20 * 7.5

= 150

(The total weight is the weight of potatoes plus the weight of carrots.)

So, total weight = 750 + 150

= 900

The maximum land which Edith can carry safely in the van is 920 kilograms.

∵ 900 < 920

∴ She can use her van safely.

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Answer:

5 less than or equal to x

Step-by-step explanation:

make x subject

Answer:

It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).

Step-by-step explanation:

The normalized form of the equation

(x+2)^2= - 16

x^2 + 4x + 4 = - 16

x^2 + 4x + 20 = 0

We have in the form ax^2 + abx + c = 0

a = 1

b = 4

c = 20

Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64

Discriminant is negative, therefore, no Real solutions.

The given conditional statements are false, true, false, True.

They are determined by following:

(a) False - The statement "If 10<7,10<7, then 3=43=4" is false, since 10 is not less than 7.
(b) True - The statement "If 7<10,7<10, then 3=43=4" is true, since 7 is less than 10.
(c) False - The statement "If 10<7,10<7, then 3+5=83+5=8" is false, since 10 is not less than 7.
(d) True - The statement "If 7<10,7<10, then 3+5=83+5=8" is true, since 7 is less than 10.

Conditional statements are used in mathematics and logic to express relationships between events and conditions. These statements consist of an "if-then" structure, where the "if" clause is the antecedent or condition, and the "then" clause is the consequent or outcome.

The truth value of the conditional statement depends on whether the condition is true or false. If the condition is true, then the outcome is also true, and the statement is considered true.

If the condition is false, then the outcome may be true or false, and the statement is considered false. Conditional statements are widely used in mathematical proofs, programming, and reasoning to establish logical connections between different events and conditions.

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(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.

(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.

The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.

A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.

(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.

(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.

Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.

Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.

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Jen has 54 pages left to read to meet her assignment requirement.

The inequality that represents this situation is p ≥ 85 - 31

To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.

The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:

p = 85 - 31

p = 54

Therefore, Jen has 54 pages left to read.

To represent this situation with an inequality, we can use:

p ≥ 85 - 31

This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).

Solving for p:

p ≥ 85 - 31

p ≥ 54

This means that Jen must read at least 54 more pages to meet her assignment requirement.

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Answer: profit

Step-by-step explanation:

3.95 (price of one share) multiplied by 40 (the amount of shares bought) would have cost $158. so selling all for $200 would be a $42 profit

Answer:

Step-by-step explanation:

150

As per the given APR, the sum of amount after 18 years is $66,373. 60, and the total deposits made over the time period is  $43,200. (option d).

To calculate this, we can use the formula for future value of an annuity:

FV = PMT x (((1 + r)⁻¹) / r)

where FV is the future value, PMT is the monthly payment, r is the monthly interest rate (which is calculated by dividing the APR by 12), and n is the number of payments (which is 18 x 12 = 216 in this case).

Plugging in the numbers, we get:

FV = $200 x (((1 + 0.045/12)²¹⁶ - 1) / (0.045/12)) = $66,373.60

Therefore, you would have approximately $66,373.60 in your investment plan after 18 years.

Now let's compare this amount to the total deposits made over the time period. In this case, the total deposits would be:

$200 x 12 x 18 = $43,200

Hence the correct option is (d).

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Answer:

Step-by-step explanation:

we have perimeter 16

for perimeter 4+4+4+4 we add together it's 16

for area we have 4 times 16

The abiotic factor that can prevent the organism from becoming preserved, AFTER it has been buried is groundwater.

An abiotic factor refers to a non-living component of an ecosystem that influences the survival and growth of living organisms.

Groundwater can cause the dissolution of minerals present in the sediment that encases the buried organism.

This process can lead to the destruction of the fossilized remains, as the minerals provide the framework for the preservation of the organism's hard parts (such as bones or shells).

Groundwater can also cause the erosion of the sediment, which can expose the buried remains and make them vulnerable to biotic factors such as scavengers, predators, and decomposers.

Predators and animals that eat bones, scavengers and plants that use the nutrients of fossils, and other animals of the same species as the organism that died are all biotic factors that can affect the preservation of the organism, but they do so before or during the burial process.

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