ABCD is a rectangle with sides 8cm and 6cm PQRS is a rhombus

obtained by joining the midpoints of the sides of the rectangle. find
a)The lengths of the diagonals of PQRS?
b)The area of PQRS?

The 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).

We can use the conversion factor of 1 carat = 0.2 g to convert carats to grams.

Diamond weight in grams: 35.99 carats x 0.2 g/carat = 7.198 g (rounded to three decimal places)

We can use the conversion factor of 1 ounce = 28.3495 g to convert the weight in grams to ounces.

Diamond weight in ounces: 7.198 g / 28.3495 g/o z = 0.254 o z (rounded to three decimal places)

Carats are now commonly used to measure the weight of gemstones, including diamonds, and are abbreviated as "ct." A 1-carat diamond, for example, weighs 0.2 grams while a 2-carat diamond weighs 0.4 grams.

As a result, the 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).

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The inequality that represents the cost c per 14 squares for a new carpet with a budget of $700 is: c ≤ 700/14 = 50 Therefore, the answer is:

The inequality is c ≤ 50.

Assuming that the price of the carpet is constant per square foot, we can write the following inequality to represent the cost c per 14 squares:

c/14 ≤ 700

This inequality states that the cost per 14 square feet (c/14) cannot exceed $700, which is the total amount of money available to purchase the carpet.

To write an inequality representing the cost of a new carpet per 14 square feet, we need to first define the cost per square foot. Let's say the cost per square foot is $x. Then, the cost of the carpet for 14 square feet would be 14x.

Since we have a budget of $700, we can write the inequality:

14x ≤ 700

This inequality represents that the cost of the carpet for 14 square feet should be less than or equal to $700. We can solve for x by dividing both sides by 14:

x ≤ 50

This means that the cost per square foot of the carpet should be less than or equal to $50 for it to fit within the budget of $700.

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Answer:

A. First, outer, inner, last.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the volume of a cylinder, V = πr^2h, where r is the radius, h is the height, and π is Pi, we can find the radius by rearranging the equation and solving for r.

V = πr^2h, so r^2 = V / (πh)

Taking the square root of both sides, we have:

r = √(V / (πh))

Substituting the given values:

r = √(950 / (π * 10))

Since Pi is approximately equal to 3.14, we can calculate the approximate value of r:

r = √(950 / (3.14 * 10))

r ≈ 7.46

Therefore, the radius of the cylinder with a volume of 950 cubic inches and a height of 10 inches is approximately 7.46 inches.

The probability that one card is a spade and the other is a king when two cards are drawn at random from a deck of 52 cards is 0.0196.

To calculate the probability that one card is a spade and the other is a king when two cards are drawn at random from a deck of 52 cards, we need to first determine the total number of possible outcomes, which is the number of ways to select two cards from a deck of 52. This can be calculated using the formula for combinations, which is:

nCr = n! / r!(n-r)!

where n is the total number of objects (52 cards in this case), r is the number of objects to be selected (2 cards), and ! denotes the factorial operation.

So, the total number of possible outcomes is:

52C2 = 52! / 2!(52-2)! = 1326

Next, we need to determine the number of favorable outcomes, which is the number of ways to select one spade and one king from the deck. Since there are 13 spades and 4 kings in a deck, there are 13 x 4 = 52 ways to select one spade and one king.

However, we need to divide this number by 2 to avoid double counting the two possible orders (king-spade or spade-king), which gives us 26 favorable outcomes.

P = favorable outcomes / total outcomes = 26 / 1326 = 0.0196 or about 1.96%

So, there is a very low probability of selecting one spade and one king when two cards are drawn at random from a deck of 52 cards.

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Answer:

Step-by-step explanation:

Let's say Trace's age is "x".

Then, Hunter's age would be (x+3)

And Jacob's will be 2*(x+3)

The Total of three ages would be

x+(x+3)+2*(x+3)=49

4x+9=49

4x=40    

x=10

So Trace is 10 years old

     Hunter is 13 years old

     Jacob is 26 years old.

The profit is £1,370. Then the percentage profit of the company will be 124.54%.

A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running, or creating anything.

The profit is given as,

Profit = Selling price - Cost price

The number of pins left after the donation to charity is given as,

⇒ (1 - 0.35) x 1,000

⇒ 0.65 x 1,000

⇒ 650 pins

The selling price when 60% are sold for £3 and 40% are sold for £5 is given as,

Selling price = 0.60 x 650 x £3 + 0.40 x 650 x £5

Selling price = £1,170 + £1,300

Selling price = £2,470

The cost price is given as,

Cost price = £1.10 x 1,000

Cost price = £1,100

The profit is given as,

P = £2,470 - £1,100

P = £1,370

Then the percent of profit is given as,

P = [(£1,370) / £1,100] x 100

P = 124.54%

The profit is £1,370. Then the percentage profit of the company will be 124.54%.

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The solution of the expression at x = 2 is 53 and at x = 7 is 33.

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

Given that the expression is h(x) = −4x + 61. The value of the expression at x = 2 and x = -7 will be calculated as:-

At x = 2,

h(x) = −4x + 61

h(2) = -4 x 2 + 61

h(2) = -8 + 61

h(2) = 53

At x =7

h(x) = −4x + 61

h(2) = -4 x 7 + 61

h(2) = -28 + 61

h(2) = 33

Therefore, the values are 53 and 33.

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The value of csc(3π/2) is -1.

What is a trigonometric function?

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.

The given trigonometry function is csc(3π/2)

Assume that y = csc(3π/2)

Break the angle:

y = csc(π + π/2)

Applying the formula csc(π + θ) = -csc θ:

y = - csc(π/2)

y = -1 [since csc(π/2) = 1]

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The probability that the line pressure will surpass 13.0 bars during any measurement is P [Z > 13] = 0,1587, or 15.87%.

If the line pressure exceeds 13.0 bars, there is a chance that:

P [ Z > 13 ] = 1 - P [ Z ≤ 13]

P [Z 13] will be located in the z table when z (score) =

Z (score) equals (Z - 0) /

Z = (13 - 12)/1 (score).

the z-table, we then discover

P [ Z ≤ 13] = 0,8413

Finally . P [ Z > 13 ] = 1 - P [ Z ≤ 13]

P [ Z > 13 ] = 1 - 0,8413

P [Z > 13] = 0,1587, which is equal to 15,87%.One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprovable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it.

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D. The length is 18 inches and the width is 9 inch

What is a scale factor?

A scale factor resembles a unit scale in several ways. It is a ratio that assesses the relationship between scale and real dimensions. Because it doesn't provide any specified units, it differs.

It is given that the scale factor of the gardener is 1:15.

The dimensions of his drawing are 6 inches long by 3 inches wide.

Therefore the original dimensions are 6*15= 90 inches.

3*15= 45 inches.

The scale of his partner is 1:5.

So, we have to divide the original dimensions by 5.

The dimensions of the scale drawing are 90/5= 18 inches long

45/5=9 inches wide.

Therefore length is 18 inches and the width is 9 inches.

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We can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

So, as we have the equation:

12x + 3 = 3(5x + 9)

Now, as we can see, Sadio took out 3 as common from LHS and RHS and solved the equation.

Which gave her the value of x as -8.

Amir, on the other hand, did not take out anything as common and directly multiply 3 with other terms in the brackets to solve the equation.

He also got -8 as the value of x.

Hence, we can conclude that yes both the ways of solving the equation is correct which is done by Sadio and Amir.

Therefore, we can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

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No, if the figures on the left side of the area model were changed to 20, 10, and 5, the product would retain the same.

Area model multiplication is what?

The area model approach is based on the straightforward equation that may be used to calculate the area of a rectangle: LxW=A. As this anchor chart from Primary Punch illustrates, students typically begin by learning basic arrays for one-digit multiplication. When we multiply each digit of one number by each digit of another number while maintaining the place value of each digit, the resulting numbers are called partial products.

According to the supplied query,

30 and 5 on the left side of the area model are altered to 20,10, and 5 

Thus, after multiplying partial products, we obtain:

First row = 20×100+20×20+8×20

               = 2000+400+160 = 2560

Second row = 10×100+10×20+10×8

                     = 1000+200+80 = 1280

Third row = 5×100+5×20+5×8

                = 500+100+40 = 640

Adding all the rows we get,

2560+1280+640 = 4480

The item we receive when the dimensions are 30 and 5 is the same as this. In each instance, the area product stays the same.

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Answer: Frank is going to plant "b" vegetables in one garden and "2b + 1" vegetables in another garden. So, the total number of seeds he is going to plant is b + (2b + 1) = 3b + 1.

Step-by-step explanation:

The answer is c. Statistic because the value is a numerical measurement describing a characteristic of a sample.

A statistic is a value that summarizes a characteristic of a sample. In this case, the percentage of employees in the sample who own a television (45%) is a statistic because it summarizes a characteristic of the sample of employees that was selected. A parameter, on the other hand, is a value that summarizes a characteristic of a population. For example, if we were to consider the percentage of all employees in the company who own a television, then the mean or median percentage of television ownership would be a parameter because it would describe a characteristic of the entire population of employees. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.

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With the help of given table of data of travelling time to work for 50 people, the estimated mean travelling time is 24.8 minutes.

To estimate the mean travelling time from the given frequency table, we can use the midpoint method, where we calculate the midpoint of each class interval and multiply it by the frequency of that interval. We then sum up the products and divide by the total frequency to get the estimate of the mean travelling time. The midpoint of each interval can be calculated as the average of the lower and upper bounds of the interval. Using this method, we get:

Class interval 0 < t < 10 | 10 < t < 20 |  20 < t < 30 | 30 < t < 40 |  40 < t < 50

Midpoint (m)    5                     15               25                 35                  45

Frequency (f)    5                    15               13                  10                   7

Midpoint x Frequency 25      225            325               350               315

Total | | 50 | 1240

To estimate the mean travelling time, we can now calculate the sum of the products of the midpoint and frequency for each interval, which is 1240. We then divide this by the total frequency, which is 50. Therefore, the estimate of the mean travelling time for these 50 people is: Mean  travelling time = Sum of (midpoint x frequency) / Total frequency

Mean travelling time = 1240 / 50 = 24.8

Thus, the estimated mean travelling time is 24.8 minutes.

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Complete Question

The table shows the travelling time to work of 50 people.

-Travelling time (t)  in minutes- -Frequency-

0 <t<10                                           5

10 < t < 20                                     15  

20 < t < 30                                    13

30 < t < 40                                    10

40 < t < 50                                    7

Calculate an estimate of the mean travelling time

Using the unit conversions, the height of the tree in yards is 126.33 yd

Let h be the height of the tree.

It is given that the Height of the tree is 379 feet and we need to find the height of the tree in yards.

From the given statement, Hyperion is the tallest tree in the park, with a height of approximately 379 feet,

We need to convert the height of the tree from feet to yards. So, We divide the height of the tree by three for the yard.

So, for one foot: h = (1/3) yd

For, 379 feet: h = 379/3 yd

                         = 126.33 yd

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Answer:

Hello if you are solving for x the for the equation -4x+4y=-4

your answer is x=y+1

Step-by-step explanation:

4y -4x= -4

subtract 4y from both sides

-4x = -4y- 4

divide both sides by -4

x= y+1

I HOPE THIS HELPS!

The probability that exactly 16 people out of 25 favor the new building project is 0.1285.

The probability that at most 16 people out of 25 favor the new building project is 0.3528.

The probability that between 12 and 19 (including 12 and 19) people out of 25 favor the new building project is 0.9088.

A binomial distribution is a probability distribution that describes the number of successes in a fixed number of trials, where each trial has two possible outcomes (success or failure) and the trials are independent.

The distribution of x, the number of people who favor the new building project when 25 people are chosen at random, can be modeled using a binomial distribution.

In this case, the probability of success (favoring the new building project) is 0.61, and the probability of failure (not favoring the project) is 0.39. The number of trials is 25, since we are choosing 25 people at random.

Thus, we can write x ~ Bin(25, 0.61), which means that x follows a binomial distribution with 25 trials and a probability of success of 0.61.

To find the probability that exactly 16 people out of 25 favor the new building project, we can use the binomial probability formula:

[tex]P(X = k) = (^n_k) * p^k * (1 - p)^{n - k}[/tex]

where X is the random variable (in this case, the number of people who favor the project), k is the number of successes we are interested in (in this case, 16), n is the number of trials (25), p is the probability of success (0.61), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.

Plugging in the values, we get:

P(X = 16) = (25 choose 16) * 0.61¹⁶ * 0.39⁹ = 0.1285

Therefore, the probability that exactly 16 people out of 25 favor the new building project is 0.1285.

To find the probability that at least 16 people out of 25 favor the new building project, we need to add up the probabilities of all the events where the number of successes is 16 or greater. We can do this using the cumulative distribution function (CDF) of the binomial distribution, which gives us the probability of X being less than or equal to a certain value.

Using a calculator or a table, we can find that P(X ≥ 16) = 0.3528.

Therefore, the probability that at least 16 people out of 25 favor the new building project is 0.3528.

To find the probability that at most 16 people out of 25 favor the new building project, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of its complement (the event not occurring). In this case, the complement event is the number of people who favor the project being greater than 16.

Using the same CDF, we can find that P(X > 16) = 0.6472. Therefore,

P(X ≤ 16) = 1 - P(X > 16) = 1 - 0.6472 = 0.3528

We can do this using the binomial probability formula for each possible value of k, and then summing the results.

P(12 ≤ X ≤ 19) = P(X = 12) + P(X = 13) + ... + P(X = 19)

Using a calculator or a table, we can find the probabilities for each value of k, and then add them up:

P(12 ≤ X ≤ 19) = 0.0309 + 0.0746 + 0.1322 + 0.1821 + 0.2001 + 0.1821 + 0.1322 + 0.0746 = 0.9088

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Answer:

x = 4

Step-by-step explanation:

Move the x to the left-hand side and change its sign

2x - x = 9 - 5

x = 9 - 5

Answer:

x=4

Step-by-step explanation:

Subtract 1x from both sides

Subtract 5 from both sides to isolate the variable

x=4

Answer:

4cm

Step-by-step explanation:

∵∆DEF ~ ∆ABC，AB/AC =2/3，

∴DE/DF=2/3.

∵DF=6cm，

∴DE=6*2/3=4cm.

Explanation:

The left-most digits are more significant than digits on the right.

For example, in the very large number 1,234,567 the "1" and "2" are more important than the "6" and "7". We focus on the more important digits when rounding. This would mean 1,234,567 rounds to 1,200,000 = 1.2 million = 1.2*10^6

Going back to 3.162, we have "3" and "1" as the left-most digits. We'll bump 3.1 up to 3.2 because of the digit 6 fits the criteria of "5 or larger".

Put another way: 3.162 is closer to 3.2 than it is to 3.1

This is why 3.2 is the final answer.

ABCD is a rectangle, and P, Q, R, and S are mid points of the sides AB, BC, CD, and DA, respectively. show that the quadrilateral PQRS is a rhombus

The man can wear 15 different outfit combinations by mixing and matching his six different sport shirts and four different pairs of slacks.

Combination is a way of counting the number of different groups of items that can be selected from a larger set without regard to the order in which they are selected.

In this case, the man has six different sport shirts and four different pairs of slacks, and he wants to know how many different outfit combinations he can wear. We can use the formula for combinations to calculate the number of possibilities.

The formula for combinations is:

ⁿCₓ = n! / (x! * (n - x)!)

Where n is the total number of items, x is the number of items being selected, and the exclamation mark (!) represents the factorial of a number (i.e., the product of all positive integers up to that number).

Using this formula, we can calculate the number of different combinations the man can wear as follows:

Number of sport shirts (n) = 6

Number of slacks (x) = 4

Number of combinations = ⁶C₄ = 6! / (4! * (6 - 4)!)

= (6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (2 * 1)]

= 15

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Answer: The total amount paid for shoes = $63.75

Step-by-step explanation:

The original price of the shoes = $ 80

Sale Discount = 25 %

So, the discount offered = 25 % of 80 = 20

So, the Discounted Price  = Marked price - discount

= $ 80 -$ 20 = $ 60

Now, we need to calculate the sale tax of 6.25 % on $ 60.

Also, we know that  Sales Tax = Sales Tax rate x Sale Price

= $ 60 x 0.0625  = $ 3.75

Total Cost = Sale Price + Sales Tax

=  $ 60 + $ 3.75  = $63.75

Hence, the total amount paid for shoes = $63.75 included sales tax

The expression 4^n+3 x 16^n - 8^3n cannot be solved for n

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

4^n+3 x 16^n - 8^3n

The question implies that we solve for n

This in other words mean that we determine the solution for n

The given parameter is an expression (not an equation or an inequality)

To solve for a variable, the given parameter must be an equation or an inequality

Hence, the value of n cannot be determined or it has infinite many solutions

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If a 12-ft-by-15-gt rectangular swimming pool has a 3-ft-wide no-slip surface around it. The outer perimeter of the no-slip surface around the rectangular swimming pool is 78 feet.

The key idea in this problem is to recognize that the no-slip surface around the pool consists of a rectangular strip of uniform width that runs parallel to the edges of the pool. To find the outer perimeter of this strip, we need to add up the lengths of all four sides of the rectangle formed by the outermost edges of the no-slip surface.

Let's start by finding the length of the no-slip surface that runs along the length of the pool. Since the pool is 12 feet long and the no-slip surface extends 3 feet beyond each end of the pool, the total length of the no-slip surface is:

12 + 2(3) = 18 feet

The "2(3)" term in this equation represents the 3-foot-wide extension on each end of the pool. Next, we need to find the length of the no-slip surface that runs along the width of the pool. Since the pool is 15 feet wide and the no-slip surface extends 3 feet beyond each side of the pool, the total width of the no-slip surface is:

15 + 2(3) = 21 feet

Now we have the lengths of the two parallel sides of the rectangle formed by the outermost edges of the no-slip surface. To find the lengths of the other two sides, we simply add up the lengths of the corresponding sides of the pool.

Therefore, the length of the rectangle is 12 + 2(3) = 18 feet, and the width of the rectangle is 15 + 2(3) = 21 feet.

Finally, we can add up the lengths of all four sides of the rectangle to find the outer perimeter of the no-slip surface:

2(18) + 2(21) = 36 + 42 = 78 feet.

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Answer:

Step-by-step explanation:

14 doughnuts in total

Answer:

4x - 5y - z

Step-by-step explanation:

3x − 4y + z − 2z + x − y

Add like terms

= 4x - 5y - z

Answer: 4x-5y-z

Step-by-step explanation: 3x + x -4y-y -2z + z

It becomes a lot easier to simplify if you reorganize the equation so that the same variables are next to each other