find the square root of 24-16√2​

Applying the linear pair postulate:

y = 30

m<ACB = 160°

According to the linear pair postulate, the sum of two adjacent angles that form a linear pair is equal to 180 degrees.

Given the following:

m<ACB = (4y + 40)°

m<DCE = (y - 10)°

Angles ACB and DCE are a linear pair. Therefore:

m<ACB + m<DCE = 180°

Substitute

(4y + 40) + (y - 10) = 180

Solve for y

4y + 40 + y - 10 = 180

Combine like terms

5y + 30 = 180

Subtract 30 from both sides

5y + 30 - 30 = 180 - 30

5y = 150

Divide both sides by 5

5y/5 = 150/5

y = 30

Find m<ACB:

m<ACB = (4y + 40)°

Plug in the value of y

m<ACB = 4(30) + 40

m<ACB = 120 + 40

m<ACB = 160°

Thus, applying the linear pair postulate:

y = 30

m<ACB = 160°

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The radius of gyration of the plate about the x-axis is \(6 \sqrt{6} / 5\) units.

To find the radius of gyration of a plate covering the region bounded by \(y = x^2\), x = 6, and the x-axis with respect to the x-axis, we need to use the formula:

\(k_x = \sqrt{(I_x / A)}\)

where \(k_x\) is the radius of gyration, \(I_x\) is the moment of inertia of the plate about the x-axis, and A is the area of the plate.

We can calculate the area A of the plate as follows:

\(A = \int\limits^6_0 { x^2}\, dx\\= [x^3/3]\ from\ 0\ to\ 6\\= 72\)

To find the moment of inertia \(I_x\), we can use the formula:

\(I_x = \int\ {y^2} \, dA\)

where y is the perpendicular distance of an element of area \(dA\) from the x-axis. We can express y in terms of x as y = x². Therefore, we have:

\(dA = y dx = x^2 dx\\I_x = \int\limits^6_0 { x^2 (x^2)} dx\\= \int\limits^6_0 {x^4}\, dx\\= [x^5/5]\ from\ 0\ to\ 6\\= 6^5/5\)

Substituting these values into the formula for \(k_x\), we get:

\(k_x = \sqrt{(I_x / A)}\\= \sqrt{((6^5/5) / 72)}\\= \sqrt{(6^3 / 5)}\\= 6 \sqrt{6} / 5\)

Therefore, the radius of gyration of the plate about the x-axis is \(6 \sqrt{6}/ 5\) units.

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Answer:

59 degrees

Step-by-step explanation:

98+23=121

180 (total angle in a triangle) - 121 = 59 degrees

brainliest plz

Answer:

A. 59°

Step-by-step explanation:

Answer:1. B.4968

2. A. $6.25x+$7.50= $26.25

Step-by-step explanation:

For no.1 :

Get the population for the second year first,

115/100*4500= 5175

Get the population of the third year

96\100*5175=4968

For no.2 :

The total is gotten by adding the admission fee to the total cost for all the games, and (x) is the number of games, therefore :

$6.25x+$7.50=$26.25

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer: 40 cm

So the diagonal formula is -  1/2* (d1*d2) d1 is the first diagonal and d2 is the second diagonal.  

So,

1/2 * (18*d2)= 360

18*d2= 360*2

d2= 720/18

d2= 40

The critical value of the correlation coefficient for a two-tailed test at alpha = 0.05 with a sample size of n = 23 is approximately plus/minus 0.497.

To understand why this is the case, we need to consider the distribution of the correlation coefficient, which follows a t-distribution. In a two-tailed test, we divide the significance level (alpha) equally between the two tails of the distribution. Since alpha = 0.05, we allocate 0.025 to each tail.

With a sample size of n = 23, we need to find the critical t-value that corresponds to a cumulative probability of 0.025 in both tails. Using a t-distribution table or statistical software, we find that the critical t-value is approximately 2.069.

Since the correlation coefficient is a standardized measure, we divide the critical t-value by the square root of the degrees of freedom, which is n - 2. In this case, n - 2 = 23 - 2 = 21.

Hence, the critical value of the correlation coefficient is approximately 2.069 / √21 ≈ 0.497.

Therefore, the correct answer is A. Plus/minus 0.497.

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The X and Y intercepts of the following equations are:

(a) Y = 3X - 1 : intercepts are [ 1/3 , -1 ]

(b) Y = X - 2 : intercepts are [ 2 , -2 ]

To find the x-intercept we put y = 0 and solve the equation for x. This is because when y = 0 the line crosses the x - axis. To find y-intercept: put      x = 0 and solve for y. See the attached figure for understanding the intercepts.

For example: Find the X and Y intercepts of the equation: X - Y = 5.

for X intercept put Y = 0, we get X = 5

for Y intercept put X = 0, we get Y = -5

Here, we have (a) equation Y = 3X - 1

For X intercept put Y = 0, we get X = 1/3

For Y intercept put X = 0, we get Y = -1

so, the X and Y intercepts of the equation Y = 3X - 1 are [ 1/3, -1 ]

now, we have (b) equation Y = X - 2

For X intercept put Y = 0, we get X = 2

For Y intercept put X = 0, we get Y = -2

so, the X and Y intercepts of the equation Y = X - 2  are [ 2 , -2 ]

Hence, The X and Y intercepts of the following equations are:

(a) Y = 3X - 1 : intercepts are [ 1/3 , -1 ]

(b) Y = X - 2 : intercepts are [ 2 , -2 ]

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Disclaimer: The question given was incomplete on the portal. Here is the complete question.

Question: Find the X and Y intercept of the following equation:

(a) Y = 3X - 1

(b) Y = X - 2

Answer:

(1)55.5 feet

(2)7.5 feet

Step-by-step explanation:

Question 1

The diagram is attached below.

Using Trigonometric ratio

\(\tan 48^\circ = \dfrac{h}{50} \\h=50 \times \tan 48^\circ\\h=55.5$ feet (to the nearest tenth)\)

The height of the house is 55.5 feet to the nearest tenth.

Question 2

In the diagram, we are required to find the distance the bird must fly to be directly above the fish. This has been represented by x.

Using Trigonometric ratio

\(\tan 15^\circ = \dfrac{2}{x} \\x \tan 15^\circ=2\\x=2 \div \tan 15^\circ\\x=7.5 $ feet (to the nearest tenth)\)

The distance the bird must fly to be directly above the fish is 7.5 feet.

Answer:

Step-by-step explanation:

Cost price of three machines with repairment charge ( CP ) = 5400 × 3 + 4000

= Rs 20200

Selling price of 1 machine = Rs 7000

Selling price of 3 machines ( S.P )= Rs 7000 × 3

= Rs 21000

Since , SP > CP , he made a profit

Profit = SP - CP

= Rs 21000 - Rs 20200

= Rs 800

--------------------------------------------------------------

Further more explanation

Profit and loss

In any business , owners have intension to have profit by selling articles. The price at which an article is purchased is called it's Cost price ( C.P ) and the price at which it is sold is called Selling price ( S.P ).

If the selling price is less than cost price of an article then there is a loss.

\( \mathrm{Loss \: = \: Cost \: Price \: (C.P) - Selling \: Price \: (S.P)}\)

If the selling price is more than cost price of an article then there is a profit ( gain )

\( \mathrm{Profit = Selling \: Price \: (S.P) - Cost \: Price \: (C.P)}\)

So, If S.P > C.P, there is profit in dealing.

If C.P > SP , there is loss in dealing.

Hope I helped!

Best regards!!

The cytoplasmic membrane consists of phospholipids, proteins, and other molecules.

The cytoplasmic membrane, also known as the plasma membrane, is a vital component of cells in both prokaryotes and eukaryotes. It surrounds the cell, separating its internal contents from the external environment. The main structural component of the cytoplasmic membrane is phospholipids. These phospholipids form a lipid bilayer, with hydrophilic (water-loving) heads facing outward and hydrophobic (water-fearing) tails facing inward. This lipid bilayer provides a barrier that controls the movement of substances in and out of the cell.

In addition to phospholipids, the cytoplasmic membrane contains proteins. These proteins are embedded within the lipid bilayer and have various functions. Some proteins act as transporters, facilitating the movement of molecules across the membrane. Others serve as receptors, allowing the cell to detect and respond to signals from the environment. Enzymes involved in cellular metabolism can also be found in the cytoplasmic membrane. Additionally, the cytoplasmic membrane may contain other molecules such as cholesterol, which helps maintain the fluidity and stability of the membrane.

Overall, the cytoplasmic membrane is a complex structure composed of phospholipids, proteins, and other molecules. It plays a crucial role in maintaining the integrity of the cell and regulating the exchange of substances with the external environment.

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Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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Answer:

$21600

Step-by-step explanation:

Answer:

100,000=10^5,  and 1/100,000= 1/10^5=10^-5

so this is your answer

10^5 x 10^-5

Step-by-step explanation:

Sample answer from Edmentum.

The exponential value of  1,00,000 and 1/1,00,000 is 10⁵ and 10⁻⁵.

The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given numbers 1,00,000 and 1/1,00,000

factors of 1,00,000 = 10 x 10 x 10 x 10 x 10

1,00,000 in exponential form is 10⁵ because 10 is multiplying continuously 5 times.

and 1/1,00,000 = 1/(10⁵)

using formula 1/aⁿ = a⁻ⁿ

so  1/(10⁵) = 10⁻⁵

Hence exponential for numbers is  10⁵ and  10⁻⁵.

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The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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Answer:

We can start by simplifying both sides of the equation:

5x² + 18x = 25x + 15 + 3x²

2x² - 7x - 15 = 0

Now we need to factor this quadratic equation:

2x² - 7x - 15 = (2x + 3)(x - 5)

Setting each factor equal to zero gives us the solutions:

2x + 3 = 0 or x - 5 = 0

Solving for x, we get:

x = -3/2 or x = 5

Therefore, the solutions to the quadratic equation are x = -3/2 and x = 5.

So, the correct answer is (x - 5)(2x+3).

Adding 16 to the given equation we get:

Simplifying the above result we get:

Dividing the above equation by 7 we get:

Simplifying the above result we get:

Answer:

Answer:

Step-by-step explanation:

7x-16=-2how do i find the solution of x

7x - 16 = -2

7x = - 2 + 16

7x = 14

x = 14 : 7

x = 2

-------------------------------

check

7 × 2 - 16 = -2               (remember PEMDAS)

14 - 16 = -2

-2 = -2

the answer is good

The correct pair of constraints that needs to be added to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units is: P24 - P25 <= 80; P25-P24 <= 80. Therefore, the correct option is 5.

Here, the given information is Pij = the production of product i in period j. We need to find the pair of constraints that will specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Thus, let the production of product 2 in period 4 and in period 5 be represented as P24 and P25 respectively.

Therefore, we can write the following inequalities:

P24 - P25 <= 80

This is because the production of product 2 in period 5 can be at most 80 units less than that of period 4. This inequality represents the difference being less than or equal to 80 units.

P25-P24 <= 80

This is because the production of product 2 in period 5 can be at most 80 units more than that of period 4. This inequality represents the difference being less than or equal to 80 units.

Therefore, we need to add the pair of constraints P24 - P25 <= 80 and P25-P24 <= 80 to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Hence, option 5 is the correct answer.

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Answer:

30

Step-by-step explanation:

\(\sqrt{50}\) * \(3\sqrt{2}\)

= \(\sqrt{50 * 18}\) (\(3\sqrt{2}\) = \(\sqrt{18}\))

= \(\sqrt{900}\)

= 30

Answer:

  225

Step-by-step explanation:

When you fill in values of n, you find the series is an arithmetic series of 15 terms with a first term of 1 and a common difference of 2. The formula for the sum of such a series can be used.

Looking at terms of the series for different values of n, we find ...

  for n = 1: 2(1) -1 = 1 . . . . . the first term

  for n = 2: 2(2) -1 = 3 . . . . the second term; differs by 3-1=2

  for n = 15: 2(15) -1 = 29 . . . . the last of the 15 terms

The sum of the terms of an arithmetic series is the product of the average term and the number of terms. The average term is the average of the first and last terms.

  Sum = (1 +29)/2 × 15 . . . . . . average term × number of terms

  Sum = 15 × 15 = 225

The sum of the series is 225.

__

Additional comment

Based on the first term (a1), the common difference (d), and the number of terms (n), the sum can also be written ...

  S = (2×a1 +d(n -1))(n/2)

For the parameters of this series, the sum is ...

  S = (2(1) +2(15 -1))(15/2) = 30(15/2) = 225

Answer:

83°

Step-by-step explanation:

m<ABC = 180° because that's a straight line

42 + 5x + 7x + 6 = 180°

12x + 48 = 180

12x = 180 - 48

12x = 132 divide by 12

x = 11

CBE = 7x + 6 ➡ 7×11 + 6 = 83°

Answer:

132/7

Step-by-step explanation:

180 = 42 + 7x + 6

180 = 7x + 42 +6

180 = 7x + 48

(180 - 48) = 7x (+ 48 - 48)

132 = 7x

7x = 132

7x / 7 = 132 / 7

x = 132/7

I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

Answer:

23.81%

Step-by-step explanation:

The total number of ways to select 5 out of 10 will be;

10 C 5 = 252

The number of ways of selecting 2 boys out of 6 will be

6 C 2 = 15 ways

The number of ways of selecting 3 girls out of 4 will be

4 C 3 = 4 ways

The probability of both will be;

(4 * 15)/252 = 60/252 = 0.238095238095

To the nearest percentage, that will be 23.81%

Answer:

\(\fbox {Work is attached below.} \downarrow\)

Step-by-step explanation:

Answer:

85.5 miles

Step-by-step explanation:

From the attached diagram, distance between the two rest stops :

Rest stop A to Rest stop B = 2 1/4 inches

Scale factor :

1 in = 38 miles

Acrual distance would be :

2 1/4 inches would be :

2 1/4 * 38 miles

9/4 * 38 = 85.5 miles

Answer:

x = -20

Step-by-step explanation:

2.5(x - 4) = -60

~Distribute left side

2.5x - 10 = -60

~Add 10 to both sides

2.5x = -50

~Divide 2.5 to both sides

x = -20

Best of Luck!

∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx equals approximately 1932.5

To evaluate the given integrals, let's first identify the functions f(x) and g(x) and their respective intervals.

f(x) = 4x^2 - 3x + 2

g(x) = 2x^3 - 5x + 1

Interval: [3, 8]

Now, let's evaluate the integrals step by step.

∫[3, 8] f(x) dx:

We integrate the function f(x) over the interval [3, 8].

∫[3, 8] (4x^2 - 3x + 2) dx

To find the integral, we can use the power rule for integration. For each term, we increase the exponent by 1 and divide by the new exponent.

= [4 * (x^3/3) - 3 * (x^2/2) + 2x] evaluated from 3 to 8

Now we substitute the upper and lower limits into the integral expression:

= [(4 * (8^3/3) - 3 * (8^2/2) + 2 * 8) - (4 * (3^3/3) - 3 * (3^2/2) + 2 * 3)]

Simplifying further:

= [(4 * 512/3) - (3 * 16/2) + 16 - (4 * 27/3) + (3 * 9/2) + 6]

= [(1706.67) - (24) + 16 - (36) + (13.5) + 6]

= 1683.17

Therefore, ∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx:

We integrate the function g(x) over the interval [3, 8].

∫[3, 8] (2x^3 - 5x + 1) dx

Using the power rule for integration:

= [(2 * (x^4/4)) - (5 * (x^2/2)) + x] evaluated from 3 to 8

Substituting the upper and lower limits:

= [(2 * (8^4/4)) - (5 * (8^2/2)) + 8 - (2 * (3^4/4)) + (5 * (3^2/2)) + 3]

Simplifying further:

= [(2 * 4096/4) - (5 * 64/2) + 8 - (2 * 81/4) + (5 * 9/2) + 3]

= [(2048) - (160) + 8 - (162/2) + (45/2) + 3]

= 1932.5

Therefore, ∫[3, 8] g(x) dx equals approximately 1932.5

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Answer:

28×4/7=16

Step-by-step explanation:

well it seems as the most logical answer but it also seems the realist one to pick for me personally but I would think it is better to see mixed opinions but I think it's the 2nd one