What is the length of the DF? (Round to the tenths place)

There are a total of 4 + 3 + 2 + 1 = 10 marbles in the bag. The probability of picking a red marble is the number of red marbles divided by the total number of marbles:

Probability of picking a red marble = 4/10 = 2/5

Therefore, the probability Aisha picks a red marble is 2/5 or 0.4 when written as a decimal.

The heart will pumps 31,536 litres in 1 year and pumps 2,207,520 liters in 70 years.

There are 72 heartbeats in a minute.

If heart pumps 7 × 10⁻² litre per heartbeat,

then in 1 min,

7 × 10⁻² x 72 = 5.04 litres/minute

In one year (365 days), the heart pumps:

5.04 x 60 x 24 x 365 = 31,536 litres/year

Hence in 1 year, heart pumps 31,536 litres

In 70 years, the heart would pump:

31,536 x 70 years = 2,207,520 litres

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The coordinates of the points B' and C' are B' = (-1, 10) and C' = (-6, -5)

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

A = (-2, -4)

This point is translated to

A' = (-3, -1)

This means that the rule of transformation is

(x, y) = (x - 1, y + 3)

Given that

B = (0, 7) and C = (-5, -8)

When this transformation is applied on B and C, we have

B' = (0 - 1, 7 + 3) and C' = (-5 - 1, -8 + 3)

Evaluate

B' = (-1, 10) and C' = (-6, -5)

Hence. the coordinates of B' and C' are B' = (-1, 10) and C' = (-6, -5)

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To be 90% certain that the sample percentage is within 5.5 percentage points of the genuine population percentage, we need to survey at least 384 randomly chosen plane passengers.

To calculate the sample size required for the survey, we can use the formula:

[tex]n = \dfrac{(Z^2 \times p \times q)} { E^2}[/tex]

where:

Z = the z-score associated with the level of confidence (90% in this case), which is 1.645

p = the estimated proportion of passengers who prefer aisle seats (unknown)

q = 1 - p

E = the maximum allowable error (5.5 percentage points)

Since we don't know the proportion of passengers who prefer aisle seats, we can assume a conservative estimate of 50%. This means that p = 0.5 and q = 0.5.

Substituting these values into the formula, we get:

[tex]n = \dfrac{(1.645^2 \times 0.5 \times 0.5)} { (0.055^2) }= 383.8[/tex]

We need to round up to the nearest integer, so the minimum sample size required is:

n = 384

Therefore, we need to survey at least 384 randomly selected air passengers to be 90% confident that the sample percentage is within 5.5 percentage points of the true population percentage.

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The roots of the quadratic equation y = 5 · x²  + 2 · x + 7 are contained by x = - 1 / 5 ± i √34 / 5.

In this problem we must solve a quadratic equation, whose roots must be found. This can be done by using algebra properties, by completing the square. First, write the entire quadratic equation:

y = 5 · x²  + 2 · x + 7

Second, use algebra properties to find all roots:

y = 5 · [x² + (2 / 5) · x + 7 / 5]

y = 5 · [x² + (2 / 5) · x + 1 / 25] + 5 · (34 / 25)

y = 5 · (x + 1 / 5)² + 34 / 5

Third, use y = 0:

5 · (x + 1 / 5)² + 34 / 5 = 0

5 · (x + 1 / 5)² = - 34 / 5

(x + 1 / 5)² = - 34 / 25

x + 1 / 5 = ± √(- 34) / 5

x = - 1 / 5 ± √(- 34) / 5

x = - 1 / 5 ± i √34 / 5

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[tex]\blue{\boxed{\bold{\mathbb{SOLUTION}}}}[/tex]

[tex]\cos C=\dfrac{CE}{AC}\\=\dfrac{8}{\sqrt{8^2+3^2}}\\=\dfrac{8}{\sqrt{64+9}}\\=\dfrac{8}{\sqrt{73}}\\=\boxed{0,936}[/tex]

[tex]\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\boxed{\mathfrak{answered \: by: \: akbarsdtazm}}}}[/tex]

Answer:

19, 100, and 25

Step-by-step explanation:

Let's call the first number "x", the second number "y", and the third number "z". We know that:

x + y + z = 144   (the sum of three numbers is 144)

We also know that:

x = z - 6   (the first number is 6 less than the third)

y = 4z      (the second number is 4 times the third)

We can substitute the expressions for x and y into the first equation:

x + y + z = 144

(z - 6) + 4z + z = 144

Combining like terms, we get:

6z - 6 = 144

Adding 6 to both sides:

6z = 150

Dividing by 6:

z = 25

Now that we know z, we can use the other equations to find x and y:

x = z - 6 = 25 - 6 = 19

y = 4z = 4(25) = 100

So the three numbers are 19, 100, and 25.

Let first number be a

second number be b

Third number be c

As per the question The first number is 6 less than the third. The second number is 4 times the third.

First number, a = c - 6 ....(i)

second number, b = 4c ....(ii)

Also sum of the three numbers is 144.

a + b + c = 144

c - 6 + 4c + c = 144

c + 4c + c = 144 + 6

6c = 150

c = 150/6

c = 25

Put value of c in equation (i) & (ii)

in equation (i)

a = c - 6

a = 25 - 6

a = 19

in equation (ii)

b = 4c

b = 4 × 25

b = 100

Hence thee required numbers will be 19, 100 and 25.

Answer:

D

Step-by-step explanation:

First consider a part of the numerator 5 + 3y2. This can be verbally described as "the sum of 5 and 3 times the square of y".

Then, the entire expression in the numerator, (5 + 3y2)3, can be written as "the cube of the sum of 5 and 3 times the square of y".

Next, consider a part of the denominator (4y), which can be verbally described as "the product of 4 and y".

Then, the entire expression in the denominator, (4y)3, can be written as "the cube of the product of 4 and y".

Dividing the two expressions yields the complete expression shown below.

So, the given expression can be interpreted as "the cube of the sum of 5 and 3 times the square of y divided by the cube of the product of 4 and y".

The required, difference between the perimeters of the two rectangles is 46.03 in. None of the options is correct.

Since rectangles LMNP and WXYZ are similar, their corresponding sides are proportional. Let's denote the scale factor as k. Then:

k = XY / LM = 2.22 / 19

To find the value of k, we can divide 2.22 by 19:

k ≈ 0.117

The area of rectangle LMNP is given as 140.6 in^2. We can use this to find the length of NP:

LM * NP = area of LMNP

19 * NP = 140.6

NP ≈ 7.4 in

Since the sides of WXYZ are proportional to those of LMNP, we can find the length of YZ:

XY / YZ = LM / NP

2.22 / YZ = 19 / 7.4

YZ ≈ 1.167 in

Now we can calculate the perimeters of both rectangles:

Perimeter of LMNP = 2(LM + NP) = 2(19 + 7.4) = 52.8 in

Perimeter of WXYZ = 2(XY + YZ) = 2(2.22 +1.167) = 6.77in

The difference between the perimeters is:

52.8 - 6.77 = 46.03 in

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The perimeter of the regular nonagon will be; 840.7 units

The in-radius of the regular nonagon is given as:

Radius, r =17

The perimeter is then calculated by:

P = 18r/Tan(π/9)

Substitute 17 for r;

P = 18(17)/Tan(π/9)

Evaluate the product of 18 and 17;

P =  306/Tan(π/9)

Evaluate the quotient

P =  840.7

Hence, the perimeter of the regular nonagon = 840.7 units

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There are 4 cubes of size 1/4 foot would fill the inside of the prism.

We have to given that;

Height of cuboid = 3 feet

Length of cuboid = 3/4 feet

Width of cuboid = 1/2 feet

We know that;

Volume of cuboid = Length x width x height

Hence,

V = 3/4 x 3 x 1/2

V = 9/8

Thus, Number of 1/4-foot cubes which would fill the inside of the prism is,

= (9/8) ÷ (1/4)

= (9/8) x 4

= 9/2

= 4.5

Thus, There are 4 cubes of size 1/4 foot would fill the inside of the prism.

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Answer:

Step-by-step explanation:

You want the resultant force equivalent to the two forces ...

There are a number of ways the resultant force can be found. One of them is to add the components of the two forces. Another makes use of the law of cosines:

  r² = u² +v² -2uv·cos(θ)

where θ is the supplement of the angle between the two forces.

  r² = 100² +90² -2·100·90·cos(135°) ≈ 30827.922061

  r ≈ 175.579 ≈ 175.58

The resultant force is about 175.58 pounds.

The angle added to that of v can be found using the law of sines:

  sin(φ)/100 = sin(135°)/175.58

  φ = arcsin(sin(135°)·100/175.58) ≈ 23.749°

The angle East of North is then ...

  55° +23.7° = 78.7°

The direction of the resultant is N 78.7° E.

__

Additional comment

The angles used in the second attachment are bearing angles measured clockwise from north. The rectangular coordinates shown as the sum of the forces represent (north) + (east)i.

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If player gains 20 points If die shows "6" and loses 3 points if die does not show "6", then there will be a gain of 83 points, Option(c) is correct.

To find the expected total gain or loss for the player, we need to find the expected value of the points earned or lost on each roll of the die and then multiply that by "number-of-rolls".

Let X be the random-variable representing the points earned on a single roll of the die.

If "6" appears on die, then , X = 20,

If "6" does not appear on die, then X = -3,

The probability of getting "6" is = 1/6, and

The probability of not getting "6" is = 5/6.

So, the expected-value of X is : E(X) = (1/6) × 20 + (5/6) × (-3) = 0.83,

It means that, on average, the player can expect to earn about 0.83 points per roll of the die.

To find the expected total gain or loss for 100 rolls of the die, we multiply the expected value of X by 100;

⇒ E(total) = 100 × E(X) = 100 × 0.83 = 83,

The "Expected-Value" is positive, the player can expect to gain about 83 points over 100 rolls of the die.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

In a certain game, a fair die is rolled and a player gains 20 points if the die shows a "6." If the die does not show a "6," the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?

(a) A gain of about 1,700 points

(b) A gain of about 583 points

(c) A gain of about 83 points

(d) A loss of about 250 points

(e) A loss of about 300 points

For a company that charges $5.10 plus 5.747 cents per kilowatt-hour (kWh) for customers using up to 1300 kWh, and charges 5.788 cents per kilowatt-hour (kWh) for the extra kWh used after the first 1300 kWh, if more than 1300 kWh are used, the total charge for 1,300 kWh is $79.811.

The total charge is the product of the multiplication of the unit rate by the total kilowatt-hours used by the customer plus the fixed rate.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication involves the multiplicand, the multiplier, and the product.

Fixed charge = $5.10

Variable charge per kilowatt-hour = 5.747 cents ($0.05747)

Total usage  = 1,300 kWh

The total charge = $79.811 ($5.10 + $0.05747 x 1,300)

Thus, the total charge for 1,300 kWh for the nonextreme weather month is $79.811.

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The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

We have,

To convert kilometers (km) to meters (m), we need to multiply the distance by 1000.

a) 1.241 km = 1.241 × 1000 m = 1241 m

b) 6.002 km = 6.002 × 1000 m = 6002 m

c) 5.168 km = 5.168 × 1000 m = 5168 m

d) 3.4 km = 3.4 × 1000 m = 3400 m

e) 21.32 km = 21.32 × 1000 m = 21320 m

f) 0.895 km = 0.895 × 1000 m = 895 m

Therefore,

The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

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Based on its second derivative and given initial values, the function is equal to f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + 4.

In this problem we find the definition of the second derivative of a function, whose form must be dertermined by integration and the use of initial values. First, write the second derivative:

f''(x) = 2 · x + 6 · sin x

Second, determine the first derivative of the function:

f'(x) = x² - 6 · cos x + C

2 = 0² - 6 · cos 0 + C

2 = - 6 + C

C = 8

f'(x) = x² - 6 · cos x + 8

Third, determine the function:

f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + C

4 = (1 / 3) · 0³ - 6 · sin 0 + 8 · 0 + C

4 = C

C = 4

f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + 4

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4

add 2 and 2 together and you get 4.

Answer:

4

Step-by-step explanation:

2x2 is the same as 2+2, so 2+2 is 4.

The simplified expression for h(x) is h(x) =  4 log₂(x) - 4.

Given information:

f(x) = (log₂(x) + 2) and g(x) = (log₂(x³) - 6)

h(x) = f(x) + g(x) = (log₂(x) + 2) + (log₂(x³) - 6)

Using the rules of logarithms, we can simplify g(x) as follows:

g(x) = log₂(x³) - 6

= 3 log₂(x) - 6.

Now we can substitute this into the expression for h(x):

h(x) = (log₂(x) + 2) + 3 log₂(x) - 6

= 4 log₂(x) - 4

Therefore, the simplified expression for h(x) is h(x) =  4 log₂(x) - 4.

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$15,556.84

Paulanwill have approx $15,556.84 if she investb$5k that earns 4.10% apr compound quarterly..

Answer:

I’m pretty sure it’s $11,780.60

Step-by-step explanation:

We can use the formula for compound interest to determine how much money Paula will have in 25 years:

A = P(1 + r/n)^(nt)where:A = the total amount of money after t years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have:

P = $5,000

r = 4.10% = 0.041 (as a decimal)

n = 4 (compounded quarterly)

t = 25 years

Plugging these values into the formula, we get:

A = $5,000(1 + 0.041/4)^(4*25)

A = $5,000(1 + 0.01025)^100

A = $5,000(1.01025)^100

A = $5,000(2.356)

A = $11,780.60

Therefore, Paula will have approximately $11,780.60 in her account after 25 years.

Answer:

2 yards

Step-by-step explanation:

2 yards equals 6 feet because 2x3=6 or 72 inches because 6x12 equals 72. 1 yard is equal to 3 feet.

Answer:

$79,618

Step-by-step explanation:

7 years x 3% = 21%

$65,800 x 21% = $13,818

$65,800 + $13, 818 = $79,618

The probability that a viewer will turn to channel 8 during Jimmy's performance is 2.67%.

The show is 30 minutes long, which is equivalent to 1800 seconds. Jimmy's performance starts at 6:06 pm, which is 366 seconds into the show, and ends at 6:14 pm, which is 414 seconds into the show. Therefore, Jimmy's performance lasts for 48 seconds.

The probability of a viewer turning to channel 8 during Jimmy's performance can be calculated by dividing the length of Jimmy's performance by the length of the entire show:

P = (length of Jimmy's performance) / (length of entire show) = 48 / 1800 = 0.0267

Multiplying by 100 gives the probability as a percentage: 2.67%

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The formula to calculate the monthly payment needed to achieve a future value in an annuity is:

PMT = FV * (r / 12) / [(1 + r / 12)^(n * 12) - 1]

where PMT is the monthly payment, FV is the future value, r is the annual interest rate (as a decimal), and n is the number of years.

In this case, FV = $1,500,000, r = 0.06, and n = 30. Plugging these values into the formula, we get:

PMT = $1,500,000 * (0.06 / 12) / [(1 + 0.06 / 12)^(30 * 12) - 1]

PMT = $1,500,000 * 0.005 / [1.06^(360) - 1]

PMT = $1,500,000 * 0.005 / 5.743

PMT = $1,244.23 (rounded to the nearest cent)

Therefore, the amount that needs to be deposited each month to achieve a future value of $1,500,000 in 30 years is $1,244.23.

Answer:

the guys above me is correct

Step-by-step explanation:

because i did it and the answer was correct for me

A) The total cost for 45khw of electricity is 27.50c.

B) The total cost for 60khw of electricity is 76.70c.

C) Total cost for 100khw of electricity is 76.70c.

To calculate the cost of electricity for different amounts of kWh, we need to use the sliding scale tariffs provided by the local municipality. Here are the calculations for the given scenarios:

A. For 45 kWh of electricity:

The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c

There is no electricity used beyond the first 50 kWh, so the total cost is 27.50c.

B. For 60 kWh of electricity:

The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c

The next 10 kWh cost 0.82c per kWh, so the cost is 10 x 0.82 = 8.20c

The total cost is 27.50c + 8.20c = 35.70c.

C. For 100 kWh of electricity:

The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c

The next 60 kWh cost 0.82c per kWh, so the cost is 60 x 0.82 = 49.20c

The remaining 40 kWh are not covered by the sliding scale tariff and their cost is unknown.

The total cost is 27.50c + 49.20c = 76.70c.

In summary, the cost of electricity varies depending on the amount of kWh used, and we need to use the sliding scale tariffs to calculate it correctly.

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The difference in the students who chose peach pie and apple pie is 46

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

From the above, we have the percentage difference to be

Difference = 38% - 15%

When the given values are substituted, we have

Difference = 23%

This means that

Students = 23% * 200

Evaluate

Students = 46

Hence, the number of students is 46

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The study conducted on wild Jackalopes population shows a sample mean weight of 69.9 pounds, with a test statistic of  -1.327 and a p-value of  0.190. Therefore, at a significance level of 0.01, the null hypothesis can be rejected, indicating that the population mean weight is different from 65 pounds. This suggests the population health is in danger, and grants may be needed to re-establish their wild populations.

Pt1

Null Hypothesis The population mean of wild Jackalopes is equal to 69.9 lbs.

Alternative Hypothesis The population mean of wild Jackalopes is not equal to 69.9 lbs.

Test Statistic t = (X - μ) / (s / √n), where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Using a calculator or statistical software, we find that the test statistic is t = -1.327 and the p-value is 0.190.

At the 0.01 significance level, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population mean of wild Jackalopes is different from 69.9 lbs.

Pt2

To show that the population is actually in danger, we could change the null hypothesis to reflect a lower population mean weight. For example:

Null Hypothesis The population mean of wild Jackalopes is equal to 65 lbs.

Alternative Hypothesis The population mean of wild Jackalopes is greater than 65 lbs.

Using the same formula for the test statistic, we find that the test statistic is t = -5.457 and the p-value is 2.29 x 10⁻⁷, which is much smaller than the significance level of 0.01.

At the 0.01 significance level, we reject the null hypothesis. There is strong evidence to conclude that the population mean weight of wild Jackalopes is greater than 65 lbs. This suggests that the health of the population is in danger and that grants to help reestablish wild populations should be pursued.

Our report to the US Fish and Wildlife Service should reflect these findings and suggest taking action to support the health and survival of wild Jackalopes.

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The factorised forms of the Polynomials using difference of squares are;

a). (x - 6) (x + 6)

b). 3 (x - 2) (x + 2).

The factorised forms of the polynomials using the trinomial method are;

a). (x + 3)²

b). 4 (x -5) (x + 3)

Recall that from the difference of squares concept;

a² - b² = (a - b) (a + b) where a² and b² are perfect squares.

Therefore, if we have; x² - 36; we have; x² - 6²

x² - 36 = (x-6) (x + 6).

For, 3x² - 12; = 3 (x² - 4)

= 3 (x -2) (x + 2).

For the trinomials;

x² + 6x + 9;. x² + 3x + 3x + 9

= (x + 3) (x + 3) = (x+3)².

Also, for 4x² - 8x - 60; we have

4 (x² - 2x - 15)

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

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