Question 10
Solve for b.

b³ = 8

Enter your answer in the box.

Answer:

34ft

Step-by-step explanation:

Area1=5*2=10ft

Area2=4*6=24ft

Total Area=Area1+Area2=24+10=34ft

The equation of the ellipse is (x - 6)² / 4 + (y - 1)² / (16/9) = 1, the center is (6,1), and the directrices are x = 0 and x = 12.

The center of the ellipse is the midpoint of the major axis. The midpoint of the line segment connecting (4,1) and (8,1) is ((4+8)/2, (1+1)/2) = (6,1). Therefore, the center of the ellipse is (6,1).

The distance between the center and one of the vertices (say, (8,1)) is the length of the semi-major axis, a. This distance is (8-6) = 2. Therefore, the semi-major axis is a = 2.

The eccentricity, e, is given as 1/3.

The distance between the center and one of the foci, c, is related to the semi-major axis and eccentricity by the equation c = ae. Plugging in the values we know, we get c = (1/3)(2) = 2/3.

We can write the equation of the ellipse in standard form:

(x - 6)² / 2² + (y - 1)^2 / b² = 1

where b is the semi-minor axis. We can solve for b using the relationship between the semi-major axis, semi-minor axis, and eccentricity:

So the equation of the ellipse is:

(x - 6)² / 4 + (y - 1)² / (16/9) = 1

The directrices are located a distance of a² / c = (2²) / (2/3) = 6 units away from the center along the major axis. These are the lines x = 6 - 6 = 0 and x = 6 + 6 = 12.

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Answer:

[tex]{ \tt{2x + 3y = 27x}} \\ { \tt{27x - 2x = 3y}} \\ { \tt{25x = 3y}} \\ \\ { \tt{x = \frac{3}{25}y }}[/tex]

Answer: To satisfy the given condition, we need to place the numbers in the boxes in a way that the sum of any three adjacent boxes is divisible by 3.

We can divide the boxes into three groups as follows:

Group 1: Boxes {1, 4, 7}

Group 2: Boxes {2, 5, 8}

Group 3: Boxes {3, 6, 9}

For any three boxes in a group, the sum of their contents must be divisible by 3. We can place any multiple of 3 in the middle box of each group, and the other two boxes will have to be filled accordingly.

Step-by-step explanation:

For Group 1:

If we place 3 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 1.

If we place 6 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 5}, {1, 8}, {4, 5}, {4, 8}, {7, 5}, {7, 8}. This gives us another 6 possible ways to fill the boxes in Group 1.

For Group 2:

If we place 3 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 2.

If we place 6 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 8}, {1, 5}, {4, 8}, {4, 5}, {7, 8}, {7, 5}. This gives us another 6 possible ways to fill the boxes in Group 2.

For Group 3:

If we place 3 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 9}, {2, 6}, {5, 9}, {5, 6}, {8, 9}, {8, 6}. This gives us 6 possible ways to fill the boxes in Group 3.

If we place 6 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 6}, {2, 3}, {5, 6}, {5, 3}, {8, 6}, {8, 3}. This gives us another 6 possible ways to fill the boxes in Group 3.

Therefore, the total number of ways to fill the boxes is:

6 x 6 x 6 x 6 = 1296.

Thus Bian can write the integers 1 to 9 in these ways.

hope it helps...

Answer:

450

Step-by-step explanation:

270/3=90, 90*5=450

Scott's age is 11x

Georgia's age is 6x = 4y

therefore y=1.5x

Fiona's age is 7x

Oscar's age is 3y

therefore 3(1.5x)=4.5x

Fiona's age: Oscar's age

7x : 4.5x

7 : 4.5

Carlo should consider the sample size, sampling method, response rate, and sampling frame when determining which survey result is likely to be more accurate. By investigating these factors, Carlo can make an informed decision as to which survey result is likely to be more accurate.

Sample size is the number of participants or observations in a given study or experiment. It is an important factor in determining the validity and accuracy of the results. Large sample sizes are typically needed for experiments that involve multiple variables and for research with a small population. Sample size also affects the power of a test, which is the probability of correctly rejecting the null hypothesis.

In order to determine which survey result is more accurate, Carlo should first consider the sample size of each survey. If the sample size of one survey is significantly larger than the other, it is likely to be more accurate. Additionally, Carlo should consider the sampling method used in each survey. If one survey used a random sampling method while the other was not, then the random sample is more likely to be more representative of the entire population of players in the soccer league. Carlo should also consider the response rate for each survey, as surveys with higher response rates tend to be more accurate. Finally, Carlo should investigate the sampling frame used in each survey. If one survey used a sampling frame that was more representative of the population than the other, then it is likely to be more accurate.

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The Area of Composite figure is 131cm² we can find it by dividing the figure in two parts.

Rectangle is a plane which one side is long and other side is short and and all angle between these sides are 90° and opposite sides are parallel to each other.

We can divide this figure in two part Rectangle and Triangle.

The Rectangle having length = 10 cm and breadth = 5 cm.

Whereas, Triangle have sides having length 6cm (Base) and 3 cm (Perpendicular).

[tex]Area\ of\ Rectangle = Length (l) * Breadth (b)[/tex]

= 10 x 5 cm²

= 50 cm².

[tex]Area\ of\ Triangle =\frac{1}{2} *b*h[/tex]

For this we have to find third side,

[tex]Third\ Side = \sqrt{(First\ Side)^{2} +(Second\ Side)^{2} }[/tex] ( Using Pythagoras Theorem)

[tex]Third\ Side = \sqrt{(6)^{2} +(3)^{2} }[/tex]

Third Side = 6.7 cm

[tex]s= \frac{a + b + c}{2}[/tex] , where a, b, c are three sides

[tex]= \frac{6.7 + 6 +3}{2}[/tex]

= 7.85 cm.

Now we use Heron's formula to find the area of triangle,

Area of Triangle = [tex]\sqrt{s\ (s-a)\ (s-b)(\ s-c)}[/tex][tex]=\sqrt{7.85\ (7.85-6.7)\ (7.85-6)\ (7.86-3)}[/tex]

= 81 cm²

So the Area of Composite figure = (50 + 81) cm²

= 131 cm²

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Answer:

Because in the left-hand case the incoming ray is perpendicular to the surface so it is not refracted.

Step-by-step explanation:

Short answer: Because in the left-hand case the incoming ray is perpendicular to the surface so it is not refracted. In other words the angle of incidence is zero in contrast to the right-hand case.

Answer:

See graph

Step-by-step explanation:

The transformation is as follows

The transformation of h(x) to -h(x) - 4 is a combination of two transformations

1. A reflection around the x -axis. Every point(x, y) in h(x) becomes (x', y') where x' = x and y' = -y so (x, y) → (x, -y)

2. A translation of each reflected point 4 units down; x value does not change but y values are shifted down so the new y is y'-4 = -y -4

The result of both transformations is:
every coordinate (x, y) in h(x) will be transformed to (x, -y -4)

Seeing as the graph consists of two straight lines meeting at the origin, all we need to do is take any 3 points in h(x), find the transformed coordinates and connect them with straight ilnes

h(x0              -h(X) - 4

(-2, 4)    ⇒      (-2, -4-4) = (-2, -8)

(0, 0 )   ⇒       (0, -0 - 4) = (0, -4)

(4, 2)    ⇒       (4, -2 -4)   = (4, -6)

take these three points and plot

The total cost of buying a postal order of N15 would be N15.50.

To calculate the cost of buying a postal order of N365, we need to determine the commission associated with the value of N365 in the postal order table.

Since N365 is between N100 and N50, the commission for this amount would be N5.50.

Therefore, the total cost of buying a postal order of N365 would be N365 + N5.50 = N370.50.

To find the cost of buying a postal order of N15, we look at the postal order table and find that the commission associated with N15 is 50k.

Therefore, the total cost of buying a postal order of N15 would be N15 + 50k = N15.50.

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The answer to this question is 4 Gallons and 1 quart or we can say 17 quarts.

The US Customary System defines a unit of liquid volume or capacity as 4 quarts (3.79 liters).

we have to find the value of 10 gallons and 11 quarts in gallons and quarters after dividing by 3.

As we know,

1 gallon = 4 quarts

10 gallons = [tex]10 * 4[/tex]=40 quarts

so 40 quarts + 11 quarts= 51quarts

It must be divided by 3 (According to the question we have to divide by 3 )

So, it becomes,

[tex]\frac{51}{3} =17[/tex]

Now we get 17 quarts.

And 17 quarts= 4 gallons and 1 quarts

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The time to reach 125 feet is 1.3 seconds, the time to reach a maximum height of 147.52 ft is 2.5 seconds

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

h(t) = -16t^2 + 79t + 50

To do this, we set h(t) = 125

So, we have

-16t^2 + 79t + 50 = 125

Using a graphing tool, we have

t = 1.3

So, the time taken is 1.3 seconds

We have

h(t) = -16t^2 + 79t + 50

Differentiate and set to 0

-32t + 79 = 0

So, we have

32t = 79

This gives

t = 2.46875

t = 2.5

Next, we have

h(2.46875) = -16 * 2.46875^2 + 79 * 2.46875 + 50

Evaluate

h(2.46875) = 147.52

Hence, the maximum height is 147.52 ft

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Answer:

Midpoint of AB is (-2,-2)

Step-by-step explanation:

thats the answer

When a is equal to -2, the ordered pair is an equational solution.

The places where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation is the solution set of the system of linear equations.

y=3x+7

Ordered pair (-3,a)

introducing x=-3 as a value in the equation

y=3(-3)+7

y=-9+7

y=-2

Hence,value of a is -2 that makes the ordered pair a solution of the equation.

y=3x+7 represents the equation of a straight line. So, it can satisfy infinite ordered pair.

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122 degrees Fahrenheit is equal to 50 degrees Celsius.

Fahrenheit is a temperature scale where water freezes at 32 degrees and boils at 212 degrees under standard atmospheric pressure.

It is primarily used in the United States, the Bahamas, Belize, and the Cayman Islands.

For example, a typical comfortable room temperature of 72 degrees Fahrenheit would be 22.2 degrees Celsius on the Celsius scale.

Using the formula F = (9/5 x C) + 32, we can find the temperature in Fahrenheit when the temperature is 50 degrees Celsius.

F = (9/5 x C) + 32

F = (9/5 x 50) + 32

F = (90) + 32

F = 122

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Telling Marvin the number 18 should get us into the museum.

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is the inverse of multiplication, and is used to find out how many times one number is contained within another number.

To get into Marvin's Magic Museum, we need to figure out which number Marvin likes based on the given information.

Marvin likes the number 14, but not 15. This suggests that he likes even numbers, since 14 is even and 15 is odd.

Marvin likes the number 21, but not 26. This suggests that he likes numbers that are divisible by 3, since 21 is divisible by 3 and 26 is not.

Marvin likes the number 35, but not 39. This suggests that he likes numbers that are not divisible by 4, since 35 is not divisible by 4 and 39 is.

Putting these clues together, we can see that the number Marvin likes must be even, divisible by 3, and not divisible by 4. The only number in the list that meets these criteria is 18, since it is even, divisible by 3 (6 times), and not divisible by 4.

Therefore, telling Marvin the number 18 should get us into the museum.

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Answer:321.125 and i think the R that you are trying to say stands for remainder

Step-by-step explanation:

The height of the rock is described by the quadratic equation:

h = -16t² + 79t + 50.

a. The rock will be 125 feet above the beach for approximately 3.66 and 1.28 seconds.

b. The rock will reach its maximum height in about 2.5 seconds, reaching a height of around 147.5 feet.

An equation of the form f(x) = ax² + bx + c, where a 0 and a, b, and c are numbers, is a quadratic equation.

a. The following is how the rocket's height function is presented:

h(t) = -16·t² + 79·t + 50

The time at which the height is 125 feet is as follows:

h(t) = 125 feet

h(t) = 125 = -16·t² + 79·t + 50

-16·t² + 79·t + 50 - 125 = 125 - 125 = 0

-16·t² + 79·t - 75 = 0

The quadratic formula indicates:

t = (-79 ± √(79² - 4 × (-16) ×(-75)))/(2 × (-16)) = (79 ± √(1441))/32

t = (79 ± √(1441))/32

t = (79 + √(1441))/32 ≈ 3.66

t = (79 - √(1441))/32 ≈ 1.28

Therefore, the times at which the height of the rock is 125 feet above the beach are t ≈ 3.66 seconds, and t ≈ 1.28 seconds.

b.The formula for determining the input value at the maximum value of a quadratic function, which is: at the maximum height, x = -b/2a, can be used to determine the time at which the rock is at the maximum height.

Consequently, we obtain at the highest height;

t = -79/(2 (-16)) = 2.46875 is the time.

The rock climbs to its highest point in 2.46875 seconds, or 2.5 seconds.

Hence, h (2.46875) = -162.46875² + 792.46875 + 50 = 147.515625 147.5 is the maximum height.

The rock can rise up to a height of approximately 147.5 feet.

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The complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C is [tex]\frac{-4\pi i}{a}[/tex] if a < 1, and 0 if a > 1.

From the question, we are to evaluate the given complex integral when a <1 and a > 1

We can evaluate the complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C using the residue theorem. Since the function has a pole of order 2 at z = a, we need to compute the residue of the function at that point.

If a < 1, then the point a is inside the unit circle C. To compute the residue at z = a, we can expand the function in a Laurent series centered at z = a:

[tex]\frac{zdz}{(z-a)^2}= (\frac{1}{(z-a)})^2 d(z-a)[/tex]

= (1/(z-a))^2 dz - (2/(z-a))^1 da + ...

[tex](\frac{1}{(z-a)})^2dz -(\frac{2}{(z-a)})^1 da + ...[/tex] (Laurent series expansion)

The residue of the function at z = a is given by the coefficient of the [tex](z-a)^{-1}[/tex] term in this expansion, which is:

[tex]Res[z=z0] \frac{z dz}{(z-a)^2} = \frac{-2}{(a - 0)^1} = \frac{-2}{a}[/tex]

Therefore, by the residue theorem, the value of the integral is given by:

[tex]\oint \frac{c zdz}{(z-a)^2} = 2\pi i \times \frac{-2}{a} = \frac{-4\pi i}{a}[/tex]

If a > 1, then the point a is outside the unit circle C. Since the function is holomorphic on and inside the unit circle, it has no singularities inside C and the integral is zero:

[tex]\oint \frac{c zdz}{(z-a)^2} = 0[/tex]

Hence, the complex integral is [tex]\frac{-4\pi i}{a}[/tex] when a < 1, and 0 if a > 1.

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Answer:

terms:  'k' and '-3d'

coefficient of 'k' is 1

coefficient of '-3d' is -3

Step-by-step explanation:

if a variable exists by itself then its coefficient is 1, otherwise

whatever value precedes a variable is its coefficient

Answer: 1945

Step-by-step explanation:

Answer:

Harriet Tubman was born in 1820.

Step-by-step explanation:

Showing how brave and resourceful she was in running such a dangerous operation. A black woman operating in slave territory could be highly noticeable. It is a testament to her courage, brains, and fortitude that she was successful. Also, kudos to the many white persons who manned the stations along the Underground Railroad who coordinated with her.

Her impact on America—demonstrating an individual with struggle can accomplish much and correct wrongful structures in our land.

If we assume that your mass is m kilograms, then you would need to eat 80 times your mass in food each day. Therefore, you would eat:

80m kilograms of food per day

To find how much you would eat in a month, we need to multiply the amount of food you eat in a day by the number of days in a month. We'll assume a month has 30 days.

Number of kilograms of food eaten per month = Number of kilograms of food eaten per day x Number of days in a month

= 80m x 30

= 2400m

Therefore, you would eat 80m kilograms of food per day and 2400m kilograms of food per month.

52 applicants apply, 30 employees will be hired and at least 30 of them will pass the background test.

To determine how many applicants need to apply to meet the hiring target, we need to work backwards from the desired number of hires.

Let X be the total number of applicants needed to hire 30 new employees.

Out of all applicants, 10% do not meet the base business requirements. Therefore, the number of applicants who do meet the base business requirements is:

[tex]$0.9X$[/tex]

Out of these applicants who meet the base business requirements, 12% do not pass the pre-screening assessment. Therefore, the number of applicants who pass the pre-screening assessment is:

[tex]$0.88(0.9X) = 0.792X$[/tex]

Out of these applicants who pass the pre-screening assessment, 23% do not show up for the interview. Therefore, the number of applicants who show up for the interview is:

[tex]$0.77(0.792X) = 0.6108X$[/tex]

Out of these applicants who show up for the interview, 5% fail the background test. Therefore, the number of applicants who pass the background test is:

[tex]$0.95(0.6108X) = 0.58026X$[/tex]

Since we need to hire 30 new employees, we can set this equal to 30 and solve for X:

[tex]$0.58026X = 30$[/tex]

[tex]$X \approx 51.74$[/tex]

Therefore, Company B needs approximately 52 applicants to apply to meet their hiring target.

To meet the hiring target, Company B will need to ensure that at least 30 employees pass the background test. From the above calculations, we know that 0.58026X applicants pass the background test. Therefore, we can solve for X:

[tex]$0.58026X = 30$[/tex]

[tex]$X \approx 51.74$[/tex]

This means that if 52 applicants apply, 30 employees will be hired and at least 30 of them will pass the background test.

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The symbolic quantified statement is given as:

For all real integers x and y, if x³ = y³, then x = y.

Using quantifiers, this can be written as:

∀x,y∈ℝ, (x³ = y³) → (x = y)

The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.

The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.

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240 full glasses of juice can be poured from the large can of juice.

Calculating the volume of the large can of juice and the volume of the tiny glass is necessary to answer this problem. The volume of the can must then be divided by the volume of the glass to determine how many glasses can be filled.

The formula V = r2h, where r is the radius and h is the height, determines the volume of a cylinder.

The radius for the large juice can is equal to half the diameter, or r = 6 inches. It is 15 inches tall. Hence, the huge can's volume is as follows:

V large is equal to (1620)(6)2(15) cubic inches.

The radius for the little glass is equal to half its diameter, or 1.5 inches. It is 3 inches tall. Hence, the little glass's volume is as follows:

V small is equal to 1.5 x 2 x 3 or 6.75 cubic inches.

We divide the volume of the large can by the volume of the tiny glass to determine how many glasses can be filled:

V large/V small is equal to (1620)/(6.75), or 240.

As a result, the enormous can of juice can be used to fill 240 glasses to the brim.

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The area that was used for planting peas is given as follows:

2.6675 feet².

The area that was used for planting peas is obtained applying the proportions in the context of the problem.

The total area of the garden is given as follows:

10 and (2/3) feet².

Hence the decimal representation of the area is given as follows:

10 + (2/3) = 10.67 feet².

(conversion from mixed number to decimal).

The area that was used for planting is one fourth of the total area of the garden, hence it is given as follows:

1/4 x 10.67 = 2.6675 feet².

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Answer:

Ivanna takes 9.6 minutes per mile.

To find out, you can divide the total time by the total distance:

time per mile = total time ÷ total distance

time per mile = 96 minutes ÷ 10 miles

time per mile = 9.6 minutes/mile

Step-by-step explanation:

In response to the query, we can state that As a result, $1,154.74 is the interest response to the original query.

To calculate simple interest, divide the principal by the interest rate, the duration, and other variables. The marketing formula is simple return = capital + interest + hours. The easiest way to compute interest is with this method. The most common method for calculating interest is as a percentage of the principal amount. For instance, if he borrows $100 from a buddy and promises to pay it back at 5% interest, he will only pay his portion of the 100% interest. $100 (0.05) = $5. Interest must be paid when you borrow money and must be added to any loans you make. The annual percentage of the loan amount is frequently used to calculate interest. This percentage represents the loan's interest rate.

Now we can apply the following calculation to figure out how much a mortgage will cost each month:

(P x I / (1 -)

[tex]$1,575 = ($150,000 x 0.003875) / (1 - (1 + 0.003875)^(-360))[/tex]

After calculating the unknown variable, we obtain:

[tex]1 - (1 + 0.003875)^(-360) = ($150,000 x 0.003875) / $1,575\s(1 + 0.003875)^(-360) = 0.9900162785\s1 + 0.003875 = (0.9900162785)^(-1/360)[/tex]

0.003162 is the monthly interest rate.

In the second month, the following principle was paid:

Principal payment is $1,575 less $576.61 to equal $998.39.

Hence, at the end of the second month, the total interest paid is:

Total interest paid equals the sum of the first month's interest and the second month's interest.

Total interest paid equals $1,154.74 ($578.13 + $576.61).

As a result, $1,154.74 is the response to the original query.

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