20 POIINNTSS FOR FAST ANSWERRRR
Find two numbers such that the sum of the first and three times the second is 5 and the sum of second and two times the first is 8.

To find the volume of the smallest cube-shaped box that can contain the pyramid, we need to first determine the length of the smallest edge of the box. Since the base of the pyramid is a square, the smallest edge of the box will be the diagonal of the square base of the pyramid.

Using the Pythagorean theorem, we find that the diagonal is:√(10² + 10²) = √200 = 10√2 inches Thus, the length of each edge of the smallest cube-shaped box that can contain the pyramid will be 10√2 inches. The volume of a cube is given by the formula

V = s³, where s is the length of one of its edges. Therefore, the volume of the box will be:(10√2)³ = 1000√8 cubic inches To simplify this expression, we can use the fact that √8 = √(4 · 2) = 2√2. Thus, the volume of the box is:1000√8 = 1000 · 2√2 = 2000√2 cubic inches Therefore, the volume of the smallest cube-shaped box that can contain Eric's pyramid is 2000√2 cubic inches, or approximately 2827.43 cubic inches to two decimal places.

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Answer:

see explanation

Step-by-step explanation:

Using the rules of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\(a^{m}\) ÷ \(a^{n}\) = \(a^{(m-n)}\)

(a)

\(4^{9}\) × 4³ = \(4^{(9+3)}\) = \(4^{12}\)

(b)

\(6^{5}\) × 6² = \(6^{(5+2)}\) = \(6^{7}\)

(c)

\(8^{6}\) ÷ 8 = \(8^{(6-1)}\) = \(8^{5}\)

(d)

\(7^{8}\) ÷ \(7^{6}\) = \(7^{(8-6)}\) = 7²

The rate of filling water in the tank is 23450t gallons per hour.

Let's assume that the time taken to fill the tank is t hours.

The volume of water filled into the tank at time t is given by the expression V(t) = 23450t.

The tank is originally empty, which means its volume = 0 gallons.

After 5 hours,

t= 5 hours

The volume of water filled in is given by \(V(5) = 23450 * 5= 1,17,250\) gallons of water.

Therefore, 1,17,250 gallons of water are filled in the tank after 5 hours.

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The graph of g(x) is obtained by vertically compressing and right-shifting the graph of f(x).

The graph of g(x) can be obtained by applying a vertical compression and a rightward shift to the graph of f(x). When we compress the graph of f(x) vertically, it means that the values of the y-coordinates of the points on the graph of f(x) are multiplied by a constant factor less than 1. This causes the graph to become narrower.

Additionally, when we shift the graph of f(x) to the right, we are moving all the points on the graph horizontally towards the positive x-axis by a specific amount. This shift changes the x-coordinates of the points while keeping their y-coordinates the same. By applying these transformations, we can obtain the graph of g(x) from the original graph of f(x) with the desired vertical compression and rightward shift.

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Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

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

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Answer:

60.96

Step-by-step explanation:

127 times 0.48

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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The sample space of flipping a coin twice consists of four outcomes: HH, HT, TH, and TT, representing the combinations of heads (H) and tails (T) in each flip.

The sample space of a coin flipped twice includes four possible outcomes. Each flip of the coin is assumed to be a fair coin toss and is referred to as an independent event. The four possible outcomes are listed below:

HH: This indicates that both coin flips resulted in heads.HT: This represents the coin toss resulting in heads on the first flip, and tails on the second.

TT: This means that both coin tosses resulted in tails. HT: This represents the coin toss resulting in tails on the first flip, and heads on the second.

The experiment of flipping a coin twice has the above-mentioned outcomes. As each toss is independent of the other, there are a total of four possible outcomes.

These four outcomes constitute the sample space of the experiment. In the above experiment, the coin has only two sides. It can either show heads or tails when flipped. Therefore, there are only four possible outcomes.

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Answer: False

Step-by-step explanation:

The financing section deals with only the transactions that have to do with equity and debt. The Investing section deals with capital expenditure such as fixed assets and investments in other company securities.

The $50,000 should therefore be recorded in the Investing section as a Cash outflow.

The $100,000 is not a cash transaction but will be recorded in the Notes to the Statement of Cashflows as a Non-Cash transaction for disclosure purposes.

Answer:

xnxnxnzznchamschdntjekdfurnthsjdnfjdjdjdkdkr

Step-by-step explanation:

xmxmxnxmxmxnxmxnxndmsndfhakxufmrjdkxddjrf7sjrifxisufkf8dhrkfdkshgshdbfjdddnfjfkdnfmcmcmdmdkfkfkkfdkfkfkfkfkfkfkfkkfkfkfkfkfkdkdkdmdkdkdkdkdmdmrmddmrm1520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126

Answer:

48 and 32

Step-by-step explanation:

both numbers get rounded by 8 going up and down rounding it to 40

Q6: Approximately 68.3% of the cherry tomatoes sold by Berkeley Bowl fall within the specified diameter limits of 20 mm to 32 mm.

Q7: To achieve half of the Six Sigma Quality, the standard deviation of the process should be approximately 0.22 mm for Berkeley Bowl's cherry tomatoes.

In Q6, we can use the concept of the normal distribution to determine the percentage of tomatoes within the specification limits. Since the average diameter is 26 mm and the standard deviation is 3 mm, we can assume a normal distribution and calculate the percentage of tomatoes within one standard deviation of the mean. This corresponds to approximately 68.3% of the tomatoes falling within the specified limits.

In Q7, achieving Six Sigma Quality means that the process has a very low defect rate. In this case, half of the Six Sigma Quality means reducing the variability in diameter to half the acceptable range.

The acceptable range is 32 mm - 20 mm = 12 mm. To achieve half the range, the standard deviation should be approximately half of 12 mm, which is 6 mm. Since the standard deviation is given as 3 mm, the process would need to be improved to reduce the standard deviation to approximately 0.22 mm for it to meet half of the Six Sigma Quality.

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Answer:

B.(-6,-1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

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Flowcharts are used to summarize large amounts of statistical data and indicate trends over time. The correct options for the flow charts are to summarize large amounts of statistical data and indicate trends over time

Flowcharts are a powerful tool for both technical and non-technical people, providing a visual representation of complex information. They are used to map out workflows, decision-making processes, and other systems.

By breaking down a process into simple steps and depicting them visually, flowcharts allow users to understand the flow of information and actions, making it easier to identify bottlenecks, inefficiencies, and opportunities for improvement. Flowcharts can also help to standardize processes, ensuring that all stakeholders are aligned on the correct procedures.

Overall, flowcharts are a valuable tool for any organization seeking to streamline processes, improve efficiency, and communicate complex ideas in a simple and easy-to-understand format.

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A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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The total number of combinations of the numbers 1 through 10, using only 5 integers, that can combine to add up to 15 is the product of the number of ways in which we can choose 5 integers out of 10 and the number of ways in which we can divide these 5 integers into 4 parts such that their sum is 15. This is equal to 252 × 21 = 5292. The total number of combinations is 5292.

We can use a combination formula which is given by C(n,r) = n! / (r! * (n-r)!).Here, n is the total number of integers available (10 in this case) and r is the number of integers we are choosing (5 in this case).So, we can choose any 5 integers out of 10 in C(10,5) ways which is equal to 252.
Then, we need to find the number of ways in which these 5 integers can combine to add up to 15. We can use a stars and bars method to do that.Let's assume that we have 5 stars representing the 5 integers we chose. Now, we need to divide these stars into 4 parts using 3 bars, such that the sum of stars on the left of the first bar, between the first and second bars, between the second and third bars, and on the right of the third bar, adds up to 15.Each bar divides the stars into two groups.
So, we can say that we are placing 3 identical objects (bars) in a row of 5 identical objects (stars). Using a combination formula, the number of ways in which we can place 3 identical objects in a row of 5 identical objects is C(5+3-1, 3-1) = C(7, 2) = 21.So, the total number of combinations of the numbers 1 through 10, using only 5 integers, that can combine to add up to 15 is the product of the number of ways in which we can choose 5 integers out of 10 and the number of ways in which we can divide these 5 integers into 4 parts such that their sum is 15.

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One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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The flux of the vector field F(x, y, z) = xzi + yz] + z³ k through the portion of the cylindrical surface x² + y² = 1 that is shown below, with inward orientation, is equal to 3π.

The solution to this problem is to use the divergence theorem. The divergence theorem states that the flux of a vector field F through a closed surface S is equal to the triple integral of the divergence of F over the region enclosed by S. In this case, the region enclosed by S is a cylinder with radius 1 and height 2. The divergence of F is equal to x² + y² + z³. Therefore, the flux of F through S is equal to:

```

∫_0^2π∫_0^1∫_0^2(x² + y² + z³)r dz dr dθ = 3π

```

The explanation of this result is as follows. The flux of a vector field through a surface is the amount of fluid flowing through the surface per unit time. In this case, the vector field F represents a fluid that is flowing in the positive z-direction. The cylinder S has an inward orientation, which means that the fluid is flowing out of the cylinder. The divergence theorem tells us that the flux of F through S is equal to the amount of fluid flowing out of the cylinder per unit time. The integral in the solution represents the amount of fluid flowing out of the cylinder per unit time. The integral is equal to 3π, which means that the flux of F through S is equal to 3π.

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The solution to the system of linear equation x, y are -6, 6

A system of linear equations is a collection of two or more linear equations that contain the same variables. Linear equations are equations of the form ax + by = c, where a, b, and c are constants and x and y are variables.

There are different methods to solve a system of linear equations, such as substitution, elimination, and graphing. Each method has its own advantages and limitations, and the choice of method depends on the form of the equations and the type of solution.

In this problem, we have two system of equations which are given as;

Combining both equations and solving via substitution method, the values of x and y are -6 and -6

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Using classical probability, we found that the chance of one minority candidate getting hired is 2/5.

What is meant by probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The degree to which something is likely to happen is basically what probability means.

Given,

  Number of total candidates = 5

Number of candidates from minority = 2

a) Probability that one of the minority candidates is hired

= number of favourable events/total events = 2/5

b) Classical probability is used.

   This is because since the candidates are selected by lottery, each candidate has an equal chance of getting selected. So the classical probability is used.

Therefore using classical probability, we found that the chances of one minority candidate getting hired is 2/5.

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60% of the seats on the train are empty

you have to divide 900 by 9 to get 100 because percents are out of 100, then you have to divide 540 by 9 also.

Answer:

60%

Step-by-step explanation:

Because there are 540 empty, and 900 total, you need to divide 540 by 900.

540/900=54/90=6/10=60/100

When you get 60/100, or 0.6, you know that it is 60 percent because percent is out of 100.

The integrating factor, \(u(t)\), for the given initial value problem is\(\(u(t) = e^{\int \frac{-7}{8(t+1)} dt}\).\)

To find the integrating factor, we start by computing the integral \(\(\int \frac{-7}{8(t+1)} dt\).\) The integral simplifies as follows:

\(\[\begin{aligned}\int \frac{-7}{8(t+1)} dt &= \frac{-7}{8} \int \frac{1}{t+1} dt \\&= \frac{-7}{8} \ln|t+1| + C,\end{aligned}\]\)

where \(C\) is the constant of integration. Therefore, the integrating factor \(u(t)\) is given by \(\(u(t) = e^{\frac{-7}{8} \ln|t+1| + C}\).\)

Next, we can simplify the expression for \(u(t)\) using logarithmic properties:

\(\[\begin{aligned}u(t) &= e^{\frac{-7}{8} \ln|t+1| + C} \\&= e^{\ln|t+1|^{-\frac{7}{8}} + C} \\&= e^C |t+1|^{-\frac{7}{8}} \\&= C_1 |t+1|^{-\frac{7}{8}}, \quad \text{where } C_1 = e^C.\end{aligned}\]\)

Now, we can proceed to find the solution \(y(t)\) by multiplying the given differential equation by the integrating factor:

\(\[C_1 |t+1|^{-\frac{7}{8}} \cdot 8(t+1) \frac{dy}{dt} - 7C_1 |t+1|^{-\frac{7}{8}} y = 7t.\]\)

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Given:

The total number of marbles are 26.

Red marbles=10

Black marbles=8

Green marbles=8

The two marbles are drawn randomly,

To find the probability that both marbles are green,

The probability that first marbles chosen is green,

Condition is given that the first is not returned before the second one is drawn.

Now the we have 7 green marbles and total marbles are 25.

Probability is given by,

The total probability of getting both green marbles without replacement is,

Answer: Probability is 0.08615.

The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.

To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:

1. Calculate the perimeter of the given rectangular field:

  Perimeter = 2 * (Length + Width)

            = 2 * (120 meters + 80 meters)

            = 2 * 200 meters

            = 400 meters

2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:

  Side length = Perimeter / 2

             = 400 meters / 2

             = 200 meters

3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.

4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:

  Width = Perimeter / 2 - Length

        = 400 meters / 2 - 200 meters

        = 200 meters - 200 meters

        = 0 meters

5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.

In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.

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The series solution corresponding to the indicial root Y=0 is given by Y(x) = x.

To solve the differential equation XY"-xy' + y = 0, we assume a series solution of the form Y(x) = Σᵢ aₙxⁿ.

Indicial Equation:

Substituting the series solution into the differential equation, we get XY" - xy' + y = Σᵢ aₙxⁿ(Xn(n-1) - nx + 1) = 0.

Equating the coefficients of like powers of x to zero, we obtain the indicial equation Xn(n-1) - nx + 1 = 0.

Indicial Roots:

The indicial equation is a quadratic equation. To find the roots, we solve for n using the quadratic formula:

n = (-(-1) ± √((-1)² - 4X(1)(X)))/(2X) = (1 ± √(1 - 4X²))/(2X).

The indicial roots are the values of n that satisfy the indicial equation. Since we are given the indicial root Y = 0, we substitute n = 0 into the indicial equation:

(0 - 0 + 1) = 0,

which is true. Hence, n = 0 is an indicial root.

Recurrence Relation:Since the indicial root is 0, we have one recurrence relation of the form: Cₖ₊₁(k + r + 1) - cₖz(k + r) = 0.

Solution Corresponding to Indicial Root:

To determine the series solution corresponding to the indicial root Y = 0, we substitute n = 0 into the assumed series solution:

Y(x) = Σᵢ aₙxⁿ = a₀.

Thus, the series solution corresponding to the indicial root Y = 0 is Y(x) = x.

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The equation of a circle in the xy-plane is found as (x + 2)² + (y - 1)² = 5.

A circle is a two-dimensional closed figure in which the set of all points with in plane is equidistant from the a given point known as the "centre."

Circle Formula: (x - h)² + (y - k)² = r² ;

Where, (h, k) is the centre & r is the radius of the circle.

Use the distance formula for(-2, 1) and (0,2)

\(\begin{aligned}&r=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} \\&r=\sqrt{(0+2)^2+\left(2-1\right)^2} \\&r=\sqrt{(2)^2+\left(1\right)^2}\end{aligned}\)

Further simplifying;

r = √(4 + 1)

r = √5

Centre (h, k) = (-2, 1)   Radius (r) = √5.

(x - h)² + (y - k)² = r²

(x + 2)² + (y - 1)² = √5²

(x + 2)² + (y - 1)² = 5 is the equation of the circle.

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Answer:

still 0.16

Step-by-step explanation:

cuz if u round to 1 d.p itll be 0.2 .

2 d.p theres nth after 6 so its gonna stay the same

The first three terms of the given sequence are -17, -27 and -37

A sequence is an ordered list of objects. Like a set, it contains elements. The number of ordered elements (possibly infinite) is called the length of the sequence.

Given that, an arithmetic sequence formula an = -10n - 7

We are asked to find the first three terms of this sequence.

Therefore,

Put n = 1 for first term,

a₁ = -10(1)-7

a₁ = -17

Put n = 2 for second term,

a₂ = -10(2)-7

a₂ = -27

Put n = 3 for third term,

a₃ = -10(3)-7

a₃ = -37

Hence, the first three terms are -17, -27 and -37

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Answer:

Step-by-step explanation:

from top down:

xᵃ⁻ᵇ

xᵃ⁺ᵇ

1

xᵃˣᵇ

1/xᵃ