x²+2xy+y²=144, (x+y)³?​

If the sand falls at a rate of 16 cubic millimeters per second, a player would have approximately 6.25 seconds for their turn.

The rate of sand falling from the hourglass is given as 16 cubic millimeters per second. We need to find out the time available for a turn. Let's assume that the hourglass is filled with 'x' cubic millimeters of sand.

We can use the formula:

Volume = Rate x Time

Here, the volume of sand is 'x' cubic millimeters, the rate is 16 cubic millimeters per second, and we need to find the time available for a turn, which we can represent as 't' seconds.

So,

x = 16t

We can rearrange this equation to find 't':

t = x/16

This means that the time available for a turn is equal to the volume of sand in the hourglass divided by the rate at which the sand falls.

We don't know the exact volume of sand in the hourglass, but let's assume it's 100 cubic millimeters.

Then,

t = 100/16

t = 6.25 seconds

So, in this case, a player would have approximately 6.25 seconds for their turn before all of the sand falls to the bottom of the hourglass.

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Answer:

-9x-2

Step-by-step explanation:

-7-3x+5-6x

=(-3x-6x) + (-7+5)

=(-9x)+(-2)

= -9x - 2

First, use the associative property of addition to reorder the terms in parentheses. Then, combine like terms and you will get your simplified answer of -9x - 2. Hope this helps!

The test statistic for this test is -0.213.

To test the hypothesis that two populations have the same mean, we can use a two-sample t-test. The test statistic for this test is calculated by taking the difference between the sample means and dividing it by the standard error of the difference.

In this case, the sample averages are 6 and 7, and the standard deviations for the two samples are 16 and 15, respectively. Both samples have 32 observations.

To calculate the test statistic, we first need to calculate the standard error of the difference. This is given by:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

where s1 and s2 are the standard deviations for the two samples, and n1 and n2 are the sample sizes. Plugging in the values we have, we get:

SE = sqrt[(16^2/32) + (15^2/32)]
  = 4.698

Next, we calculate the t-statistic:

t = (x1 - x2) / SE

where x1 and x2 are the sample means. Plugging in the values we have, we get:

t = (6 - 7) / 4.698
 = -0.213

The test statistic for this test is -0.213.

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Answer:

x = 5

y = 3

Step-by-step explanation:

x + 4y = 17

2x + 5y = 25

We multiply the first equation by -2

-2x - 8y = -34

2x + 5y = 25

-3y = -9

y = 3

Now we put 3 in for y and solve for x

x + 4(3) = 17

x + 12 = 17

x = 5

Let's Check the answer

5 + 4(3) = 17

5 + 12 = 17

17 = 17

So, x = 17 and y = 3 is the correct answer.

Answer:

B. Triangles are similar by SAS

Step-by-step explanation:

3.8/2=1.9

4.6/2=2.3

therefore they are similar

Answer:b

Step-by-step explanation:

Answer:

12 and -9

Step-by-step explanation:

12 x -9 = -108

12 + -9 = 3

The expected number of tosses until either a head comes up or four tails are obtained is 7/4

Let X be the random variable representing the number of tosses until either a head comes up or four tails are obtained.

Let's consider the first toss. There are two possible outcomes: heads or tails. If a head comes up on the first toss, then we stop and X = 1. If a tail comes up, we need to continue tossing until we get four tails in a row or a head.

Let Y be the random variable representing the number of additional tosses needed if the first toss is a tail. There are two possible outcomes for the second toss: heads or tails. If a head comes up, we stop and X = 2. If a tail comes up, we need to continue tossing until we get three tails in a row or a head.

Similarly, we can define Z as the random variable representing the number of additional tosses needed if the first two tosses are tails. There are two possible outcomes for the third toss: heads or tails. If a head comes up, we stop and X = 3. If a tail comes up, we need to continue tossing until we get two tails in a row or a head.

Finally, let W be the random variable representing the number of additional tosses needed if the first three tosses are tails. There are two possible outcomes for the fourth toss: heads or tails. If a head comes up, we stop and X = 4. If a tail comes up, we need to continue tossing until we get four tails in a row.

We can write X in terms of Y, Z, and W as follows

X = 1 + Y if the first toss is heads

X = 1 + 1 + Z if the first two tosses are tails and the third toss is heads

X = 1 + 1 + 1 + W if the first three tosses are tails and the fourth toss is heads

X = 1 + 1 + 1 + 1 if the first four tosses are tails

Now, we need to compute the expected values of Y, Z, and W.

If the first toss is a tail, the probability of getting another tail on the second toss is 1/2, and the probability of getting a head is also 1/2. Therefore,

E[Y] = 1/2(1) + 1/2(1 + Z)

If the first two tosses are tails, the probability of getting another tail on the third toss is 1/2, and the probability of getting a head is also 1/2. Therefore,

E[Z] = 1/2(1) + 1/2(1 + W)

If the first three tosses are tails, the probability of getting another tail on the fourth toss is 1/2, and the probability of getting a head is also 1/2. Therefore,

E[W] = 1/2(1) + 1/2(4)

Note that the expected value of W is 2, not 3, because if we get three tails in a row, we stop and X = 4.

Putting it all together, we have:

E[X] = 1/2(1) + 1/2(1 + E[Z])

= 1/2(1) + 1/2(1 + 1/2(1) + 1/2(1 + E[W]))

= 1/2(1) + 1/2(1 + 1/2(1) + 1/2(1 + 2))

= 7/4

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Answer:

$45

Step-by-step explanation:

Answer:

Subtraction property of equality

Step-by-step explanation:I took the test

Answer:

are u sure the question is completed?

Answer:

Y=21

Step-by-step explanation:

add 13 on both sides you get Y=21

Equation of the tangent line to the curve  \(xe^{y} + ye^{x} = 5\) at5 the point (0,5) is y = - (\(e^{5}\) + 5)x + 5.

Given curve is,

\(xe^{y} + ye^{x} = 5\)

We will differentiate both sides with respect to x,

\(\frac{d}{dx}\)\([xe^{y} + ye^{x} ]\) = \(e^{y} + xe^{y}\frac{dy}{dx} + e^{x}\frac{dy}{dx} + ye^{x}\) = 0

⇒ \(\frac{dy}{dx}\) \([xe^{y} + e^{x} ] = - [e^{y} + ye^{x} ]\)

⇒ \(\frac{dy}{dx}\) = \(- \frac{e^{y}+ye^{x} }{xe^{y}+e^{x} }\)

We have to find the equation at point (0,5).

Therefore substituting values of x and y,

that is x = 0 and y = 5.

\(\frac{dy}{dx} = - \frac{e^{5}+(5)e^{0} }{(0)e^{5} + e^{0} }\)

    = \(- \frac{e^{5} + 5}{1}\)

\(\frac{dy}{dx}\)  = - [\(e^{5}\) + 5] = gradient

Therefore the equation of tangent line is

(y - y1) = [m(x - x1)]

where m is the gradient

⇒ y - 5 = - [(\(e^{5}\)+5)(x - 0)]

⇒  y = - (\(e^{5}\) + 5)x + 5

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Answer:

A

Step-by-step explanation:

This is because of same shape but different size of angles

Answer:

c

Step-by-step explanation:

Because you can't have multiple x-values. You can only have multiple y-values.

Answer:

f = 1, w = 4

Step-by-step explanation:

Given the 2 equations

5w = 23 - 3f → (1)

4f = 12 - 2w (add 2w to both sides )

2w + 4f = 12 ( subtract 4f from both sides )

2w = 12 - 4f → (2)

Multiplying (1) by 4 and (2) by - 3 and adding the result will eliminate f

20w = 92 - 12f → (3)

- 6w = - 36 + 12f → (4)

Add (3) and (4) term by term to eliminate f

14w = 56 ( divide both sides by 14 )

w = 4

Substitute w = 4 into either of the 2 equations and solve for f

Substituting into (1)

5(4) = 23 - 3f

20 = 23 - 3f ( subtract 23 from both sides )

- 3 = 3f ( divide both sides by - 3 )

1 = f

Answer:

Step-by-step explanation:

By applying total cost concept, it can be concluded that the expression represents the total cost is 1.45d (option A).

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.

It is usually used to solve a problem in various fields of study, such as chemistry, biology, economics, and so on.

One of the most familiar uses of algebra is how to calculate the total cost:

Total cost = n x p , where:

n = number of products

p = product price per piece

We know that Jim is going to buy donuts for his family:

p = $1.45

n = d

So the total cost can be calculated by multiplying 1.45 by d, which equals 1.45d.

Thus the expression represents the total cost is 1.45d (option A).

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The solution of the system of equation are as follows:

System of equation can be solved using various method such as substitution method, elimination method and graphical method.

We will use substitution method to solve the system of equation.

Therefore,

y = 2x

x = 2y – 2

substitute the value of x in equation(i)

Hence,

y = 2(2y - 2)

y = 4y - 4

y - 4y = -4

-3y = -4

divide both side by -3

y = -4 / -3

y = 4 / 3

Let's find the value of x using equation(ii)

x = 2y - 2

x = 2(4 / 3) - 2

x = 8 / 3 - 2

x = 8 - 6/ 3

x = 2 / 3

Therefore,

x = 2 / 3 and y = 4 / 3

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Answer:

C

Step-by-step explanation:

2 x pi x r = circumfrence

2 x 7 x pi = 43.96

Answer: 43.96 m

Step-by-step explanation: To find the circumference of the circle shown here, start with the formula for the circumference of a circle which is shown below.

Circumference = 2πr

Notice that the radius of the circle is 7 meters.

So we can plug in 7 meters for r in the formula.

So we have (2)(π)(7m) which is equal to 14π m.

So the circumference of the circle shown here is 14π m.

Remember that π is approximately equal to 22/7 or 3.14 so we can estimate the value of the circumference by plugging in 3.14 for π.

So we have (14)(3.14) which is equal to 43.96.

So the circumference of the circle is

approximately equal to 43.96 m.

To construct a box plot for the given data, we need to find the five key statistics: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

These values will determine the positions of the five movable parts of the box plot. To construct the box plot, we start by ordering the data in ascending order: 45, 45, 46, 47, 49, 55, 59, 61, 70, 70, 79, 79. The minimum value is 45, and the maximum value is 79. The median is the middle value of the dataset, which in this case is the average of the two middle values: (55 + 59) / 2 = 57. The first quartile (Q1) is the median of the lower half of the dataset, which is the average of the two middle values in that half: (45 + 46) / 2 = 45.5. The third quartile (Q3) is the median of the upper half of the dataset, which is the average of the two middle values in that half: (70 + 70) / 2 = 70.

Now that we have the five key statistics, we can construct the box plot. The plot consists of a number line where we place the movable parts: minimum (45), Q1 (45.5), median (57), Q3 (70), and maximum (79). The box is created by drawing lines connecting Q1 and Q3, and a line is drawn through the box at the median. The whiskers extend from the box to the minimum and maximum values. Any outliers, which are data points outside the range of 1.5 times the interquartile range (Q3 - Q1), can be represented as individual points or asterisks. In this case, there are no outliers.

In summary, the box plot for the given data will have the following positions for the movable parts: minimum (45), Q1 (45.5), median (57), Q3 (70), and maximum (79).

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Answer:

A = 61

Step-by-step explanation:

Complementary angles add to 90 degrees

A+B = 90

A +29 = 90

A = 90-29

A = 61

Answer:

∠A = 61°

Step-by-step explanation:

We know that sum of both angles of complementary angle is 90°.

∠A + ∠B = 90°

∠A + 29° = 90° ... (∠B = 29° - given )

subtract 29° from each side

∠A + 29° - 29° = 90° - 29°

∠A = 61°

Answer:  \(\frac{28}{27}\) or \(1\frac{1}{27}\)

Step-by-step explanation:

\(\frac{7}{9} /\frac{6}{8} = \frac{7}{9}(\frac{8}{6})\)

\(\frac{7}{9} (\frac{8}{6} ) = \frac{28}{27}\)

\(\frac{28}{27} = 1 \frac{1}{27}\)

Answer:

28 cm

Step-by-step explanation:

volume of a rectangle: l*w*h

the first cuboid: 7*4*2= 56

56=2*1*y

56=2y

28=y

Answer:

28cm

Step-by-step explanation:

Since the two cuboids have the same volume, we use the volume of cuboid one to find the length of side y,

Volume of a cuboid = \(length * breadth * height\)

Volume of the cuboid with all sides given is = 7 * 4 * 2 = 56cm cubed.

Now we use that volume to calculate the length y,

56 = 1 * 2 * y

56 = 2y

y = 56/2

y = 28cm

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

It says to go up by 1/8 so the little lines on the graph are going up by 1/8

1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8

But some of these can be simplified so it comes out

1/8, 1/4, 3/8, 4/8, 5/8, 3/4, 7/8

Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1