If a side of a square is doubled and an adjacent side is diminished by 3, a rectangle is formed whose area is numerically greater than the area of the square by twice the original side of the square. Find the dimensions of the original square

Answer:

i think it is the 2nd one and the 5th one.

Step-by-step explanation:

hope this helped!

p.s it would be cool if you gave me brainliest

Answer:

A = (6,6)

Hope this helps!

Question: if n  balls are randomly placed into n cells, determine the probability that exactly one cell remains empty.

The probability that exactly one cell remains empty when n balls are randomly placed into n cells can be calculated as \((n-1)/n^n\).

Let's consider the scenario where n balls are randomly distributed into n cells. To determine the probability that exactly one cell remains empty, we need to calculate the number of favorable outcomes (arrangements where exactly one cell is empty) and divide it by the total number of possible outcomes.

The total number of possible outcomes is given by n^n since each ball has n choices (n cells) for placement, and there are n balls in total.

To calculate the number of favorable outcomes, we focus on the cell that remains empty. There are n choices for selecting the empty cell. For the remaining (n-1) cells, each ball has n-1 choices for placement, as it cannot be placed in the empty cell. Therefore, the number of favorable outcomes is (n-1)*(n-1)*(n-1)*...*(n-1) (n-1 repeated n-1 times).

Dividing the number of favorable outcomes by the total number of possible outcomes, we obtain \((n-1)/n^n\) as the probability that exactly one cell remains empty when n balls are randomly placed into n cells.

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Answer:

y = -53x

Step-by-step explanation:

since 0,0 is a point, there is no b, and -5/3 times 3 is -5

a) The given equation is a² + xy + y² = 1. Let us differentiate the above equation w.r.t x.  d/dx (a² + xy + y² = 1) => (d/dx) (a²) + (d/dx) (xy) + (d/dx) (y²) = (d/dx) (1) => 0 + x(dy/dx) + 2y(dy/dx) = 0 => dy/dx = -x/2y.

Let us differentiate the above equation w.r.t y.

d/dy (a² + xy + y² = 1) => (d/dy) (a²) + (d/dy) (xy) + (d/dy) (y²) = (d/dy) (1) => 0 + x(dy/dy) + 2y(dy/dy) = 0 => dy/dy = -x/2y = -x/y.

Thus, dy/da = (dy/dx) / (da/dx) = (-x/2y) / 2a = -x / 2ay.

b) The given equation is a² + xy + y² = 1.

Substituting the point (1,0) in the above equation, 1² + (1)(0) + 0² = 1 => 1 = 1, which is true.

Let us differentiate the equation w.r.t x. d/dx (a² + xy + y² = 1) => 2a(da/dx) + y + x(dy/dx) + 2y(dy/dx) = 0.

Substituting the point (1,0) in the above equation, 2(1)(da/dx) + 0 + 0 + 2(0)(dy/dx) = 0 => da/dx = 0.

Thus, the slope of the tangent line to the curve at the point (1,0) is dy/dx = (-x/2y) = -(1/0) = undefined.

Hence, the slope of the tangent line is undefined.

Answer: The expression for dy/da using implicit differentiation is dy/da = -x/2ay and the slope of the tangent line to the curve at the point (1,0) is undefined.

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The change in the goalie's rating points after his team loses 8 games in a row is -20 and 4/5.

The goalie loses 235 rating points each time his team loses. If his team loses 8 games in a row, we need to calculate the total change in his rating points.

To find the total change, we multiply the loss per game (235) by the number of games lost (8).

235 * 8 = 1880

Therefore, the goalie's rating points decrease by 1880. However, the answer options provided are in mixed number format, so we need to convert 1880 to a mixed number.

To convert 1880 to a mixed number, we divide 1880 by the denominator (5) and express the remainder as the numerator:

1880 ÷ 5 = 376 with a remainder of 0

Hence, the mixed number representation of 1880 is 376 and 0/5, which simplifies to 376.

Therefore, the change in the goalie's rating points after losing 8 games in a row is -376, or in mixed number form, -376 and 0/5, which further simplifies to -376 and 4/5.

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The cost of one computer is £600 and the cost of one printer is £800.

Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.

Let the cost of a computer be x and the cost of a printer be y.

Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)

4x + 5y = 6000 ---------------------- (2)

Solving equations (1) and (2) simultaneously:x = 600y = 800

Therefore, the cost of a computer is £600 and the cost of a printer is £800..

:Therefore, the cost of one computer is £600 and the cost of one printer is £800.

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The probability of finding oil (to 1 decimal) is 0.7.

Probability is a statistic that is used to show the possibility or chance that a certain event will occur. Probabilities can be expressed as fractions from 0 to 1, in contrast to percentages from 0% to 100%. The four main types of probability that mathematicians study are axiomatic, classic, empirical, and subjective. Given that the terms potential and probability are interchangeable, you could define probability as the probability that a particular event will take place.

To determine probability the  Preliminary geologic  , we obtain,

P(oil)=0.3+0.4

P(oil)=0.7.

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Answer:

\(x {}^{2} - 5\)

Answer:  \(\large \boldsymbol {A=19683}\)

Step-by-step explanation:

\(\large \boldsymbol {} \displaystyle \bigg( \frac{1}{3} \bigg)^{-9x}=A^x \\\\\\ (3^{-1})^{-9x} =A^x \\\\\\( 3^{9} )^x=A^x \\\\\\ A=3^9=19683\)

Answer:

3⁹

Step-by-step explanation:

\(\sf{(\frac{1}{3})^{-9x} = A^{x} }\)

\(\sf{(3^{-1})^{-9x} = A^{x} }\)

\(\sf{3^{9x} = A^{x} }\)

\(\sf{\boxed{A = 3^9 }}\)

Answer:

y = 2x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (2, 7) ← 2 points on the line

m = \(\frac{7-3}{2-0}\) = \(\frac{4}{2}\) = 2

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 2x + 3 ← equation of line

Answer:

Expression represents this situation is 50+5 pesos.

Step-by-step explanation:

A ticket costs 50 pesos for a member of a club.

Non club member ticket cost is 5 pesos more than the member.

So, expression represents this is 50+5 pesos

The logarithmic expression as a single logarithm is \(log_{2}\)(a\(b^{2}\)/\(c^{3}\))

A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction.

\(log_{2}a + 2log_{2}b - 3log_{2}c\)

\(2log_{2}b\) may be simplified as \(log_{2}b^{2}\)

\(3log_{2}c\) may be simplified as \(log_{2}c^{3}\)

Which reduces the expression as

\(log_{2}a\) +  \(log_{2}b^{2}\) -  \(log_{2}c^{3}\)

factor out log2 since it is common

and replace addition sign with multiplication and subtraction sign with division

\(log_{2}(\frac{a * b^{2} }{c^{3} })\) which finally becomes \(log_{2}(ab^{2} /c^{3})\)

In conclusion, the simplified form of the logarithmic expression is  \(log_{2}(ab^{2} /c^{3})\)

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The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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Answer:

10% = 0.1 x 400 = 40

400 - 40 = 360$

By calculation, your grade in the class now is 78.7

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

Score of 47.2 in 60

Represent the score in 100% with x

So, we have the following equation

47.2/60 = x/100

Multiply both sides of the equation by 100

So, we have

100 * 47.2/60 = x/100 * 100

This gives

100 * 47.2/60 = x

So, we have

x = 100 * 47.2/60

Evaluate

x = 78.7

Hence, your grade in the class now is 78.7

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Answer:

see explanation

Step-by-step explanation:

cos C = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{24}{51}\) = \(\frac{8}{17}\)

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

tan Z = \(\frac{opposite}{adjacent}\) = \(\frac{XY}{ZY}\) = \(\frac{15}{20}\) = \(\frac{3}{4}\)

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

sin C = \(\frac{opposite}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{60}{65}\) = \(\frac{12}{13}\)

Answer:

(x+3)(y+2)

Step-by-step explanation:

(xy+2x)+(3y+6)

x(y+2)+3(y+2)

(x+3)(y+2)

Answer:

12.8 feet/second

Step-by-step explanation:

Answer: 12.9

Step-by-step explanation: the other person was right BUT I’m pretty sure they want it rounded up to the tenths so 12.9 simply divide the 278.48 by 21.6 to get the answer

Answer:

your answer is B AB CE and BE DE

So mark me as brainliest

The statements that are necessary and sufficient to prove that ABCD is a parallelogram are, (B), (C) and (D).

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The area of a parallelogram is base multiples by height as two triangles form a parallelogram.

From the properties of parallelograms the statements that are necessary and sufficient to prove that ABCD is a parallelogram are,

\(\overline{AE}\) ≅ \(\overline{CE}\) and \(\overline{BE}\) ≅ \(\overline{DE}\)  as diagonal of a parallelogram bisect each other.

\(\overline{AB}\) ≅ \(\overline{CD}\) and \(\overline{BE}\) ≅ \(\overline{CE}\) opposite sides of a parallelogram are equal.

m∠ABC + m∠BAD is 180° as the sum of the adjacent sides in a parallelogram are supplementary.

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Answer:

46,288

Step-by-step explanation:

40,000 + 6,000 + 200 + 80 + 8

46,288

Hope this helps :D

The population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.

To find out when the population will be twice what it was in 1980, we need to set up an equation and solve for t.

Let's first determine the population in 1980:

N(0) = 217e0.0102(0) = 217

So, the population in 1980 was 217 million.

Now, we want to find out when the population will be twice that amount:

2(217) = 434

We can set up an equation:

434 = 217e0.0102t

Divide both sides by 217:

2 = e0.0102t

Take the natural logarithm of both sides:

ln(2) = 0.0102t

Solve for t:

t = ln(2)/0.0102

t ≈ 67.8

Therefore, the population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.

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Answer: 32

2+6(6-2)

8(4)

32

For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

The "Rule of 72" is a quick estimation method to determine the time it takes for an investment or savings to double in value. By dividing 72 by the interest rate, you can obtain an approximation of the doubling time. For an interest rate of 3%, it would take approximately 24 years for the savings to double. For an interest rate of 8%, it would take around 9 years for the savings to double.

To calculate the doubling time using the Rule of 72, divide 72 by the interest rate. This provides an approximation of the number of years it takes for an investment or savings to double in value.

For an interest rate of 3%, we divide 72 by 3: 72 / 3 = 24. Therefore, it would take approximately 24 years for the savings to double.

For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

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The number line is plotted on the graph below

A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.

If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions

It displays information as a series of data points called 'markers' connected by straight line segments

Given data ,

Let the number line be represented by graph A

Now , the points on the graph are

A = { 4 , -3 , 1 }

The opposites of the number points A is given by

A' = { -4 , 3 , -1 }

The values of the sets A and A' are plotted on the line plot graph

Hence , the line plot is solved

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To calculate the inclusion probability for unit 6 (PSU level) in the first stage of PPS without replacement, we need to divide the number of sampling units in the population by the total number of sampling units selected in the first stage.

Looking at the provided data, we can see that there are a total of 10 sampling units (Mi) in the dataset.

In PPS without replacement, the first sampling unit is selected with certainty. So, the inclusion probability for unit 6 (PSU level) is:

Inclusion probability = 1 / Total number of sampling units selected in the first stage

                    = 1 / 10

                    = 0.1

Therefore, the inclusion probability for unit 6 (PSU level) in the first stage of PPS without replacement is 0.1 or 10%.

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Cevap:

Salı

Adım adım açıklama:

İlk depozito (Pazartesi) = 8 lira

Günlük yatırılan miktar = 3 lira

74 liraya sahip olmak için gereken gün sayısı;

Gün sayısı = x olsun

8 + 3x = 74

3x = 74 - 8

3x = 66

x = 66 / 3

x = 22 gün

Pazartesiden 22 gün sonra; Salı gününe denk gelecek

Therefore, the correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

Based on the given information, D represents the null hypothesis (H₀) and E represents the alternative hypothesis (Hₐ).

The null hypothesis (H₀) is a statement that there is no significant difference between the observed data and the expected results. In this case, the null hypothesis is that the population mean (μ) is greater than or equal to 1000.

The alternative hypothesis (Hₐ) is a statement that there is a significant difference between the observed data and the expected results. In this case, the alternative hypothesis is that the population mean (μ) is less than 1000.

Correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

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