A square based pyramid is built using identical cube- shaped blocks, with 1 on top. 4 on the next layer , 9 on the next, and so on. What is the minimum number of blocks needed if the pyramid is to be dismantled and rebuilt into 2 separate cubes with no blocks left over

Answer:

To simplify the expression 2√20 - 2√5, you can start by applying the rule that the square root of a product is the product of the square roots of the factors. This means that you can rewrite √(20) as √(4*5) = 2√(5).

Applying this rule, the expression simplifies to:

2√(5) - 2√(5) = 2√(5) - 2√(5) = 0

Therefore, the simplified expression is equal to 2√(5).

Step-by-step explanation:

The value of function which cross the y-axis at point (0, 7) will be;

⇒ y = x + 7

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The point which cross the function = (0, 7)

Now,

Since, The point which cross the function = (0, 7)

Hence, The point must be satisfy the function.

By option (1);

⇒ y = x + 7

Put (x, y) = (0, 7)

⇒ 7 = 0 + 7

⇒ 7 = 7

Thus, The correct function which passes through the point (0, 7) is,

⇒ y = x + 7

Option (i) is true.

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Answer:

Irrational numbers and real numbers

Step-by-step explanation:

f(x)=2x

f(-3)=2(-3)

f(-3)=-6

Answer:

A. -6

Step-by-step explanation:

Just plug in -3 to where x is.

Answer:

Sample answer: Its main goal is political and economic integration among its members. So far the EU has helped its poorer members raise their standard of living, created a single currency (the Euro €), reduced costs in air travel and cell phones, combined efforts on crime and terror prevention, and set up free trade among its members’ borders.

Step-by-step explanation:

Answer:

3,641 cups drank

Step-by-step explanation:

A quart is 4 cups

At the start of the party, there were 912 quarts, multiply that by 4 to get 3,648 cups

At the end of the party, only 7 cups remained

3648 - 7 = 3,641 cups drank

Substract '-3.4x' at LHS nad the RHS of the above expression.

Add '4' on both LHS and RHs of the above expression.

9514 1404 393

Answer:

  year 2066

Step-by-step explanation:

In order to do this, we need to make some assumptions. We'll assume that the 2010 wages are also in 2009 dollars. (If not, there's an inflation factor that needs to be accounted for.) We also need to assume the form of the change in wages over time. The simplest assumption there is that wages change linearly.

Then we can write equations for men's and women's wages as follows:

Using the 2-point form of the equation for a line, we have ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Men's wages

  y = (42800 -38907)/(2010-1960)(x -1960) +38907

  y = 77.86(x -1960) +38907

  y = 77.86x -113,698.6 . . . . . where x is the year

Women's wages

  y = (34700 -23606)/(2010 -1960)(x -1960) +23606

  y = 221.88x -411,278

These values are equal when ...

  77.86x -113,698.6 = 221.88x -411,278

  297,580.2 = 144.02x . . . . . . . add 411278 -77.86x

  2066.2 = x . . . . . . . divide by the coefficient of x

Based on this data we predict women's wages might catch up to men's in the year 2066, about 56 years from 2010.

_____

Alternate solution

In the 50 years from 1960 to 2010, the fraction of men's wages that women receive has increased from 23606/38907 ≈ 0.606729 to 34700/42800 ≈ 0.810748. That is a change of about 0.204 of men's wages in 50 years. The remaining fraction of 1-0.810748 = 0.189 might be expected to be wiped out in another (0.189/0.204)(50 years) = 46.4 years. That would be the year 2056.

The different results come from different assumptions. For the second solution, we assumed that the fraction improved linearly. Under the first assumption, that wages improved linearly, the fractional improvement is non-linear, and decreases over time.

_____

Additional comment

The usual assumption regarding things financial is that they change exponentially over time. If we use an exponential model, instead of a linear one, wage parity is reached in about 2046.

During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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Answer:

approximately 254.5

btw area of circle= pi multiplied by radius

Step-by-step explanation: I got you bro

Answer: Circle area = π * r² = π * 81 [inch²] ≈ 254.47 [in²]

but because it asks for nearest tenth

254.5 in²

this is your real answer

Answer:

The answer is y = 4x - 1.

Step-by-step explanation:

The answer is y = 4x - 1.

Step-by-step explanation:

☆The equation we'll be using: y = mx + b

☆Since we already have the slope. we have to find the y-intercept.

☆\begin{gathered}y = mx + b \\ \\ 7 = 4(2) + b \\ 7 = 8 + b \\ \frac{ - 8 = - 8 \: \: \: \: \: \: \: \: \: \: \: }{ - 1 = b \: \: \: \: \: \: \: \: \: \: } \end{gathered}

y=mx+b

7=4(2)+b

7=8+b

−1=b

−8=−8

Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step

Answer:

x=3

Step-by-step explanation:

Hey there!

In order to solve this equation, we must first distribute the 3

3x + 9 = -4x + 30

Now we combine like terms

7x = 21

Then we divide both sides by 7 to get x by itself

x = 21/7

x = 3

Answer: x=3

Step-by-step explanation:

To solve the given equation, it means to find the value of x. We want to use inverse properties to isolate x. The inverse properties are add/subtract and multiply/divide. Be sure to use the corresponding inverse operation.

3(x+3)=-4x+30                 [distribute]

3x+9=-4x+30                    [add both sides by 4x]

7x+9=30                            [subtract both sides by 9]

7x=21                                 [divide both sides by 7]

x=3

Therefore, we get x=3.

Answer: a = (1/4)a

Step-by-step explanation:

(a) P(B | A) = 0.5454

(b) P(B' | A) = 0.4546

(c) P(A | B) = 0.6667

(d) P(A' | B) = 0.3333

(e) Given that the selected individual has at least one card, the probability that he or she has a Visa Card is 0.7857.

(a) The probability that the selected individual has a MasterCard given that they have a Visa card is -

P(B | A) = P(A ∩ B) / P(A) = 0.30 / 0.55 = 0.5454

(b) The probability that the selected individual does not have a MasterCard given that they have a Visa card is -

P(B' | A) = 1 - P(B | A) = 1 - 0.5454 = 0.4546

(c) The probability that the selected individual has a Visa card given that they have a MasterCard is -

P(A | B) = P(A ∩ B) / P(B) = 0.30 / 0.45 = 0.6667

(d) The probability that the selected individual does not have a Visa card given that they have a MasterCard is -

P(A' | B) = 1 - P(A | B) = 1 - 0.6667 = 0.3333

(e) To find the probability that the selected individual has a Visa card given that they have at least one card, we can use the formula -

P(A | A ∪ B) = P(A ∩ (A ∪ B)) / P(A ∪ B)

= P(A) / P(A ∪ B) = 0.55 / (0.55 + 0.45 - 0.30) = 0.55 / 0.70 = 0.7857

Hence, the probability that the selected individual has a Visa card given that they have at least one card is 0.7857.

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Answer:

I believe it is four hours but I may be wrong

Step-by-step explanation:

Check other answers just in case we get the same answer

Answer:

they make the same amount in 5 hours

Step-by-step explanation:

refer to image

The measures of the two complementary angles are 44° and 132°.

Given that the difference between the measures of two complementary angles of any given triangle is 88°, it means that one angle is 88° smaller than the other. To find the measures of the two angles, divide the sum of the difference by 2. That is given as, (88°/2) = 44°. One angle is given as  44°, and the other angle is equal to the sum of the two angles in a triangle, which is 180°, minus the first angle, which is 44°, which is equal to 136°.

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The value of x that makes ∠U and ∠V to be supplementary angles are; x = 15°

When we are talking about angle theorem and congruency in mathematics, it is well know that supplementary angles are defined as angles whose sum is equal to 180 degrees.

Now, we are given;

∠U = 3x°

∠V = 3(∠U)

Thus;

∠V = 3(3x°) = 9x°

From definition of supplementary angles, we can say that;

3x° + 9x° = 180°

12x = 180°

x = 180/12

x = 15°

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The top right line (second line) best fits the data in this problem, as it has the lowest residuals.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a line of best fit, we have that the residuals are the lowest possible, meaning that the points are the closest to the line.

Hence the top right line best fits the data in this problem, as it has the lowest residuals.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$15000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)

\(15000=P\left(1+\frac{0.06}{4}\right)^{4\cdot 4}\implies 15000=P(1.015)^{16} \\\\\\ \cfrac{15000}{1.015^{16}}=P\implies 11820.47\approx P\)

The equation that can be used to determine the measure of ∠A is tanA = 9.4/6.7. The correct option is A. tanA=9.4/6.7

From the question, we are to determine which of the given equations can be used to determine the measure of ∠A

In the diagram,

If ∠A is the included angle

Then,

Using SOH CAH TOA

Opposite = 9.4

Adjacent = 6.7

Thus,

tanA = 9.4/6.7

Hence, the equation that can be used to determine the measure of ∠A is tanA = 9.4/6.7. The correct option is A. tanA=9.4/6.7

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The function oscillates between two horizontal asymptotes, y=3 and y=-3, as x approaches the vertical asymptotes.

How to study graph?

To graph the function y=3cot(x) between 0 and 2, we can start by identifying the key characteristics of the cotangent function. The cotangent function is defined as the ratio of the adjacent side to the opposite side of a right triangle, with respect to a given angle. As such, the cotangent function is periodic with a period of π and has vertical asymptotes at x=nπ, where n is an integer.

The coefficient of 3 in the given function y=3cot(x) vertically stretches the function by a factor of 3, and does not affect the period or the vertical asymptotes.

Between 0 and 2, there are two vertical asymptotes at x=0 and x=π. To graph the function, we can plot a few points along the curve, using the symmetry properties of the cotangent function. Specifically, the cotangent function is odd, meaning that cot(-x)=-cot(x), and thus the graph is symmetric about the origin.

At x=π/4, we have cot(π/4)=1, and thus y=3cot(π/4)=3. Similarly, at x=3π/4, we have cot(3π/4)=-1, and thus y=3cot(3π/4)=-3. Using the symmetry property, we can also plot points at x=-π/4 and x=-3π/4, with y=3cot(-π/4)=-3 and y=3cot(-3π/4)=3, respectively.

Connecting these points with smooth curves, we can see that the graph of y=3cot(x) oscillates between two horizontal asymptotes, y=3 and y=-3, as x approaches the vertical asymptotes at x=0 and x=π.

Overall, the graph of y=3cot(x) between 0 and 2 can be summarized as follows:

There are two vertical asymptotes at x=0 and x=π.

The function oscillates between two horizontal asymptotes, y=3 and y=-3, as x approaches the vertical asymptotes.

The graph is symmetric about the origin.

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Step-by-step explanation:

Improper fractions have a numerator that is larger than the denominator

1 = 6/6

 so  1  1/6  = 7/6

The probability that the chosen ball is blue is 55.3%.

If the chosen ball is blue, the probability would be 3.33% that it came from the first urn.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

(a) To find P(A|B1), we use the formula P(A|B) = P(A and B)/P(B).

In this case, P(A and B1) is the probability of choosing a blue ball from the first urn, which is 7/20.

The probability of choosing the first urn is 1/2, so P(B1) = 1/2.

Plugging these values into the formula gives us P(A|B1) = (7/20)/(1/2) = 14/20 = 7/10.

To find P(A|B2), we use the same formula.

In this case, P(A and B2) is the probability of choosing a blue ball from the second urn, which is 14/19.

The probability of choosing the second urn is 1/2, so P(B2) = 1/2.

Plugging these values into the formula gives us P(A|B2) = (14/19)/(1/2) = 28/19.

To find P(A and B2), we use the formula P(A and B) = P(A|B) * P(B).

In this case, we already know that P(A|B2) = 28/19 and P(B2) = 1/2, so P(A and B2) = (28/19) * (1/2) = 28/38.

To find P(A or B2), we use the formula P(A or B) = P(A) + P(B) - P(A and B).

In this case, P(A) is the probability of choosing a blue ball overall, which is 21/38.

P(B2) is the probability of choosing the second urn, which is 1/2.

P(A and B2) is the probability of choosing a blue ball from the second urn, which is 28/38.

Plugging these values into the formula gives us P(A or B2) = 21/38 + 1/2 - 28/38 = 15/38.

The probability that the chosen ball is blue is P(A) = 21/38 = 55.3%.

(b) If the chosen ball is blue, the probability that it came from the first urn is P(B1|A) = P(B1 and A)/P(A).

We already know that P(B1 and A) is the probability of choosing a blue ball from the first urn, which is 7/20.

We also know that P(A) is the probability of choosing a blue ball overall, which is 21/38.

Plugging these values into the formula gives us P(B1|A) = (7/20)/(21/38) = 7/21.

This probability is equal to 33.3%.

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Answer:

\(\frac{1}{3^{4} } \\\\\frac{1}{81}\)

Step-by-step explanation:

Answer: -81, the product would just be 3∧4 but negative

Answer:

3

Step-by-step explanation:

3x7=21

3x10=30

Answer:

x = 28

Step-by-step explanation:

(x + 18)° + (5x - 6)° = 180° (supplementary angles)

Solve for x

x + 18 + 5x - 6 = 180

Add like terms

6x + 12 = 180

6x = 180 - 12 (subtraction property of equality)

6x = 168

x = 168/6 (division property of equality)

x = 28

Step-by-step explanation:

x = 3

y = - 2

z = 6

\(7xyz\)

Solution,

= 7 × 3 ( - 2 ) × 6

= 21 ( - 2 ) × 6

= - 42 × 6

= - 252

hence the answer is - 252....

The coordinates in the solution to the systems of inequalities is (12, 1)

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

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

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