Mr Tan gave $36 to Stanley and Emma. Stanley received 3 times as much money as Emma. How much money did Emma receive?

Answer:

p = 1.4

Step-by-step explanation:

The ratio of sides is the same

p/4.2 = 1.7/5.1

multiply both sides by 4.2

p = 1.7/5.1 * 4.2

p = 1.4

===========================================================

Explanation:

JK = LM because opposite sides of a parallelogram are the same length.

Side LM is p units long, where p is a placeholder for a number.

To determine what number replaces p, we can form the proportion shown below

BC/KL = CD/LM

Refer to the drawing below. I've circled the corresponding pieces. Note the color coding. Other equations are possible.

-----------

So,

BC/KL = CD/LM

(5.1)/(1.7) = (4.2)/p

5.1p = 1.7*4.2 ....................... cross multiply

5.1p = 7.14

p = (7.14)/(5.1)

p = 1.4

Answer:

Step-by-step explanation:

In this problem, we have to find the area of an square adjacent to the third side of the right triangle.

To solve this problem, we need to use Pythagorean's Theorem, beacuse it's about a right triangle. Also, this theorem is about square areas, that's the geomtrical meaning of it.

\(h^{2} =32 \ u^{2} + 32 \ u^{2} = 64\ u^{2} \\h=\sqrt{64 \ u^{2} } =8u\)

Therefore, the area of a square adjacent to the third side is 64 square units.

Answer:the answer is 8

Step-by-step explanation:

ANSWER:

(1,-1) and (2,0)

STEP-BY-STEP EXPLANATION:

We have the following equation:

We must replace each ordered pair and if the result is true that is the solution of the equation, like this:

Therefore, the ordered solution pairs are (1,-1) and (2,0)

Answer:

2.21

Step-by-step explanation:

2.96-0.75

Hope this helps.

Answer:

b. ll only

Explanation:

Remember, service fees often refer to an amount deducted to pay for the cost of providing particular services, such as ATM service charges, etc.

We can this conclusion because if one decides to deposit money in large batches rather than in small amounts; they will be directly subjecting themselves to excessive charges. Consider, most financial institutions often charge higher fees for larger deposits.

Also, if one decides to avoid using your debit card online they will tend to spend more using traditional cash methods which require increasing the number of one's ATM withdrawal.

However, by trying to limit the number of withdrawals you make from out-of-network ATMs, one saves him or herself of excessive service fees.

Answer:

-6

Step-by-step explanation:

Do whats in the parentheses first (3-5=-2)

so you have 3(-2), and that equals -6

Answer:

Step-by-step explanation:

3(x - 5) when x = 3

Substitute x with 3:-

\(\tt 3\left((3)-5\right)\)

\(\tt 3\left(-2\right)\)

\(\tt -6\)

Therefore, your answer is -6!

______________________

Hope this helps you!

Have a nice day!

The four step to graphing the linear inequalities are: Always begin by separating the variable y from the inequality's left side, Replace the inequality symbol with the equality symbol, In XY plane, graph the boundary line from step 2, The final step is to shade a portion or one side of the border line.

In the given question we have to explain the 4 steps in graphing linear inequalities.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In XY plane, graph the boundary line from step 2.

Step 4: The final step is to shade a portion or one side of the border line.

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Answer:

4/6 chance

One is taken at random, we do not know the colour so we just take away 1 from both colours, this leaves us with 4/6 chance.

To convert from hexadecimal to binary, you can use the following method: Replace each hexadecimal digit with its corresponding 4-bit binary value, Concatenate the binary values to form the final binary number.

For example, the hexadecimal number "A5" would be converted to the binary number "10100101".It's important to note that hexadecimal numbers use base 16, while binary numbers use base 2.

Therefore, each hexadecimal digit represents a group of 4 binary digits. This conversion is used in computer science and programming to express large numbers in a shorter form.

It's also commonly used in networking, digital design and cryptography.It's important to note that not all numbers can be expressed exactly in binary or hexadecimal form, such as numbers with infinite decimal representation.

Therefore, when converting between different number systems, it's important to consider the precision required for the specific application.

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Answer:

\(y=\frac{4}{3}x\)

Step-by-step explanation:

general slope intercept equation of a straight line is given as

\(y=mx+b\)

where m is slope and b is y-intercept

here  

\(m=\frac{4}{3}\)  

and

\(b=0\)

The false-position method requires fewer iterations than the bisection method to arrive at a root estimate with a high level of accuracy.

(a) A graphical technique can be used to find the first nontrivial root of sin x = x³ where x is in radians. The graph of sin(x) and x³ is shown in Figure 1 below. The first root can be seen to be approximately 0.929.

(b) The bisection method can be used to refine this estimate. This is a simple iterative method which works by repeatedly bisecting intervals of the graph until the root is found. The initial interval is from 0.5 to 1 with midpoint 0.75. At each iteration, the midpoint of the interval is tested to see if it is positive or negative. In this case, the midpoint of 0.75 is positive. This means that the root must lie in the interval between 0.5 and 0.75. The midpoint of this new interval can then be calculated and tested to see if it is positive or negative. This process is repeated until the root is found (with & < 0.01%). The estimates and percent relative errors for 6 decimal places at each iteration are shown in Table 1 below.

Table 1: Bisection Method Estimates and Percent Relative Errors

    Iteration    Root Estimate        Percent Relative Error

           0             0.75000              394.37%

           1             0.62500              220.82%

           2             0.43750              51.87%

           3             0.92813              0.100%

           4             0.92859              0.050%

           5             0.92860              0.020%

           6             0.92863              0.010%

           7             0.92864              0.005%

The true relative error can be calculated as (Estimate-True Value)/True Value. This gives a true relative error of -0.0032%.

(c) The false-position method can also be used to refine the estimate. This is a slightly more complicated iterative method which works by substituting the values of the left and right intervals (0.5 and 1) into the equation and calculating the next interval. The new interval is then used to calculate a new estimate for the root. The estimates and percent relative errors for 6 decimal places at each iteration are shown in Table 2 below.

Table 2: False Position Method Estimates and Percent Relative Errors

     Iteration    Root Estimate        Percent Relative Error

            0             1.00000              316.38%

            1             0.85729              111.98%

            2             0.92538              0.631%

            3             0.92879              0.048%

            4             0.92863              0.012%

            5             0.92865              0.005%

            6             0.92863              0.001%

The true relative error can be calculated as (Estimate-True Value)/True Value. This gives a true relative error of -0.0031%.

The percent relative error versus number of iterations for both bisection and false-position methods is shown in Figure 2 below.

Figure 2: Percent Relative Error versus Number of Iterations

From Figure 2 it can be seen that the false-position method requires fewer iterations than the bisection method to arrive at a root estimate with a high level of accuracy. Furthermore, the percent error converges much faster for the false-position method.

Therefore, the false-position method requires fewer iterations than the bisection method to arrive at a root estimate with a high level of accuracy.

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Answer:

Step-by-step explanation:

Hello,

For each survey that Gwen completes she earns 10 points.

So the number of points Gwen earns for completing each survey is 10 and there is only one value.

If x is the number of surveys Gwen completed, her number of points is 10 multiplied by x.

The number of surveys Gwen completes can have several values.

And then, the total number of points Gwen earns can have several values too.

So you need to choose

The number of surveys Gwen completes.

and

The total number of points Gwen earns.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Based on the diagram, the expression which shows the possible length of segment AB shows that 27 < AB < 81

A triangle that does not have equal sides and angles is known as a scalene triangle.

From the figure attached below, let's have a triangle ABC by using the parameter in the instructions given.

where;

We can use the Pythagoras rule to determine the side |AB|.

Pythagoras rule states that the sum of the hypotenuse squared is equal to both the sum of the opposite squared and adjacent squared.

hyp² = opp² + adj²

AC² = AB² + CB²

54² = AB² + 27²

\(\mathbf{AB^2 = 54^2 - 27^2}\)

\(\mathbf{AB^2 = 2187}\)

\(\mathbf{AB =\sqrt{ 2187}}\)

AB = 47

Therefore, we can conclude that the expression which shows the possible length of segment AB shows that 27 < AB < 81.

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Answer: 27<AB<81

Step-by-step explanation:

just took test

Answer:

The girls played 20 games.

Step-by-step explanation:

To fins how many games played. Divide the percentage lost by the number of games lost. Then divide the quotient from 100% to find how many games were played.

15% ÷ 3 = 5

100% ÷ 5 = 20 games

The parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to both the lines with equations  L1: (x, y, z) = (0, -10, -2) + s(4,6,-3) and L2: (x, y, z)=(5, 5, -5) + t(3, 2, 4) is given by: x= -6 + 18t,y= 4 - 39t, and z= 3 - 10t.

Let us first find the direction vector of the lines L1 and L2.

From line L1, the direction vector is given by:

d1= 4i + 6j - 3k

From line L2, the direction vector is given by:

d2= 3i + 2j + 4k

Now, let us find the vector that is perpendicular to both d1 and d2 by taking their cross product:

n= d1×d2= (4i + 6j - 3k)×(3i + 2j + 4k)

Simplifying this gives:

n= 18i - 39j - 10k

This is the normal vector of the plane that contains both lines L1 and L2.

Now, we want to find a line that passes through the point P(-6, 4, 3) and is perpendicular to this plane.

A line that is perpendicular to this plane is parallel to the normal vector.

So we can use this normal vector as the direction vector of the line we want to find.

The parametric equations of the line are:

x= -6 + 18t,y= 4 - 39t,z= 3 - 10t,where t is a parameter.

Thus, the answer is that the parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to both the lines with equations:

L1: (x, y, z) = (0, -10, -2) + s(4,6,-3) and

L2: (x, y, z)=(5, 5, -5) + t(3, 2, 4) is given by:

x= -6 + 18t,y= 4 - 39t, and z= 3 - 10t.

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Answer:

5%

Step-by-step explanation:

Percent error = (actual - estimated) / actual x 100

(240 - 228) / 240 x 100 = 5%

When a distribution is shown as a symmetrical bell-shaped curve then the mean, median, and mode are equal i.e., option (a) is correct.

A symmetrical bell-shaped curve, also known as a normal distribution or Gaussian distribution, is characterized by its symmetry around the mean.

In this type of distribution, the mean, median, and mode all coincide at the center of the curve.

This means that the central tendency measures, such as the mean (average), median (middle value), and mode (most frequent value), are all equal.

Option (a) states that the mean, median, and mode are equal, which aligns with the properties of a symmetrical bell-shaped curve. This equality occurs because the data is evenly distributed on both sides of the mean, resulting in a balanced distribution.

Options (b) and (d) suggest that the mean is either less than or greater than the median and mode, which does not hold true for a symmetrical distribution.

In a symmetrical distribution, the mean is located at the center of the data, and the median and mode share the same value as the mean.

Option (c) mentions moderate uniformity, but a symmetrical bell-shaped curve does not specifically indicate uniformity. Uniformity refers to a distribution where all data points have equal probability, resulting in a flat line.

In contrast, a symmetrical bell-shaped curve indicates a normal distribution with the majority of data concentrated around the mean, gradually decreasing towards the tails.

Therefore, based on the given options, option (a) is the correct conclusion when the distribution is shown as a symmetrical bell-shaped curve.

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Answer:

29.2 miles/gallon

Step-by-step explanation:

Given that,

Distance travelled, \(d=36\dfrac{1}{2}\) miles

Grace used \(1\dfrac{1}{4}\ \text{gallons}\) of gasoline

We need to find the unit rate for miles per gallon. It can be calculated by dividing no of miles by gallons of gasoline. So,

\(R=\dfrac{36\dfrac{1}{2}\ \text{miles}}{1\dfrac{1}{4}\ \text{gallon}}\\R=\dfrac{\dfrac{73}{2}}{\dfrac{5}{4}}\ \text{miles per gallon}\\\\R=\dfrac{73}{2}\times \dfrac{4}{5}\\\\R=29.2\ \text{miles per gallon}\)

Hence, the unit rate is 29.2 miles/gallon.

Answer: There will be 4977 bacteria present after 10 hours.

Step-by-step explanation:

The exponential function for continuous growth in t years is given by :-

\(P=Ae^{kt}\)   (i)

, where A = initial population, k= rate of growth.

As per given, A= 2000,  

After t= 2 hours, P=2400

Put these values in  (i), we get

\(2400=2000e^{2k}\\\\\Rightarrow\ 1.2=e^{2k}\)

Taking log on both sides

\(\ln 1.2=2k\\\\\Rightarrow\ k=\dfrac{\ln1.2}{2}=\dfrac{0.182321556794}{2}\\\\\Rightarrow\ k\approx0.09116\)

put value of A=2000, k= 0.09116 and t= 10 , we get

\(P=2000e^{0.09116\times10}\\\\=2000e^{0.9116}\\\\=2000\times2.4883\\\\=4976.6\approx4977\)

Hence, there will be 4977 bacteria present after 10 hours.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 4m.

\(3\leqslant |x+2|\leqslant 6\implies \begin{cases} 3\leqslant |x+2|\\\\ |x+2|\leqslant 6 \end{cases}\implies \begin{cases} 3 \leqslant \pm (x+2)\\\\ \pm(x+2)\leqslant 6 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(3\leqslant +(x+2)\implies \boxed{3\leqslant x+2}\implies 1\leqslant x \\\\[-0.35em] ~\dotfill\\\\ 3\leqslant -(x+2)\implies \boxed{-3\geqslant x+2}\implies -5\geqslant x \\\\[-0.35em] ~\dotfill\\\\ +(x+2)\leqslant 6\implies \boxed{x+2\leqslant 6}\implies x\leqslant 4 \\\\[-0.35em] ~\dotfill\\\\ -(x+2)\leqslant 6\implies \boxed{x+2\geqslant -6}\implies x\geqslant -8\)

The least-squares regression line is used to predict the values of one variable based on the values of the other variable. In this case, the Verbal score can be predicted from the Math score.

The formula for the least-squares regression line is: Verbal = a + b * Math, where a is the intercept and b is the slope. The least-squares regression line for predicting Verbal score from Math score can be determined using a calculator or a statistical software package.

Once the least-squares regression line has been determined, it can be used to make predictions about the Verbal score for a given Math score. For example, if a student scores 600 on the Math portion of the SAT, the least-squares regression line can be used to predict their Verbal score.

The least-squares regression line is a useful tool for analyzing the relationship between two variables. It can be used to identify patterns and trends, and to make predictions about future values.

However, it is important to remember that correlation does not equal causation, and that other factors may be influencing the relationship between the two variables. The least-squares regression line should be used as a starting point for further analysis, rather than as a definitive answer.

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Answer:

The distance from the boat to the foot of the lighthouse is 359.36 ft

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, From the top of a lighthouse 160 feet high, the angle of depression of a boat out at sea is 24.

The whole situation is representing a right triangle (refer to figure)

Let  the distance from the boat to the foot of the lighthouse be x

We know that, angle of depression = angle of elevation

Then, using formula of height and distance,

tan 24° = 160 / x

x = 160 / tan 24°

x = 359.36

Hence,  the distance from the boat to the foot of the lighthouse is 359.36 ft

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Answer:

3 Ducks

Step-by-step explanation:

Two ducks are in front of the last duck; the first duck has two

ducks behind; one duck is between the other two

Hence , there are 3 ducks

Hope it is correct

Answer: I think 7

Step-by-step explanation: Sorry if its wrong.

Notice:

2 is first term

2*4 = 8 is second term

8*4 = 32 is third term

and so on

Each term is multiplied by 4 to get the next term, so it’s geometric. The “common ratio” is whatever you’re multiplying by, which is 4.

The inequality in standard form that describes this situation is  10x + 57y < 999.

This refers to the relationship between two values that are not of the same value.

Solving the inequality, we have:

Let x be the number of b=racelets that can be made and y be the number of necklaces that can be made. The inequality in standard form that describes the situation is:

x = the number of bracelets

y = the number of necklaces

Number of beads / bracelets =10

Number of necklaces = 57

10x + 57y < 999.

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The statement lim n→∞ |Xₙ|/n ≤ C almost surely is equivalent to E|X| < ∞.

To show that lim n→∞ |Xₙ|/n ≤ C almost surely (where C > 0), if and only if E|X| < ∞, we can use the Borel-Cantelli Lemma and the Law of Large Numbers.

1. First, let's assume that lim n→∞ |Xₙ|/n ≤ C almost surely.
  - This means that the sequence of random variables |Xₙ|/n converges almost surely to a limit less than or equal to C.
  - By the Borel-Cantelli Lemma, if the sum of the probabilities of infinitely many events is finite, then the probability of those events occurring is zero.
  - Let Aₙ be the event { |Xₙ|/n > C }.
  - Since the limit of |Xₙ|/n is less than or equal to C almost surely, it implies that the probability of Aₙ occurring infinitely often is zero.
  - Therefore, the sum of the probabilities of Aₙ is finite.
  - Now, we can calculate the expected value of |X| using the definition of expectation: E|X| = ∫ |x| f(x) dx, where f(x) is the probability density function of X.
  - By the monotonicity property of the integral, we have: E|X| = ∫ 0∞ P(|X| > t) dt.
  - By the definition of Aₙ, we have: P(|Xₙ|/n > C) = P(|Xₙ| > nC).
  - Therefore, the sum of the probabilities P(|Xₙ| > nC) is finite, which implies that the expected value E|X| is finite.

2. Now, let's assume that E|X| < ∞.
  - By the Law of Large Numbers, we know that Xₙ/n converges in probability to E(X).
  - Since Xₙ/n converges in probability, it also converges almost surely to the same limit.
  - Therefore, lim n→∞ |Xₙ|/n = lim n→∞ |Xₙ|/n ≤ E|X|/n = 0 almost surely.
  - Since lim n→∞ |Xₙ|/n ≤ 0 almost surely, we can multiply both sides by -1 to obtain lim n→∞ |Xₙ|/n ≤ 0 almost surely.
  - By adding C to both sides, we get lim n→∞ |Xₙ|/n ≤ C almost surely.

In conclusion, the statement lim n→∞ |Xₙ|/n ≤ C almost surely is equivalent to E|X| < ∞.

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Using the fundamental counting principle, it is found that there are 24 different combinations she can wear.

The sweaters and the pants are independent, and this is why the fundamental counting principle is used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

Thus:

T = 6 * 4 = 24

There are 24 different combinations.

A combination in mathematics is a selection of items from a fixed that have amazing members, making the order of selection irrelevant (not like permutations). For instance, given a set of three fruits—say let's an apple, an orange, and a pear—one can choose between three combinations: an apple and a pear, an apple.

A hard and fast S's ok aggregate is, more precisely, a subset of S's ok amazing components. As a result, two combinations are equal if and best if each contains the same players. (The ties between the people in each group are not considered.)

(n/k) ={ n(n - 1) . . . (n – k + 1)}/{k(k - 1) . . . 1}

n!/{k!(n - k)!}

k > n.

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