A man depoited ghc 1200 in hi bank account. A imple interet of 20% per annum wa paid on hi depoit. Calculate the
a. Imple interet for the 4 year
b. Amount at the end of the 4 type

Vector w can be expressed as w=1u-2v as linear combination of vector u and v.

Vector equation would be w=Au + Bv

[1,1]=A[5,7] + B[2,3]

Here A and B are constants and we are trying to find their values.

We can split two equations as

1=5A+2B → equation a

1=7A+3B → equation b

Solving these equations by elimination method . Multiplying equation a with 3 and equation b with 2.

3=15A+6B

2=14A+6B

1=A → A=1

Putting value of A in equation b:

1=7+3B

1-7=3B

-6=3B

B=-6/3=-2

A = 1 and B = -2 . It means we can write w as 1u - 2v. We can recheck by plugging the values in any of the vector to confirm if the values are correct or not.

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A randomly selected subject has a 0.40 probability of completing more tasks than expected in 5 minutes while listening to relaxing music.

The Probability distribution is:

    X                     1                    2                3              4          

   P(x)             0.20          0.40      0.30             0.10

If listening to soothing music, the expected number of puzzles in 5 minutes can be calculated as follows:

            E(x) = ∑x p(x)

       ⇒ E(x) = 1 ×(0.20) + 2× 0.40 + 3 × 0.30 + 4× 0.1

       ⇒ E(x) = 0.20 + 0.8 + 0.9 + 0.4

       ⇒ E(x) = 2.3

Thus, a randomly selected subject could solve 5 puzzles while listening to soothing music. The probability of solving more tasks than expected in a minute is calculated as:

    P( X > 2.3) = P(X = 3) + P(X = 4)

                      = 0.30 + 0.10

                      = 0.40

Explanation for other  option:

(a) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music does not equal 0.1.

(c) 5 randomly selected participants. The probability of completing more tasks than expected in a minute of listening to relaxation music does not equal 0.8.

(d) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music is not equal to 1.

(e) The likelihood of randomly selected participants completing more tasks than expected in 5 minutes while listening to relaxing music cannot be determined.

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The length of the side KL for the given similar triangles rounded to the nearest tenth is 10.6 units.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects.

When two triangles are comparable, their respective sides and angles are equally spaced out and congruent. This is the property of similar triangles.

Given that the triangle GHI is similar to triangle JKL.

According to the property of similar triangles:

[tex]\frac{GH}{HI} = \frac{JK}{KL} \\\\\frac{45}{34} = \frac{14}{y} \\\\y= \frac{(14)(34)}{45} \\\\y= 10.577[/tex]

Rounding the value to the nearest tenth 10.57 is 10.6.

Hence, the value of side KL is 10.6 units.

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Depending on the comparable model, Energy Star appliances will save you 10% to 50% of the energy used;

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Using an energy efficient bulb will result in a significant cost saving over the long term.

Does utilising less energy cost less money?

A normal incandescent bulb uses 60W of power and lasts around 1000 hours, while a LED bulb uses around 8-12W of power and can last up to 25,000 hours.

So if you use the light 5 hours a day, 365 days a year, a 60W incandescent bulb will consume 11.25 kWh per year and cost you approximately £1.35 per year to run. In contrast, a 8W LED bulb will consume approximately 0.6 kWh per year, costing you approximately £0.072 per year to run.

Therefore, using an energy efficient bulb will result in a significant cost saving over the long term.

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The double integral. ∫∫R 2x/1 + xy dA, R = [0, 2] × [0, 1] is: 2*(1/2ln(3) - 1/2ln(1))

To calculate the double integral ∫∫R 2x/1 + xy dA, we need to integrate with respect to x and y over the region R = [0, 2] × [0, 1].

We can solve this by using the order of integration.

First we need to fix the limits of integration with respect to y and then integrate with respect to x.

∫∫R 2x/1 + xy dA = ∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy

∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy = ∫(0 to 1) ( 2*ln(1+xy)|x=0 to 2) dy

∫(0 to 1) ( 2ln(1+2y) - 2ln(1+0) ) dy

= 2*∫(0 to 1) ln(1+2y) dy

= 2*[y*ln(1+2y) - ∫(0 to 1) ln(1+2y) dy] |y = 0 to 1

= 2*[yln(1+2y) - (1/2 ln(3) - 1/2* ln(1))] |y = 0 to 1

= 2*(1ln(3) - 0ln(1) - 1/2* ln(3) + 1/2* ln(1))

= 2*(1/2ln(3) - 1/2ln(1))

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Answer:

According to phythagorian theorem

Hypotenus (square) = Base(square) + perpendicular (square)

H^2 = B^2 + P^2

now by substitution

H^2 = 9 +16

H^2 = 25

taking roots

Hypotenus= 5

Answer:

x^2 +xy+3x+2y+2

Step-by-step explanation:

(x+2)(x+y+1)

Apply the distributive property by multiplying each term of x+2 by each term of x+y+1.

x^2+xy+x+2x+2y+2

Combine x and 2x to get 3x

x^2 +xy+3x+2y+2

Answer: x^2+xy+3x+2y+2

Step-by-step explanation:

Expand and simplify

Step-by-step explanation:

5^(2x-1) = 1/125

5^2x = 5/125 => (1/25) = 5^2x

5^-2=5^2x

equating both sides

-2=2x

X=-1

hope this helps you.

By applying the first derivative of distance with respect to time, it can be concluded that the person is walking 4/3 meters per second.

Instantaneous velocity or rate is the first derivative of distance with respect to time. Mathematically it is written v = ds/dt, where v is the velocity, s is the distance and t is the time.

First, we make a simple drawing using the given information:

The walking person = 2 meters tall

The street light = 8 meters above the ground

The walking rate is constant

The person's shadow lengthening rate = 4/9 meter per second = dy/dt

We want to know the walking rate, dx/dt.

We determine the value of y:

8 / 2 = (x + y) / y

  8y = 2x + 2y

  6y = 2x

    y = x / 3

Then we substitute the value of y into the equation:

dy/dx = d(x/3) / dx

         = 1/3

Finally, we can get the rate dx/dt:

dx/dt = dy/dt * dx/dy

         = 4/9 * 3

         = 4/3

Thus, it can be concluded that the person is walking 4/3 meters per second.

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If you are asked to find the 85th​ percentile, you are being asked to find an area corresponding to a​ z-score of 0.8.

The term percentile in math is defined as the area to the left of a particular data value.

According to the definition of percentile, here they are asking about the 85th percentile.

As we all know that​ z-score is not an area under the normal curve and the distances along the horizontal axis are represented by​ z-scores where as the regions under the curve are represented by areas.

Therefore, in order to find the z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution.

Then we have to convert the given percent into decimal form, then we get it as,

=> 85% = 0.85

Here we need to find the value from the z table then we get the resulting value as 0.8.

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Answer:

[tex]-11\sqrt{5}-11\sqrt{6}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{11}{\sqrt{5}-\sqrt{6}}[/tex]

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of a binomial is where we change the sign between the two terms of the binomial.  So the conjugate of (√5 - √6) is  (√5 + √6).

[tex]\implies \dfrac{11}{\sqrt{5}-\sqrt{6}} \cdot \dfrac{\sqrt{5}+\sqrt{6}}{\sqrt{5}+\sqrt{6}}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{(\sqrt{5}-\sqrt{6})(\sqrt{5}+\sqrt{6})}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{\sqrt{5}\sqrt{5}+\sqrt{5}\sqrt{6}-\sqrt{6}\sqrt{5}-\sqrt{6}\sqrt{6}}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{5-6}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{-1}[/tex]

[tex]\implies -11(\sqrt{5}+\sqrt{6})[/tex]

[tex]\implies -11\sqrt{5}-11\sqrt{6}[/tex]

Answer: Ratios are proportional if they represent the same relationship.

Step-by-step explanation:

One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

Answer: In five days, there will be around 2,476 bacteria.

Step-by-step explanation: Using the hint given, simply plug in the numbers to calculate the predicted amount of bacteria. Hope this helps!

[tex]100(1+0.9)^{5}=2,476.099[/tex]

Answer:

2476

Step-by-step explanation:

Given formula:

[tex]\textsf{Future Amount}=\sf I(1+r)^t[/tex]

Given values:

Substitute the given values into the given formula and solve:

[tex]\begin{aligned}\implies \textsf{Future Amount}& =\sf 100(1+0.9)^5\\& =\sf 100(1.9)^5\\& =\sf 100(24.76099)\\& =\sf 2476.099\\& =\sf 2476\;(nearest\;whole\;number)\end{aligned}[/tex]

Answer:

mt =84

mns = 78

Step-by-step explanation:

since mn=124 , ns=80 , ts=72

then mt= 360-(124+80+72)=84

if we draw a line from m to s

then angle msn=124÷2=62 (inscribed angle)

and angle smn=80÷2=40 ( // // )

then angle mns=180-(62+40)=78

Answer:

Step-by-step explanation:

none of these the corrct answer is 5

Answer:

Step-by-step explanation:

Let, f(x) = y

y = 5 + √(5x - 3)

((y - 5)² = 5x + 3

y² - 10y + 25 - 3 = 5x

x = (y² - 10y +22)/5

so, [tex]f^{-1} (y)[/tex] = (y² - 10y +22)/5

[tex]f^{-1} x[/tex] = (x² - 10x + 22)/5

Both the wristband and a conventional blood test were used to measure the blood sugar of a random sample  selected group of individuals from the neighborhood at random times throughout the day.

selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.

Both the wristband and a conventional blood test were used to measure the blood sugar of a random sample  selected group of individuals from the neighborhood at random times throughout the day.

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The advantage does a Mercedes g class 6x6 squared have compared to the 4x4 squared for off road driving is explained below.

The term class in math is used to define a grouping of values by which data is binned for computation of a frequency distribution

Here we have to find the advantage does a Mercedes g class 6x6 squared have compared to the 4x4 squared for off road driving

Where we all know that in a 4x4 Transfer Case there is a 50:50 split between Front and Rear axles on the other had in a 6x6 we have the Transfer Case splits the torque 33:66 between Front & Rear Axles.

Then the next one is known as intricate rear Suspension such as Short Radius Arms and coil Springs or elliptical leaf springs/Inverted Leaf Springs.

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Answer:

[tex]\textsf{1)} \quad y=x+\dfrac{17}{4}[/tex]

[tex]\textsf{2)} \quad y=2x+4[/tex]

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.

At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

[tex]y=4+2x-x^2[/tex]

Differentiate the given function:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2-2x[/tex]

If the tangent to the parabola forms an angle of 45° with the negative direction of the x-axis, then the gradient of the tangent is 1.

Set the differentiated function to 1 to find the x-value of the point where the gradient of the tangent is 1:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=1[/tex]

[tex]\implies 2-2x=1[/tex]

[tex]\implies -2x=-1[/tex]

[tex]\implies x=\dfrac{1}{2}[/tex]

Substitute x = 1/2 into the given function to find the y-value of the point:

[tex]\implies y=4+2\left(\dfrac{1}{2}\right)-\left(\dfrac{1}{2}\right)^2=\dfrac{19}{4}[/tex]

Therefore, the point at which the tangent of the parabola forms an angle of 45° with the negative direction of the x-axis is:

Substitute the found point and slope into the point-slope formula to create an equation of the tangent:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-\dfrac{19}{4}=1\left(x-\dfrac{1}{2}\right)[/tex]

[tex]\implies y=x+\dfrac{17}{4}[/tex]

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

Given function:

[tex]y=4+2x-x^2[/tex]

Differentiate the given function:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2-2x[/tex]

If the tangent to the parabola is parallel to the line y = 2x - 4 then the gradient of the tangent is 2 (since parallel lines have the same gradient).

Set the differentiated function to 2 to find the x-value of the point where the gradient of the tangent is 2:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2[/tex]

[tex]\implies 2-2x=2[/tex]

[tex]\implies -2x=0[/tex]

[tex]\implies x=0[/tex]

Substitute x = 0 into the given function to find the y-value of the point:

[tex]\implies y=4+2\left(0\right)-\left(0\right)^2=4[/tex]

Therefore, the point at which the tangent of the parabola is parallel to the line y = 2x - 4 is:

Substitute the found point and slope into the point-slope formula to create an equation of the tangent:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-4=2\left(x-0\right)[/tex]

[tex]\implies y=2x+4[/tex]

The area of the trapezoid is 210  squared '

The area of a trapezoid be be calculated using the formula:

A = 1/2(a+b)h

where:

a is the length of one of the parallel sides of the trapezoid

b is the length of the other parallel side of the trapezoid

h is height is the distance between the two parallel sides (perpendicular to the bases)

a = 12', b = 18 + 5 = 23' and h = √(13²-5²) = 12'

A = 1/2(a+b)h

A = 1/2(12+23)12

A = (35)6

A = 210  squared '

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Answer:

Car B has the best rate

Step-by-step explanation:

A:  450 mi / 15 gal = 30 mi/gal

B:  651 mi / 21 gal = 31 mi/gal

C:  598 mi / 23 gal = 26 mi/gal

31 > 30 > 26

Answer:Car B has the best rate at 31 miles per gallon

Step-by-step explanation:  i did my math

 If a symmetric matrix can be inverted into a diagonal matrix using another matrix, then it is diagonalizable. Accordingly, it may be said that there is a matrix P that can be inverted such that P-1 * A * P = D, where D is a diagonal matrix and A is the symmetric matrix. The diagonal entries of D are the appropriate eigenvalues, while the columns of P are the eigenvectors of A.

  The matrix P is the foundation of the vector space because its columns are linearly independent and it is invertible. The inner product of any two different eigenvectors is 0, as A's eigenvectors are orthogonal to one another due to its symmetry.

 We can divide each eigenvector by its norm to get an orthonormal basis from this collection of eigenvectors. As a result, a group of eigenvectors that are orthonormal to one another and serve as the vector space's orthonormal basis are produced.

  Therefore, A symmetric matrix is diagonalizable and has an orthonormal eigen basis  consisting of orthonormal eigenvectors, which can be obtained by dividing each eigenvector by its norm.

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The number of non-similar 1000-pointed stars is

[tex]$\frac{1000-600-2}{2}= \boxed{199}.$[/tex]

If we join the adjacent vertices of the regular [tex]$n$[/tex]-star, we get a regular [tex]$n$[/tex][tex]-gon[/tex]. We number the vertices of this [tex]$n$[/tex][tex]-gon[/tex] in a counter clockwise direction: [tex]$0, 1, 2, 3, \ldots, n-1.$[/tex]

A regular [tex]$n$[/tex]-star will be formed if we choose a vertex number m where [tex]$0 \le m \le n-1$[/tex], and then form the line segments by joining the following pairs of vertex numbers:[tex]$(0 \mod{n}, m \mod{n}),$ $(m \mod{n}, 2m \mod{n}),$ $(2m \mod{n}, 3m \mod{n}),$ $\dots,$ $((n-2)m \mod{n}, (n-1)m \mod{n}),$ $((n-1)m \mod{n}, 0 \mod{n}).$[/tex]

If [tex]$\gcd(m,n) > 1$[/tex], then the star degenerates into a regular [tex]$\frac{n}{\gcd(m,n)}$-gon[/tex] or a (2-vertex) line segment if [tex]$\frac{n}{\gcd(m,n)}= 2$[/tex]. Therefore, we need to find all $m$ such that [tex]$\gcd(m,n) = 1$.[/tex]

Note that [tex]$n = 1000 = 2^{3}5^{3}.$[/tex]

[tex]Let $S = \{1,2,3,\ldots, 1000\}$, and $A_{i}= \{i \in S \mid i\, \textrm{ divides }\,1000\}$. The number of $m$'s that are not relatively prime to $1000$ is: $\mid A_{2}\cup A_{5}\mid = \mid A_{2}\mid+\mid A_{5}\mid-\mid A_{2}\cap A_{5}\mid$ $= \left\lfloor \frac{1000}{2}\right\rfloor+\left\lfloor \frac{1000}{5}\right\rfloor-\left\lfloor \frac{1000}{2 \cdot 5}\right\rfloor$ $= 500+200-100 = 600.$[/tex]

[tex]Vertex numbers $1$ and $n-1=999$ must be excluded as values for $m$ since otherwise a regular n-gon, instead of an n-star, is formed.[/tex]

The cases of a 1st line segment of (0, m) and (0, n-m) give the same star. Therefore we should halve the count to get non-similar stars.

Therefore, the number of non-similar 1000-pointed stars is

[tex]$\frac{1000-600-2}{2}= \boxed{199}.$[/tex]

[tex]Note that in general, the number of $n$-pointed stars is given by $\frac{\phi(n)}{2} - 1$ (dividing by $2$ to remove the reflectional symmetry, subtracting $1$ to get rid of the $1$-step case), where $\phi(n)$ is the Euler's totient function.[/tex] [tex]It is well-known that $\phi(n) = n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)\cdots \left(1-\frac{1}{p_n}\right)$, where $p_1,\,p_2,\ldots,\,p_n$ are the distinct prime factors of $n$.[/tex] [tex]Thus $\phi(1000) = 1000\left(1 - \frac 12\right)\left(1 - \frac 15\right) = 400$, and the answer is $\frac{400}{2} - 1 = 199$.[/tex]

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The required inequality describes for the given problem is  x < 8.5.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

she used 3.5 pounds of the wax to make vanilla-scented candles and has less than 5 pounds of wax left to make orange-scented candles.

let x represent the weight of the block of wax originally

then,inequality can be written as,

x - 3.5 < 5

x < 8.5

Thus, required inequality is x < 8.5.

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Answer:

(6-squarre root 8)^2 = 10.058874

Answer: [tex]90^{\circ}[/tex]

Step-by-step explanation:

By the converse of the alternate interior angles theorem, we need [tex]\angle CBA \cong \angle BAD[/tex].

Answer:

so the square root is x so when you point the square root at the rwaterfall you waill have your

Step-by-step explanation:

the drone would need to be 1.4 miles away from your to be the opposite value. pou pou pou pou pou pou pou pou pou pou pou pou ufo p

Step-by-step explanation:

Answer:

720 Should be the answer I think.