Sam invests £1800 in the bank for four
years.
It earns compound interest of 4% each year.
Calculate the total amount Sam has in the
bank at the end of four years (£ round to
2 dp).

The values of determinant ,

\(\left|\begin{array}{ccc}3a&3b&3c\\-d&-e&-f\\4g&4h&4i\end{array}\right| = 72\)

\(\left|\begin{array}{ccc}a&b&c\\2d&2e&2f\\g+3a&h+3b&+3ci\end{array}\right| = - 12\)

The given determinant is,

\(\left|\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right| = -6\)

This is possible when we take,

a = -1 , e = 1, i = 6, b = c = 1

And d = g = h = 0

The the determinant becomes,

\(\left|\begin{array}{ccc}-1&1&1\\0&1&1\\0&0&6\end{array}\right|\)

Since this is an upper triangular matrix,

Therefore,

Determinant be the product of diagonal element,

Thus,

⇒  -1x1x6 = -6

Now using these values we can calculate the further given determinants,

Q4: Given that,

\(\left|\begin{array}{ccc}3a&3b&3c\\-d&-e&-f\\4g&4h&4i\end{array}\right|\)

Therefore put the values of a, b, c, d, e, f, g, h, and i defined above,

\(\left|\begin{array}{ccc}3(-1)&3(1)&3(1)\\0&-1&-1\\0&0&4(6)\end{array}\right|\)

Therefore, Determinant be,

⇒ -3 x  (-1) x 24 = 72

Hence,

\(\left|\begin{array}{ccc}3a&3b&3c\\-d&-e&-f\\4g&4h&4i\end{array}\right| = 72\)

Q5 : Given determinant is,

\(\left|\begin{array}{ccc}a&b&c\\2d&2e&2f\\g+3a&h+3b&+3ci\end{array}\right|\)

put the values of a, b, c, d, e, f, g, h, and i defined above,

we get,

\(\left|\begin{array}{ccc}-1&1&1\\0&2&2\\-3&3&9\end{array}\right|\)

= -1(12) -1(6) + 1(6)

= -12

Hence, The determinant be

\(\left|\begin{array}{ccc}a&b&c\\2d&2e&2f\\g+3a&h+3b&+3ci\end{array}\right| = - 12\)

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The complete question is attached below:

Answer:

22 months

Step-by-step explanation:

variable x = number of months

800 + 100x = 3000

isolate the variable x

100x = 3000 - 800

100x = 2200

x = 2200 ÷ 100

x = 22

Answer:

15

Step-by-step explanation:

Replace each instance of 'x' with '(-6):'

f(-6) = 3 - 2(-6)

       = 3 + 12 = 15

Answer:

6.3 x 10= 63

6.3 x 10= 630

6.32 x 10= 63.2

6.32 x 100= 632

Step-by-step explanation:

Move the decimal to the right however many zeros there are in the whole number

The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.

Given:

The volume of closed right circular cylindrical cans = 128π cm³

As we know the volume of a cylinder = πr²h

By equating;

πr²h = 128π

h = 128/r²

To get the dimensions of a can with minimum surface area;

S = 2πrh + 2πr

Put h = 128/r²;

Therefore, S(r) = 256π/r + 2πr²

                 S'(r) =  -256π/r² + 4πr

                S''(r) = -(2*256π)/r³ + 4π

Now, for S(r) = 0;

               r = 4cm

         for S''(4) > 0 at r = 4 is minimum point.

Hence,

h = 128π/(π*4*4)

h = 8cm

Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.

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Expression -4/-9 equals fraction numerator 9 minus 4 in math.

Fraction definition:

It has two negative numbers, hence the result will be the same because of the rule, which is why it is equivalent (minus times minus is equal to zero)

4/9= -4/-9

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6. Applying the inscribed angle theorem, x = 33

7. m<ABP = 90°.

m<APB = 48°

The tangent theorem states that the tangent of a circle is perpendicular to the radius of that circle and therefore forms a right angle at the point of tangency.

An inscribed angle has a measure that is half the measure of the intercepted arc, according to the inscribed angle theorem.

Therefore:

Question 6:

Based on the inscribed angle theorem,

Measure of arc AB = 2(x + 3) = 2x + 6

108 + 2x + 6 = 180 [semicircle]

Solve for x

114 + 2x = 180

2x = 180 - 114

2x = 66

x = 33

Question 7:

Given that line PB is tangent to circle A, therefore, based on the tangent theorem, the measure of angle ABP = 90°.

m<APB = 180 - 90 - 42

m<APB = 48°

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Answer:

The equation x²+12x+43=0 is a quadratic equation that can be solved by factoring or using the quadratic formula.

Factoring the equation:

x²+12x+43=(x+7)(x+6)=0

x+7=0 or x+6=0

x=-7 and x=-6

Therefore, the solutions for the equation are x=-7 and x=-6.

Alternatively, you can use the quadratic formula:

x = (-b± √(b²-4ac))/2a

Where a=1, b=12, c=43

x = (-12± √(12²-4143))/2*1

x = (-12± √(144-172))/2

x = (-12± √(-28))/2

x = (-12± i*√28)/2

x = (-12+ i2√7)/2 or x = (-12- i2√7)/2

These solutions are complex numbers, x = (-6+2i√7) or x = (-6-2i√7)

The expression for the magnetic flux through the hemispherical surface of the bowl is EπR².

Hemisphere:

The word hemisphere can be divided into hemisphere and sphere. Hemisphere means half, and sphere means three-dimensional shape in mathematics. Thus, a hemisphere is a three-dimensional geometric shape that is a hemisphere that is flat on one side and a round bowl on the other. It is formed when a sphere is cut exactly down the center along its diameter, leaving two identical hemispheres.

The volume of a hemisphere is the number of unit cubes that can fit inside it. The units of volume are cubic units, such as m³, cm³, ft³ and so on.

The volume of a hemisphere = 2/3πr³

where

r is the radius of the hemisphere.

According to the Question:

Flux passing through the curved surface is equal to the flux passing through the flat surface.

Since flux through the flat surface    

ϕ flat = E× Area

         = E× πR²

The electric flux through a closed surface is 1/E₀ times the total charge unclosed.

By Gauss's law, flux ,

Since number of field lines entering from circular side is equal to number of field lines leaving the hemispherical surface, net flux is 0.

Therefore,

(Flux)h + (flux)c = 0     -------------------------(1)

[* (flux)h means flux from hemispherical surface and (flux)c means flux from circular surface]

Therefore,

(flux)h = - (flux)c     ---------------------------- (2)

Flux = E.A [ Where E and A are vectors ]

Flux = E A cos θ

(Flux)c = EA cos π [ Because field and surface area vector are anti parallel]

(flux)c = E πR² (-1)    ------------------------------ (3)

From equation (2) and (3)

   (flux)h = - (- EπR²)

⇒ (Flux)h = EπR²

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The volume of the rectangular box is 12 m3. We can't find the exact value of h because it is not given. So, the answer in terms of h is 12 h m3.

Given the area of the box as 12 m and the length of the box as 6 m, we need to find the volume of the rectangular box. The volume of the rectangular box can be found by multiplying the area of the base by its height.

That is, V = l  b  h, where l = 6 m, b =?, and h =?

As the area of one of the sides of the box is given as 12 m²,

we have:

Area of the base of the box = 12 m²

Area of the base of the box = l × b

6 m × b

= 12 m²b

= 12 m²/6 mb

= 2 m

Now we know that the base of the box is 2 m by 6 m, and the height of the box can be anything.

Thus, the volume of the rectangular box is:

V = l × b × h

V = 6 m × 2 m × h

V = 12 m²h

Therefore, the volume of the rectangular box is 12 m3. We can't find the exact value of h because it is not given. So, the answer in terms of h is 12 h m3.

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The red harvester ant is closer to ground level.

The relative distance is defined as the product of the relative distance multiplied by the specified time. The relative distance unit is the same as the length unit.

Distance is typically defined as the amount of space between two locations that can be measured. In geography, a few different types of distance are used to explain not only the physical distance between two points but also the variations in distinct racial and ethnic groups, cultural traditions, political ideals, and social mores. A unique unit of measurement known as relative distance is used in geography to explain a variety of societal aspects.

As it has dug deeper (more negative) than the black garden ant. The number -20 39/50 is more negative than -20 7/9.

Therefore, The red harvester ant is closer to ground level.

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To identify the vertical asymptotes, we have to factor the denominator. For horizontal asymptotes, we compare the degrees of the numerator and denominator.

For rational functions, there are vertical and horizontal asymptotes. To identify the vertical asymptotes, we first have to factor the denominator. After that, we should look for values that make the denominator zero. These values can be found by setting the denominator equal to zero and solving for x. The resulting x values would be the vertical asymptotes of the function.

The horizontal asymptote is the line that the function approaches as x goes towards infinity or negative infinity. For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and the denominator.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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question: An investment of $100 is now valued at $149.18 the interest rate is 8% per year, compounded continuously about how long has the money been invested

Answer:

5.2 years

Step-by-step explanation:

Applying

A = P(1+R/100)ⁿ.......................... Equation 1

Where A = amount, P = principle, R = rate, n = time.

From the question,

Given: A = $149.18, P = $100, R = 8%

Substitute these values into equation 1 and solve for n

149.18 = 100(1+8/100)ⁿ

149.18/100 = (1+8/100)ⁿ

1.4918 = (1+0.08)ⁿ

1.4918 = (1.08)ⁿ

Taking the Logarithm of both side

Log(1.4918) = Log(1.08)ⁿ

Log(1.4918) = nLog(1.08)

n = Log(1.4918)/Log(1.08)

n = 0.1737/0.0334

n = 5.2 years.

The plotting of (-4,-11) coordinates is given below in the graph .

We have given a coordinate (-4,-11) which means that x - coordinate is -4 and y- coordinate is -11 .

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The complete question is mention below :

Plot (-4,-11) coordinates over the x -axis and y-axis .

Answer:

A.

Step-by-step explanation: Because as you see the dot is past the 2 and is on the third line out of 4, the 4th line is the next number.

a0 is the regression term that describes the constant or intercept in the linear regression equation.

In a simple linear regression model, the equation takes the form of y = a0 + a1x + e1, where y is the dependent variable (or response variable), x is the independent variable (or predictor variable), a0 is the intercept or constant term, a1 is the coefficient of the independent variable, and e1 is the error term.

The intercept term, a0, represents the value of the dependent variable when the independent variable is zero. For example, in a linear regression model that predicts salary based on years of experience, the intercept would represent the starting salary for someone with zero years of experience. The intercept is an important component of the regression equation because it allows us to make predictions for values of x that are outside the range of our observed data.

The coefficient, a1, represents the change in the dependent variable for each one-unit increase in the independent variable. In the salary example, the coefficient would represent the average increase in salary for each additional year of experience.

Both the intercept and coefficient are estimated from the data using methods such as least squares regression. Once these values are estimated, we can use them to make predictions for new values of x.

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Answer: 55

Step-by-step explanation:

90+x+15+3x-5=180

Combine like terms

100+4x=180

Subtract 100 from both sides

4x=180

Divide by 4

X=20

Insert into equation

3(20)-5

=55

Answer:

15% & 3/20

Step-by-step explanation:

convert decimals to % by multiplying by 100

.15 * 100 = 15%

15/100

simplify

3/20

Answer:

0.15= 15%  

0.15= 15/100

Step-by-step explanation:

0.15 - move the point two times to the right and you have 15 so it will be 15%

15 percent - 15 per cent percent=100 so it will be 15 out of 100 which is the same as 15/100

Answer:

The interest is 634.13.

Step-by-step explanation:

Amount deposit , P = 5000

Interest, R = 4 % so, R = 4/4 = 1 %

Time, T = 3 years quarterly

n = 3 x 4 = 12

Let the amount is A.

Use the formula of the compound interest

\(A = P \left ( 1 + \frac{R}{100} \right )^n\\\\A = 5000 \left ( 1 + \frac{1}{100} \right )^{12}\\\\A = 5634.13\)

So, the interest is

I = A - P = 5634.13 - 5000 = 634.13

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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Work Shown:

Let x be the location of E on the number line.

Since C is the midpoint of E and F, this means we can find C's location by adding E and F together and dividing that sum by 2

midpoint = (endpoint1 + endpoint2)/2

C = (E+F)/2

Plug in E = x, C = -8 and F = 4. Then solve for x

C = (E+F)/2

-8 = (x+4)/2

(x+4)/2 = -8

x+4 = 2(-8) .... multiplying both sides by 2

x+4 = -16

x = -16-4 .... subtract 4 from both sides

x = -20

The location of point E on the number line is -20

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

As a check, lets add E and F to get E+F = -20+4 = -16

Then cut this in half to get -16/2 = -8, which is the proper location of point C

This confirms our answer.

Answer:

101

Step-by-step explanation:

101 X 8 = 808

Answer:

101

Step-by-step explanation:

The answer is one hundred and one (101)

Answer:

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A 0 degree and 90 degree can form a pair of complementary angles, but 90 degree and an angle that is not adjacent cannot form a pair of complementary angles.

In mathematics, complementary angles are two angles whose sum is 90 degrees. So, if one angle is 0 degrees, the other angle would have to be 90 degrees in order for them to be complementary. However, if one angle is 90 degrees, it cannot form a pair of complementary angles with an angle that is not adjacent (i.e. next to it).

To understand why, consider a straight line, which is equivalent to 180 degrees. If one angle is 90 degrees, it takes up half of the line, leaving the other half for the other angle.

If the other angle is not adjacent, it would have to be placed somewhere on the other half of the line, which is already taken up by the 90 degree angle. Therefore, the two angles cannot add up to 90 degrees and cannot be complementary.

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Answer:

\(\frac{5}{6}\)

Step-by-step explanation:

To find the slope, use the equation to find slope. The picture below shows what it looks like.

Using the equation, substitute the values in the x and y values.

Then solve

Answer:

l

Step-by-step explanation:

The correct option is -2. The range of function is found to be minimum is -2.

A function's global minimum is its lowest value across the entire function's range, whereas a localized minimum is its lowest value within a specific local area.

From the given graph of the function:

To get the lowest point of the range of the function, check the value where graph is turning.

This, shows the minima of the function which is -2 at x = 3.

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