You deposit $500 in an account that earns 6.5% annual interest compounded yearly. Write a function that represents the balance y (in dollars) after x years.

The product of a complex number and its conjugate is (a + i b) · (a - i b), where a and b are real numbers, and the result for the complex number 2 + i 3 is 13.

Let be a complex number a + i b, whose conjugate is a - i b. Where a and b are real numbers. The product of these two numbers is:

(a + i b) · (a - i b)

Then, we proceed to obtain the result by some algebraic handling:

a · (a + i b) + (- i b) · (a + i b)

a² + i a · b - i a · b - i² b²

a² - i² b²

a² + b²

If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:

[tex]z\cdot \bar z = 2^{2} + 3^{2}[/tex]

[tex]z\cdot \bar z = 13[/tex]

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The length of the brace required is 4.3m

What is sine rule?

In a ΔABC a, b and c are the sides and A, B and C are angles then,

[tex]\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

We can find the length, l as shown below:

Let AB=3m, BC=2m and AC=l

Let ∠A=25°

So, in ΔABC

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}[/tex]

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}[/tex]

[tex]\frac{2}{sin25}=\frac{3}{sinC}[/tex]

[tex]\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )[/tex]

∠C=39.34°

∠A+∠B+∠C=180°

∠B=180°-25°-39.34°

∠B=115.66°

[tex]\frac{BC}{sinA}=\frac{AC}{SinB}[/tex]

[tex]\frac{2}{sin25}=\frac{l}{sin(115.66)}[/tex]

[tex]l=\frac{2\times sin(115.66)}{sin25}[/tex]

l=4.2659

Rounding to nearest tenth of meter.

l=4.3m

Hence, the length of the brace required is 4.3m

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The distance travelled is 10 m

The velocity gained at the end of the time is 2 m/s

From the question, we are to determine distance travelled and the velocity gained

From one of the equations of motion for linear motion, we have that

S = ut + 1/2at²

Where S is the distance

u is the initial velocity

t is the time taken

and a is the acceleration

First, we will calculate the acceleration

Using the formula,

F = ma

Where F is the force

m is the mass

and a is the acceleration

∴ a = F/m

Where F is the force

and a is the acceleration

From the given information,

F = 50 N

m = 250 kg

Putting the parameters into the equation,

a =  50/250

a = 0.2 m/s²

Thus,

From the information,

u = 0 m/s (Since the object was initially at rest)

t = 10 s

S = 0(t) + 1/2(0.2)(10)²

S = 10 m

Hence, the distance travelled is 10 m

For the velocity

Using the formula,

v = u + at

Where v is the velocity

v = 0 + 0.2×10

v = 2 m/s

Hence, the velocity gained at the end of the time is 2 m/s

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Here,

y=mx+c

the slope of the line 6x+4y= -16 is -20.

if the two lines are perpendicular, the slope of 1st line * slope of second line=-1

the slope of the 2nd line is -1/2

y-y1=m(x-x1)

y-13=-1/2(x- -18)

when you solve, you get the equation of the line as 2y+x=50

In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.

If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.

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Answer:

2 hours

Step-by-step explanation:

4 square yards to feet: 4*3 = 12ft

3 cows grazing grass at 2 ft per hour: 2*2 = 6 square ft per hour

Time taken: 12ft/6ft per hour = 2 hours

Answer:

150g for 6 servings

x grams for 15 servings

150/6 = 25

15 x 25 = 375

375g of sugar will be required to make 15 servings.

Option 2) the first set of data has values that are closer to the mean because the standard deviation is lower is correct

If two samples have the same mean, then it means that the two values in the two samples are centered around the same value. However, this does not mean that the data values in the samples vary equally around this center and thus the standard deviations may also differ.

It depends what the standard deviations are. The standard deviation is a measure of how close the results are to the mean, a low standard deviation means that the measurements are accurate, so close to the mean. A high standard deviation means that the measurements are more spread out.

We need to find that if two sets of data both have a mean of 76. however, the first set has a standard deviation of 1.4 and the second set has a standard deviation of 5.7. what must be true about the two sets

The first set of data has values that are closer to the mean because the standard deviation is lower because in first set standard deviation is 1.4 and in second set standard deviation is 5.7

The one with smaller standard deviation are least spead from the mean

Hence the first set of data has values that are closer to the mean because the standard deviation is lower.

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The y-intercept which is the point at which x = 0 is; A: -10

The general form of an equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given the slope;

m = -4

Now, the line passes through the point 0, -10. Thus;

(y - y1)/(x - x1) = -4

(y + 10)/(x - 0) = -4

y + 10 = -4x

y = -4x - 10

Thus, the y-intercept which is the point at which x = 0 is; y = -10

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It is important to be able to express a clear and coherent argument visually or in writing because without establishing coherence, your reader will not be able to know or understand the key points that you are trying to express or show.

Coherence is known to be a key quality for kind of good academic write up.

Note that in the area of academic writing, the ways that ideas flows is very important and as such, it need to be smooth and logical.

Therefore  without coherent argument , the reader cannot understand the key points that a person is trying to show and thus hinders the readability of your work.

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Answer:

Step-by-step explanation:

Substitution is a method that rewrites one of the equations in terms of one variable, and substitutes that in the other equations.

We can easily rewrite x + y = 6 by subtracting y from both sides, giving us

[tex]x = -y+6[/tex]

By putting this equation in place of x in the first equation, we can solve for y:

[tex]4(-y+6)-2y=6[/tex]

[tex]-4y+24-2y=6[/tex] [Distributing 4 into the parentheses]

[tex]-6y+24=6[/tex] [Combining like terms]

[tex]-6y = -18[/tex] [Subtracting 24 from both sides]

[tex]y=3[/tex] [Dividing both sides by -6]

Since we solved for y, we can again substitute by putting it into the second equation.

[tex]x+3=6[/tex]

[tex]x=3[/tex] [Subtracting 3 from both sides]

The solution for this system of equations is (3,3).

Elimination is another method of solving systems of equations. In this method, we multiply one equation such that when both equations are combined, only one variable is left.

We can first multiply both sides of the second equation by 2.

[tex]2x+2y=12[/tex]

Now, let's add both equations to cancel out y.

[tex]4x-2y=6[/tex]

[tex]2x+2y=12[/tex]

[tex]6x=18[/tex]

Now, we can divide 6 from both sides to get the value of x.

[tex]\frac{6x}{6} = \frac{18}{6}[/tex]

[tex]x=3[/tex]

We can now substitute this value into one of the equations to get the value of y. Here, I used the second equation.

[tex]3+y=6[/tex]

[tex]y=3[/tex]

The solution to our system of equations is (3,3).

Answer:

10 m

Step-by-step explanation:

If we draw the diagonal of the rectangle, we form a right triangle where the diagonal is the hypotenuse and the legs are 6 and 8.

This is a well-known Pythagorean triple, which gives the diagonal to be 10 m.

Barack be able to bring 1029 dirham with him.

The amount of one currency needed to buy items in another is shown by conversion rates.

Currency rates and spot prices on the foreign exchange market are comparable to conversion rates.

In relation to supply and demand, conversion rates are impacted.

Governments and central banks implement policies in response to supply and demand dynamics that affect the conversion rate.

According to the question,

The conversion rate from cad to uae dirham is 2.94

Money, in dirham,  Barack would be able to bring with him,

=(350*2.94) dirham

=1029 dirham

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Answer: 115.5 cubic m

Step-by-step explanation:

[tex]V=\frac{1}{2}(7)(11)(3)=115.5[/tex]

ANSWER - The first seems more accurate according to my view it's A

Answer:

f[g(x)] = 6x + 47

Step-by-step explanation:

The expression f[g(x)] represents a composite function. You need to plug the function g(x) into the "x" value of the f(x) function. Then, you can simplify.

f(x) = 6x + 11               g(x) = x + 6

f[g(x)]                                                    <----- Composition expression

f[g(x)] = 6(x + 6) + 11                             <----- Plug g(x) into x

f[g(x)] = 6x + 36 + 11                             <----- Multiply terms in parentheses by 6

f[g(x)] = 6x + 47                                  <----- Add 36 and 11

Applying the area of a rectangle, the cost to make the part of the compass is: $129.85.

Area of a triangle = 1/2(base)(height).

Find the height of the triangle using the Pythagorean theorem:

Height = √(5² - 1²) ≈ 4.9 cm.

Base = 2 cm

Area of the two triangles = 2[1/2(base)(height)]

Area of the two triangles = 2[1/2(2)(4.9)] = 9.8 cm².

Cost to to make this part of the compass = 9.8 × $13.25 = $129.85.

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Answer: 129.82

Step-by-step explanation: its on edge I got it right :)

Answer:

1083 seats

Step-by-step explanation:

i just answered that.

arithmetic sequence

a1 = 10

an = an-1 + 1 = a1 + (n-1)×1 = 10 + (n-1) = 9 + n

a38 = 9 + 38 = 47 seats

the sum of such an arithmetic sequence

n×(a1 + an)/2

in our case

38×(10 + 47)/2 = 19×57 = 1083 seats

Answer:

Total cost is $177.50.

Step-by-step explanation:

Rackets:

Divide the cost for racket by 6 to find the cost per racket.

186÷6=31

Multiply 31 by 5 to find the cost for 5 rackets.

31×5=155

$155

Tubes of balls:

Divide 27 by 6 to find the cost per a tube of balls.

27÷6=4.50

Multiply 4.50 by 5 to find the cost for 5 tubes of balls.

4.50×5=22.50

$22.50

Add the amounts for rackets and tubes of balls to find the total cost.

155+22.50=177.50

The total cost is $177.50.

Hope this helps!

The vertex of the transformed parabola with the equation [tex]y=a(x-h)^2+k[/tex] is (h, k).

The transformation rules are:

Translation: (x, y) → (x + a, y) or (x, y) → (x - a, y) (Horizontal shift)

Translation: (x, y) → (x , y + b) or (x, y) → (x , y - b) (Vertical shift)

It is given that, the transformed parabola is [tex]y=a(x-h)^2+k[/tex]

This parabola has vertex at (h, k).

Since this equation is obtained by shifting h units horizontally and k units vertically.

So, the original vertex is at (h - h, k - k) = (0, 0)

Thus, the equation of the actual parabola is [tex]y=ax^2[/tex]

Therefore, the given transformed equation of parabola has vertex (h, k).

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Answer:

B] (h,k)
The next answer is Vertex (-5, -4)

☆
EDGE2022; Good luck :3!!!!

The average rate of change will be 5 miles per hour from 0.75 to 1 hour.

The average rate of change is the ratio of change in the y-value or the function value by the change in the x-value.

So according to the question,

the interval between 0.75 to 1 hour is =1-0.75=0.25 hour.

At 0.75 hours elapsed, the distance traveled is 3.5 miles

at 1 hour elapsed, the distance traveled is 4.75miles.

during the interval, 0.75 hours to 1-hour distance travelled=4.75-3.5=1.25 miles.

the average rate of change will be = change in distance traveled during the interval/interval time.

=(4.75-3.5)/(1-0.75)=1.25/0.25=5 miles per hour

Therefore the average rate of change will be 5 miles per hour from 0.75 to 1 hour.

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Answer:

B

Step-by-step explanation:

If you don’t want to read

Answer:

60%

Step-by-step explanation:

324/540 x100=60%

Np!

The probability that the student will pass the test is 0.057

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli,[1] is the discrete probability distribution of a random variable which takes the value 1 with probability [tex]p[/tex] and the value 0 with probability [tex]{\displaystyle q=1-p}[/tex]. Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcomes that are boolean-valued: a single bit whose value is success/yes/true/one with probability p and failure/no/false/zero with probability q.

The student will pass if he at least answers 14 questions correctly .

This can be written as a Bernoulli distribution function [tex]P(Q=i)= 20C_{i} (\frac{1}{2} )^i(1-\frac{1}{2} )^(20-i)[/tex]

P(Q≥ 14) = P(Q=14) + P(Q=15) + P(Q=16) +P(Q=17) + P(Q=18)+ P(Q=19) +   P(Q=20)

 P(Q=14) = 20[tex]C_{14}[/tex][tex](1/2)^{20}[/tex]

 P(Q=15) = 20[tex]C_{15}[/tex][tex](1/2)^{20}[/tex]

 P(Q=16) = 20[tex]C_{16}[/tex][tex](1/2)^{20}[/tex]

 P(Q=17) = 20[tex]C_{17}[/tex][tex](1/2)^{20}[/tex]

 P(Q=18) = 20[tex]C_{18}[/tex][tex](1/2)^{20}[/tex]

 P(Q=19) = 20[tex]C_{19}[/tex][tex](1/2)^{20}[/tex]

 P(Q=20) = [tex]20C_{20}(1/2)^{20}[/tex]

On summing up all we get,

P(Q≥ 14) = (38760 + 15504 + 4845+ 1140 + 190 + 20 + 1)/2^(20)

= 15115/262144=0.057

Thus the probability that the student will pass the test is 0.057

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Generally, the equation of a circle is organized like this: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.

We're given the endpoints of the diameter: [tex](-6,-3)[/tex] and [tex](-6,-8)[/tex].

First, we can find the centre of the circle by finding the midpoint of these two endpoints.

[tex]midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

Plug in the points:

[tex]midpoint=(\dfrac{-6+-6}{2},\dfrac{-3+-8}{2})\\\\midpoint=(-6,\dfrac{-11}{2})[/tex]

Therefore, the centre of the circle is [tex](-6,\dfrac{-11}{2})[/tex]. Plug this into the general equation:

[tex](x-h)^2+(y-k)^2=r^2\\\\(x-(-6))^2+(y-(-\dfrac{11}{2}))^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=r^2[/tex]

To find the radius of the circle, we can calculate the distance between the centre and one of the given endpoints:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Plug in the centre and one of the endpoints:

[tex]d=\sqrt{(-6-x_1)^2+(\dfrac{-11}{2}-y_1)^2}\\d=\sqrt{(-6-(-6))^2+(\dfrac{-11}{2}-(-3))^2}\\d=\sqrt{(-6+6)^2+(\dfrac{-11}{2}+3)^2}\\\\d=\sqrt{(0)^2+(-5.5+3)^2}\\\\d=\sqrt{(0)^2+(-2.5)^2}\\\\d=\sqrt{(0)^2+(-\dfrac{5}{2})^2}\\\\d=\sqrt{0+\dfrac{25}{4}}\\d=\sqrt{\dfrac{25}{4}}\\\\d=\dfrac{5}{2}[/tex]

Therefore, the radius of the circle is [tex]\dfrac{5}{2}[/tex]. Plug this into the general equation:

[tex](x+6)^2+(y+\dfrac{11}{2})^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=(\dfrac{5}{2})^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]

[tex](x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]

Answer: this is the solutions

Answer:

( 3 , 4 )

Step-by-step explanation:

Midpoint Formula: ( (x1+x2)/2 , (y1+y2)/2 )

Distance Formula: d = √[(x1-x2)^2 + (y1-y2)^2]

Gradient (Slope) Formula: (y2-y1) / (x2-x1)

Midpoint Formula:

( (x1+x2)/2 , (y1+y2)/2 )

(2,3) and (4,5)

( (2+4)/2 , (3+5)/2 )

( (6)/2 , (8)/2 )

( 3 , 4 )

wyzant sean w

Answer:A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts

Step-by-step explanation:

Answer:

uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items

Step-by-step explanation:

looks like circles that meet and overlap and

the middle part explains the relationship of both circles

example

if the left circle says water & right circle says freezing the middle part would say ice

mathworldwolfram

Answer:

y = 2x + 4

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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = ( 0, 4) ← 2 points on the line

m = [tex]\frac{4-0}{0-(-2)}[/tex] = [tex]\frac{4}{0+2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 2x + 4 ← equation of line

The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³

An equation is an expression that shows the relationship between two or more numbers and variables.

The base of the pyramid is x cm while the height is x + 2, hence:

Volume of pyramid = (1/3) * area of square base * height = (1/3) * x * x * (x + 2) = (x³ + 2x²)/3 cm³

The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³

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Answer:

7/13

Step-by-step explanation:

in all there are 13 balls and the number of balls that aren't white are 7

Answer:

7/13

Step-by-step explanation:

To find the probability that it is not white

P( not white) = number of balls that are not white / total balls

The balls that are not white are red and green = 4+3

                      = (4+3)/ ( 4+6+3)

                       = 7/13