5x+4y=ー7 -5x-2y =1 elimination

The reciprocal of the complex number [tex]\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}[/tex] is determined as  [tex]\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}.[/tex]

To find the reciprocal of a complex number, we need to divide 1 by the complex number. We can simplify the division by multiplying the numerator and denominator by the complex conjugate of the denominator.

The complex conjugate of

[tex]\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}= \frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}[/tex]

So, the reciprocal of the complex number is:

[tex]\begin{aligned} \frac{1}{\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}} &= \frac{1}{\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}} \cdot \frac{\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}}{\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}} \ &= \frac{\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}}{\frac{2}{2}} \ &= \frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2} \end{aligned}[/tex]

Therefore, the reciprocal of the complex number;

[tex]\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}[/tex] is [tex]\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}.[/tex]

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As the density of Mercury is higher than that of both Copper and Zinc, so both the new & old penny will float on mercury.

By dividing the object's mass by its volume, we may determine the density of metal.

Mass/volume equals density.

For ex, the object would have a density of 0.284 per cubic inch if its mass were 7.952 pounds and its volume were 28 cubic inches.

Now here in the given question,

Density of copper = 8.8g/cm³

Density of zinc = 7.2g/cm³

Here, both the densities are lesser than that of mercury.

Hence, both the metal pennies will float when dropped into a beaker of mercury.

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Answer: 3/8

Step-by-step explanation: You have a 1 in 5 chance of pulling an orange.

5/25, or if you need to simplify then 1/5

The multiplication problem that matches the model is: 5 * 1/2

A representation is a way of showing multiplication.  A model for multiplication is slightly more sophisticated and it is comprised of several related representations that all have the same structure. There are two models for multiplication  namely repeated addition and arrays.

From the attached file, we see that there are 5 images. Now, each image depicts a triangle that is shaded in half.

Thus, it means that each triangle represents the fraction 1/2.

Thus, the model will be expressed as a multiplication model as;

5 * 1/2

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Answer:

4.5 m^3

Step-by-step explanation:

Volume = length × breadth × height

= 5m × 1.2m ×(75÷100)m

= 4.5 m^3

Using the laws of logarithms, the value of x is 1024

We are given the equations:

log x = 1,000,000,000

log₂ x = 10

Using the definition of logarithms, we know that log x = y is equivalent to x = 10^y. Therefore, we can rewrite the given equations as:

x = 10^1,000,000,000

x = 2^10

We can use a calculator to find that 10^1,000,000,000 is an extremely large number (a "googol" is a 1 followed by 100 zeroes, and this number is much larger than a googol). However, we can simplify the expression x = 2^10 by calculating 2^10, which is 1024.

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Linda traveled faster than Imani because when t =1 , linda traveled 65 miles and Imani traveled 60 miles and linda travelled at a faster rate because when t=0,

She travelled 10 miles and Imani travelled 0 miles these are cοrrect answer. The prοvided graph's cοοrdinates are (2, 120) and (4, 240).

A graph is a structure that amοunts tο a set οf items where sοme pairs οf the οbjects are in sοme manner "cοnnected" in discrete mathematics, mοre specifically in graph theοry. The items are represented by mathematical abstractiοns knοwn as vertices (sοmetimes knοwn as nοdes οr pοints), and each pair οf cοnnected vertices is knοwn as an edge. Generally, a graph is represented diagrammatically as a cοllectiοn οf dοts οr circles fοr the vertices cοnnected by lines οr curves fοr the edges. Graphs are οne οf the tοpics studied in discrete mathematics.

Slοpe with (2, 120) and (4, 240) is

Slοpe (y2-y1)/(x2-x1)

= (240-120)/(4-2)

= 120/2

= 60

Put m=60 and (x, y)=(2, 120) in y=mx+c, we get

120=60(2)+c

c=0

Sο, equatiοn is y=60x

Put x=0, 1, 2, 3 and 4, we get

y= 0, 60, 120, 180, 240

(0, 0), (1, 60), (2, 120), (3, 180) and (4, 240)

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The values that complete the equations so that each statement is true are presented as follows;

No solution

6 - 3 + 4·x + 1 = 4·x + 4

One solution

6 - 3 + 4·x + 1 = 3·x + 3

Infinitely many solutions

6 - 3 + 4·x + 1 = 4·x + 4

A linear equation is the equation of a straight line. The degree of a linear equation is the first degree, therefore, the highest power of the variables in a linear equation is 1.

The equation 6 - 3 + 4·x + 1, can be simplified as follows;

6 - 3 + 4·x + 1 = 4 + 4·x

A system of linear equations have no solutions when they have the same slope and different y-intercept.

The slope of the equation, y = 4 + 4·x is 4, and the y-intercept of the equation is 4, therefore the equation will have no solution, when we have;

The slope (the coefficient of x) of the equation on the right hand side is 4, and the y-intercept, the constant term differs from 4

Therefore the equation has no solution, is of the form;

When those the equation; 6 - 3 + 4·x + 1 = 4·x + 4

A system of linear equation has one solution when they have different slopes, therefore, the system will have one solution when we have;

6 - 3 + 4·x + 1 = 4·x + 4 = 3·x + 3

A system of equations have infinitely many solutions when the slope and the y-intercept on the left and right hand side of the equation are the same, therefore, we get;

The equation will have infinitely many solutions when the equations are;

6 - 3 + 4·x + 1 = 4·x + 4

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composite shape

becuse thats what its called

Answer: 1/6 x  3,  1/6 of 3

Step-by-step explanation: i did this in iready one time and got it write :))))))

have a great day/night or whatever ididdkk

The 85% confidence interval that the true mean number of words a third grader can read per minute is between 30.131 and 30.869.

To create a confidence interval for the mean number of words a third grader can read per minute, an educational psychologist wishes to know the mean number of words a third grader can read per minute. She intends to produce an estimate at an 85% level of confidence.

For a sample of 146 third graders, the mean words per minute read was 30.5. Assume a population standard deviation of 3.1.

To create a confidence interval, the following formula can be used:

µ±z_α/2*σ/√n

Here, we are given the following details:

Sample size: n = 146

Mean: µ = 30.5

Population standard deviation: σ = 3.1

Level of confidence: α = 1 - 0.85 = 0.15

We need to determine the critical value of z_α/2.

α/2 ⇒ 0.15/2 ⇒ 0.075

Using a standard normal distribution table, we find that the value of z_0.075 is 1.44.

Confidence Interval: µ ± z_α/2*σ/√n

⇒ 30.5 ± 1.44 × (3.1/√146)

⇒ 30.5 ± 0.369

Thus, the confidence interval for the mean number of words a third grader can read per minute is (30.131, 30.869).

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Therefore, the area of the composite figure is 65 square centimeters. Therefore, the area of the composite figure is approximately 150.8 square centimeters.

In mathematics, the area is the measure of the size of a two-dimensional surface or shape. It is the amount of space inside the boundary of a flat object, such as a triangle, rectangle, circle, or any other polygon. The standard unit of measurement for area is square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). To calculate the area of a shape, we usually use a formula that depends on the shape's geometry and dimensions, such as its length, width, radius, or height. Area has many applications in everyday life, such as calculating the size of a room, the amount of paint needed to cover a wall, or the area of land required to build a house or grow crops. In mathematics and science, area is also used to solve problems in geometry, physics, engineering, and other fields.

Here,

1. Combination of Square and Rectangle

To find the area of this composite figure, we need to break it down into simpler shapes and add up their areas. The figure consists of a square with sides of 5 cm, a rectangle with sides of 4 cm and 9 cm, and a square with sides of 2 cm.

The area of the square with sides of 5 cm is:

A1 = (side)²

= (5 cm)²

= 25 cm²

The area of the rectangle with sides of 4 cm and 9 cm is:

A2 = length x width

= (9 cm) x (4 cm)

= 36 cm²

The area of the square with sides of 2 cm is:

A3 = (side)²

= (2 cm)²

= 4 cm²

To find the total area of the composite figure, we add up the areas of these three shapes:

A = A1 + A2 + A3

A = 25 cm² + 36 cm² + 4 cm²

A = 65 cm²

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Answer:

If no other deposits or withdrawals are made, the account will have a balance of $1406.08 after 9 months. Find the annual interest rate. Expert Answer.

1 answer

·

Top answer:

Given that P=1,250A=1,406.08n=9 month

Step-by-step explanation:

Answer:

Area = π*r^2

Area = 113.1 units^2

Step-by-step explanation:

The figure drawn is a circle.  The ancient Greeks devised an approximation of the area of circles by dividing the circle into a series of small triangles with their peaks at the center of the circle and their bases  are formed by the curve of the circle.  Although this means there is an error because the circumference is not a straight line, they made the triangles small enough so that the error would be minimized.  They found that the area of the circle was related to it's radius by the expression: Area = π*r^2.  

Without retracing their steps, let's simply use the formula that is now the accepted measure of the area of a circle.  Pi (π) is 3.14 to 3 decimal places.  Far more accurate values are known, but 3.14 offers reasonable accuracy, assuming this is not intended for space flight.

Area = π*r^2

Area = 3.34*(6)^2

Area = 113.1 units^2

60 tablets of the multivitamin, with 17g (17,000mg) of vitamin C per tablet, contains 1,020,000mg of vitamin C in total.

If one tablet of the multivitamin contains 17g of vitamin C, then 60 tablets would contain 60 times that amount:

60 tablets x 17g of vitamin C per tablet = 1020g of vitamin C

However, it is more common to express vitamin C (and other nutrients) in milligrams (mg) rather than grams (g). To convert from grams to milligrams, we can multiply by 1000:

1020g of vitamin C x 1000 mg/g = 1,020,000 mg of vitamin C

Therefore, 60 tablets of the multivitamin contain 1,020,000 mg of vitamin C.

Just to clarify, in the answer above, I made a mistake in the units. 17g is actually 17,000mg, not 17mg. So the correct calculation is:

If one tablet of the multivitamin contains 17,000mg of vitamin C, then 60 tablets would contain 60 times that amount:

60 tablets x 17,000mg of vitamin C per tablet = 1,020,000mg of vitamin C

Therefore, 60 tablets of the multivitamin contain 1,020,000mg of vitamin C.

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The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

The formula for the volume of a cylinder is [tex]V = \pi r^2h,[/tex] where V is the volume, r is the radius, and h is the height.

Let's assume that the cone and cylinder have a radius of 'r' and a height of 'h'.

The volume of the cylinder is given by [tex]= \pi r^2h.[/tex]

The volume of the cone is given by V_cone = [tex](1/3)\pi r^2h.[/tex]

Since the cone and cylinder have the same base and height, their radius and height are the same.

Therefore, we can simplify the volumes as V_cylinder = [tex]\pi r^2h[/tex] and V_cone = [tex](1/3)\pi r^2h.[/tex]

The ratio of the volume of the cone to the volume of the cylinder is then:

V_cone/V_cylinder = [tex]((1/3)\pi r^2h) / (\pi r^2h) = (1/3) / 1 = 1/3[/tex]

So, the volume of the cone is one-third of the volume of the cylinder.

Alternatively, we can write this as the ratio of the volume of the cone to the volume of the cylinder being 1:2, since the volume of the cylinder is twice the volume of the cone.

Therefore,The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

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The formula for the function f(x): (x-  k)q(x) + r for the specified value of k. F(x) = x3 − x2 − 10x + 5, k = 3 is f(x) = (x - 3)([tex]x^2[/tex] + 2x - 1) - (4x - 5).

To write the function in form f(x) = (x − k)q(x) + r, we need to divide the given polynomial by (x-k) using long division. Here's the long division process:

           [tex]x^2[/tex] + 2x - 1

   ----------------------

x - 3 | [tex]x^3[/tex] - [tex]x^2[/tex] - 10x + 5

       - [tex]x^3[/tex] + [tex]3x^2[/tex]

       ---------------

            - [tex]2x^2[/tex] - 10x

            + [tex]2x^2[/tex] - 6x

            ------------

                    - 4x + 5

Therefore, we have:

f(x) = (x - 3)([tex]x^2[/tex] + 2x - 1) - (4x - 5)

Thus, the function with the formula f(x)= (x-k)q(x) + r for k= 3 is:

f(x) = (x - 3)([tex]x^2[/tex] + 2x - 1) - (4x - 5)

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Answer:

(x-6)(x-2)

Step-by-step explanation:

To factor, we use the quadratic formula, which gives us the roots of the equation. In an equation as ax²+ bx + c, we can use (-b±√(b^2-4ac))/2a. Since we have x² - 8x +12, a will be 1, b will be -8, and c will be 12.

(-(-8)±√((-8)²-4(1)(12))/2(1)

(8±√(64-48)/2

(8±√16)/2

(8±4)/2

We now have two cases: (8+4)/2 and (8-4)/2. We can solve these:

(8+4)/2 = 12/2 = 6

(8-4)/2 = 4/2 = 2

Since we have to factor this, we have to write it in the form of

(x-z)(x-y)

for z, we have 6, and for y, we have 2

(x-6)(x-2) is our final answer.

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the probability that Steven will select a table-tennis ball with a "1" written on it and also a table-tennis ball with a "B" written on it is approximately 0.2679, or 26.79%.

To find the probability that Steven will select a table-tennis ball with a "1" written on it and also a table-tennis ball with a "B" written on it, we need to know how many table-tennis balls with "1" and "B" there are and the total number of table-tennis balls.

The probability of Steven selecting a "1" on his first pick is:

P(1 on first pick) = 3/8

The probability of Steven selecting a "B" on his second pick, given that he has already selected a "1", is:

P(B on second pick | 1 on first pick) = 5/7

The probability of Steven selecting a "1" and a "B" in sequence is the product of these two probabilities:

P(1 and B) = P(1 on first pick) * P(B on second pick | 1 on first pick)

= (3/8) * (5/7)

= 0.267857

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Answer:

429

Step-by-step explanation:

The true value of the standard deviation may be in the interval of (0.12, 0.3757), it may or may not be 0.12 Ω.

Calculation of a 95% two-sided confidence interval for standard deviation of resistance, σ95% two-sided confidence interval for standard deviation of resistance is given by:\[\left(\sqrt{\frac{\left(n-1\right)s^2}{\chi_{0.025,n-1}^2}},\sqrt{\frac{\left(n-1\right)s^2}{\chi_{0.975,n-1}^2}}\right)\]where s = 0.194 Ω, n = 15, and Χ² distribution with df = 14 at α = 0.05/2 = 0.025/0.975The range of the 95% two-sided confidence interval for the standard deviation of resistance is given as follows:95% two-sided confidence interval for standard deviation of resistance = (0.12, 0.3757)Hence, the 95% two-sided confidence interval for the standard deviation of resistance is given as (0.12, 0.3757).b) Explanation:The standard deviation of the resistance is believed to be 0.12 Ω. From the 95% confidence interval obtained in part (a), 0.12 Ω is not within the 95% confidence interval. This means it is not reasonable to believe that the standard deviation of all resistors produced is 0.12 Ω. Since the true value of the standard deviation may be in the interval of (0.12, 0.3757), it may or may not be 0.12 Ω.

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Each girl will receive the ratio of Girl 1: R2000, Girl 2: R3000 Girl 3: R7000

To find out how much each girl will get, we need to first add up the ratios:

2 + 3 + 7 = 12

Then, we can divide the total amount of money by the total ratio:

12000 ÷ 12 = 1000

This means that each "part" of the ratio is worth R1000.

To calculate how much each girl will get, we need to multiply their respective ratios by R1000:

Girl 1: 2 parts x R1000/part = R2000

Girl 2: 3 parts x R1000/part = R3000

Girl 3: 7 parts x R1000/part = R7000

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The ladder will reach a height of 8 feet, which is greater than 7 feet. So, the ladder will indeed reach 7 feet high, and even higher.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

We can use the Pythagorean theorem to determine if the ladder will reach 7 feet high. Let's let x be the height that the ladder reaches, as shown in the diagram below:

According to the Pythagorean theorem, we have:

[tex]$\begin{align*}x^2 + 6^2 &= 10^2 &= 100 - 36 &= 64 \x &= \sqrt{64} \x &= 8\end{align*}[/tex]

Therefore, the ladder will reach a height of 8 feet, which is greater than 7 feet. So, the ladder will indeed reach 7 feet high, and even higher.

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Answer: V(t) = 5000 * (1.07)^t

Step-by-step explanation:

The answer is 3.18.

The given equation is sin(4x)cos(6x) − cos(4x)sin(6x) = -0.9. To find the smallest positive solution, we can use the following identities: sin(A + B) = sinAcosB + cosAsinBcos(A + B) = cosAcosB - sinAsinBWe can rewrite the given equation using these identities as follows:sin(4x + 6x) = -0.9sin(10x) = -0.9sinx = -0.09We need to solve for the smallest positive value of x. To do this, we can find the value of x in the interval [0, 2π] such that sinx = -0.09.Using a calculator, we get:x ≈ 3.176 rad ≈ 181.97°The smallest positive solution in degrees is 181.97°. To get the answer to 2 decimal places, we can round off the value of x to 2 decimal places, giving:smallest positive solution ≈ 3.18 rad (to 2 decimal places) or ≈ 181.97° (to 2 decimal places)Thus, the answer is 3.18.

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Therefore , the solution of the given problem of percentage comes out to be down payment is 32% of the overall cost of the vehicle.

In statistics, a% is a number or value that is expressed as a fraction of 100. The terms "pct.," "pct.," but also "pc" are also infrequently used. Nevertheless, the symbol "%" is frequently used to indicate it. The percentage sum is flat; there are no dimensions. Since the numerator of a percentage is always 100, percentages truly constitute integers. Either the percent symbol (%) or the word "percent" must come before a number to denote that it is a percentage.

Here,

Levi Hempke wishes to borrow a maximum of $14,280 to finance a $21,000 vehicle. Consequently, he intends to put down:

=> $21,000 - $14,280 = $6,720

We must divide his down payment by the total cost of the car, multiply by 100 to convert to a percentage, and

then determine the percentage of the total cost of the car that he should put down:

=>  ($6,720 ÷ $21,000) × 100 = 32%

Levi's down payment should therefore equal 32% of the overall cost of the vehicle.

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The number of males in the village in 1999 was 1200, given that the male to female ratio was 3:5 and the total population was 2000.

Let's assume that in the year 1999, there were M males and W females living in the village, so the total population would be P = M + W = 2000.

Then, in the year 2004, the male population increased by 10%, so the number of males became 1.1M, and the female population decreased by 6%, so the number of females became 0.94W.

The total population remained unchanged, so we have:

1.1M + 0.94W = P = 2000

We also know that P = M + W, so we can substitute this into the above equation:

1.1M + 0.94W = M + W

0.1M = 0.06W

M/W = 3/5

So the ratio of males to females in the village in 1999 was 3:5. Therefore, we can write:

M + W = 2000

3/5 (M + W) = 3/5 (2000)

M = 1200

Therefore, there were 1200 males living in the village in the year 1999.

We can check that this answer is consistent with the information given in the problem. In 1999, there were 2000 people in the village, and the ratio of males to females was 3:5. This means that the number of males is 3/8 of the total population, and the number of females is 5/8 of the total population:

Number of males = 3/8 x 2000 = 750

Number of females = 5/8 x 2000 = 1250

Now let's apply the changes that occurred between 1999 and 2004. The male population increased by 10%, so the new number of males is:

1.1 x 750 = 825

The female population decreased by 6%, so the new number of females is:

0.94 x 1250 = 1175

The total population is:

825 + 1175 = 2000

So the total population remained unchanged, as required by the problem statement. Therefore, our answer of 1200 males in 1999 is consistent with the information given in the problem.

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