What complex number is represented on the graph?

4 − 5i
4 + 5i
5 − 4i
5 + 4i

\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).

the first domain is true for f(0) so we substitute value of x in the first function

\(f(x) = x \\ f(0) = 0\)

The cost of each sandwich, given the number that was sold and the profit made was  $15.

Let S be the price of a sandwich and A be the price of a salad.

From the lunch sale, we know:

14 S + 14 A = $280

From the evening sale, we know:

42S + 154 A = $ 1400

Simplify the first equation by dividing through by 14:

S + A = $20

Solving this equation for S gives:

S = $20 - A

Substitute this equation into the second equation:

42 ( $20 - A ) + 154 A = $1400

$ 840 - 42 A + 154 A = $1400

112A = $560

A = $5

Substitute A = $5 into the first equation:

S + $5 = $20

S = $15

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its both 2

Step-by-step explanation:

base on my research

The coordinates of the point on the unit circle at angle 225° are \(\bold{(-\frac{\sqrt{2} }{2}, -\frac{\sqrt{2} }{2})}\)

The coordinates of the points of the circle x² + y² = r² are \((r~cos\theta, r~sin\theta)\)

"It is a circle with radius 1."

For given example,

We have been given an angle of 225°

⇒ \(\theta\) = 225°

We need to find the coordinates of the point on the unit circle at an angle 225°.

Here, r = 1

So, the first coordinate would be,

\(r~cos\theta=(1)~cos(225^{\circ})\\\\\Rightarrow r~cos(225^{\circ})=cos(270^{\circ} - 45^{\circ})\\\\\Rightarrow r~cos(225^{\circ})t=cos(270^{\circ}) cos(45^{\circ})+sin(270^{\circ}) sin(45^{\circ})\\\\\Rightarrow r~cos(225^{\circ})=0+(-1)(\frac{1}{\sqrt{2} } )\\\\\Rightarrow r~cos(225^{\circ})=\bold{\frac{-1}{\sqrt{2} }}\\\\\Rightarrow r~cos(225^{\circ})=\bold{-\frac{\sqrt{2} }{2} }\)

Now we find the second coordinate of the point.

\(r~sin\theta=(1)~sin(225^{\circ})\\\\\Rightarrow r~sin(225^{\circ})=sin(270^{\circ} - 45^{\circ})\\\\\Rightarrow r~sin(225^{\circ})=sin(270^{\circ}) cos(45^{\circ})-cos(270^{\circ}) sin(45^{\circ})\\\\\Rightarrow r~sin(225^{\circ})=(-1)(\frac{1}{\sqrt{2} } )-0\\\\\Rightarrow r~sin(225^{\circ})=\bold{\frac{-1}{\sqrt{2} }}\\\\\Rightarrow r~sin(225^{\circ})=\bold{-\frac{\sqrt{2} }{2} }\)

Therefore, the coordinates of the point on the unit circle are \((-\frac{\sqrt{2} }{2}, -\frac{\sqrt{2} }{2})\)

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11.9% of students have height less than 136.4cm. The solution has been obtained using probability.

What is probability?

Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value.

Let the height be 'd' cm.

We are given mean as 160 cm and standard deviation of 20 cm.

Probability(x>d) = 0.12

Probability(x<d) = 0.881

Probability(z ≤ d-160/20) = 0.881

⇒d-160/20 = 1.1800  (using table)

⇒d-160 = 23.6

⇒d = 183.6

Therefore, d-mean = -23.6

⇒d-160 = -23.6

⇒d = 160-23.6

⇒d = 136.4cm

Hence, 11.9% of students have height less than 136.4cm.

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Let us identify the different place values in the given number.

Starting from the left side, we have:

8 - ten's place

7 - one's place

decimal point

9 - tenth's place

4 - hundredths place

5 - thousandths place

3 - ten-thousandths place

2 - hundred-thousandths place

7 - millionth place

As we can see above, the number in the hundred-thousandths place is 2.

The number after 2 or the number in the millionth place is 7. Since the number in the millionth place is above 5, we will round up the hundred-thousandths place by adding 1. So, 87.945327 becomes 87.94533 when rounded to the hundred-thousandth place.

The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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Answer:

(whats 1girl + 1 girl=) uhh ima go with 2girl ;)

Step-by-step explanation:

whats 1girl + 1 girl=?

well 1+1=2 so 1girl + 1 girl= 2girl

Answer:it might be A

Answer:

4 marble lost

Step-by-step explanation:

1/6×24=4

so 4 marble lost

Answer:

Step-by-step explanation:

Answer:

You will pay $42.50

Step-by-step explanation:

You will pay 50-7.5 which gives you 42.50

Explanation

Step 1

The angle 01 is located in Quadrant III,so

we know, by definition

so, by replacing

to find cos , we need to find the misssing side( adjacent side), let's use the Pythagorean theorem:

I hope this helps you

1. 76.56.

2. 96

3. The largest solution to the equation x²+16x+28=138 is 6.71.

4. The smallest solution to the equation x²+14x+14=145 is 5.96.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result (19/2)² = 76.56.

2. This is calculated by taking the coefficient of x (30) and dividing it by two (30/2) and then squaring the result (30/2)² = 96.

3. This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (16) plus or minus the square root of the coefficient of x squared (16²) minus 4 times the coefficient of the x term (4x16) minus the constant (28) divided by 2 times the coefficient of the x term (2x16).

4.  This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (14) plus or minus the square root of the coefficient of x squared (14²) minus 4 times the coefficient of the x term (4x14) minus the constant (14) divided by 2 times the coefficient of the x term (2x14).

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1.  For the given equation, c need to be 90.25 to complete the square.

2. 225

3. The largest solution to the equation x²+16x+28=138 is 6.

4. The smallest solution to the equation x²+14x+14=145 is -14.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result

(19/2)² = 90.25.

2. This is calculated by taking the coefficient of x (30) and dividing it by two which is (30/2) and then squaring the result

(30/2)² = 225.

3. The largest solution to the equation x²+16x+28=138 is 6.

This can be calculated by using the quadratic formula to solve the equation.

(a=1, b=16, c=28)

x = -8 ± √((16)² - 4(1)(28))/2(1).

x = -8 ± √(240)/2

x = 6 or -14.

Since 6 is the larger solution, it is the largest solution to the equation.

4.  The smallest solution for x2+14x+14=145 can be determined by using the Quadratic Formula.

a=1, b=14, and c=14

x = [-14 ± √(142-4(1)(14))]/(2(1))

x = [-14 ± √(196)]/2

x = [-28/2] or [14/2]

x = -14 or 7

Therefore, the smallest solution for x2+14x+14=145 is x=-14.

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Answer:

C. 3x²-x+6

Explanation:

Given the algebraic expression:

First, open the brackets:

Next, rearrange to bring the like terms together:

Finally, combine the like terms:

The correct option is C.

Answer:

the percentage profit of the company is 63.9%.

Step-by-step explanation:

Cost of making pins= £1.10

Number of pins= 1000

Total cost for making the pins

= Cost of each pin × Number of pins

= £1.10 × 1000

= £1110

Percentage of pins sold in charities

= 35% of 1000 pins

= (35/100) × 1000

= 350 pins

Left pins= 1000-350 = 650 pins

Number of pins sold at £3.00:

= 60% of 650

= (60/100) × 650

= 390

Selling price of these 390 pins

= 390 × £3.00

= £1170

Number of pins sold at £5.00 for 2:

= 40% of 650

= (40/100) × 650

= 260

These 260 pins were sold in pairs for £5.

Therefore, number of pairs sold

= 260/2

= 130 pairs

Selling price of these 130 pairs of pins

= 130 × £5.00

= £650

Therefore, total selling price

= £1170 + £650

= £1820

Profit by company

= Selling price - Cost price

= £1820 - £1110

= £710

Profit percentage

= Profit × 100 / Total cost price

= 710 × 100 / 1110

= 71000/1110

= 63.9%

Answer:

π in²

Step-by-step explanation:

We'll begin by calculating the radius of the circle. This can be obtained:

Area of sector (A) = 4π in²

Angle (θ) = 120 °

Radius (r) =?

The radius of the circle can be obtained by using the formula for calculating the area of a sector. This is illustrated below:

A = θ/360 × πr²

4π = 120/360 × πr²

4π = ⅓ × πr²

Cross multiply

3 × 4π = πr²

12π = πr²

Divide both side by π

r² = 12π / π

r² = 12

Take the square root of both side

r = √12 in

Thus, the radius is √12 in.

Finally, we shall determine the area of the sector created by 30 °. This can be obtained as follow:

Radius (r) = √12 in

Angle (θ) = 30 °

Area of sector (A) = ?

A = θ/360 × πr²

A = 30/360 × π(√12)²

A = 1/12 × 12π

A = π in²

Therefore, the area of the sector created by 30 ° us π in².

The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)

P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)

Using a calculator or software, we can find that:

P(X <= 4) = 0.000203

This means that the probability is 0.02%.

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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?

Answer:

12.56 km

Step-by-step explanation:

The circumference of a circle is given by

\(c = 2\pi \: r\)

let's find the radius

the area of a circle is given by

\(a = \pi \: {r}^{2} \)

12.56 = 3.14 r²

r² = 12.56/3.14

r² = 4

r = √4

r = 2

let's find the circumference

C = 2πr

C = 2 × 3.14 × 2

C = 12.56 km

I hope this helps

Answer:

Probability that student will be a girl = 17 / 28

Step-by-step explanation:

Given:

Total number of student = 28 student

Number of boys in the class = 11

Find:

Probability that student will be a girl = ?

Computation:

⇒ Number of girls in class = Total number of student - Number of boys in the class

⇒ Number of girls in class = 28 - 11

⇒ Number of girls in class = 17

⇒ Probability that student will be a girl = Number of girls in class / Total number of student

⇒ Probability that student will be a girl = 17 / 28

Answer:

<a=90 (right angle)

<b=180-30-90=60

<c=30 (given)

<d=180-30=150

<e=<c=30

everything is in degrees, and all you need to know to solve problems like this is that the angle of a straight line is 180 degrees (sorry my explanation isn't the best, let me know if you need any clarifications)

Answer:

The digit that fit into the blank space is 6

Step-by-step explanation:

Here, we want to enter digits into the blank space that can make the expression valid.

Let’s try 6;

6583 < 6612 < 6687

This is actually correct.

Can we have any other digit here?

No, i don’t think so.

Putting in a 5 will make the first number greater than the middle

Putting in a 7 will make the middle number greater than the last and thus render the expression invalid

The second step of calculating the present value of an ordinary annuity by the table lookup is to look up the periods and rates in the PV annuity table.

The present value of an ordinary annuity is the current value based on future cash inflows of the annuity, given a specified discount rate.

The present value is higher when the discount rate is lower, and vice versa.

The present value of an ordinary annuity, which discounts the annuity to the current time, is computed as Annuity Payment x Present value of the ordinary annuity table.

In conclusion, an annuity simply means a series of periodic payments and may involve payment at the beginning (annuity due) or at the end of the period (ordinary annuity).

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Answer:

Wes

Step-by-step explanation:

This represents a positive correlation, meaning that when x increases, so does y. Because of x, y increases meaning that Wes is correct

The number of years it would take is approximately equal to 53 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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Answer:

There will be left 80.4 of the sample in 500 years

Step-by-step explanation:

Radioactive Decay Model

Suppose N is the size of a population of radioactive atoms at a given time t, No is the size of an initial population of radioactive atoms at time t = 0, and k is the decay constant, then the equation is as follows:

\(N=N_o\cdot e^{-kt}\)

The time required for half of the original population of radioactive atoms to decay is called the half-life Th. The relationship between the half-life and the decay constant is:

\(\displaystyle T_h=\frac{ln 2}{k}\approx\frac{0.693}{k}\)

We know the half-life of radium-226 is about 1,590 years. We can find the value of k by solving the above equation:

\(\displaystyle k=\frac{ln 2}{T_h}\)

\(\displaystyle k=\frac{ln 2}{1,590}\)

k=0.000436

The initial mass of the sample is 100 gr, thus the model for the mass at time t is:

\(M(t)=100\cdot e^{-0.000436t}\)

When t=500 years:

\(M(500)=100\cdot e^{-0.000436*500}\)

\(M(500)=100\cdot 0.804\)

M(500)=80.4 gr

There will be left 80.4 of the sample in 500 years

Answer:

80.4

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:Since there is a 0.5 chance of the coin landing on heads add a zero and take off the .0 and you get 50%.

Answer:

50%

Step-by-step explanation:

The theoretical probability to get either heads or tails is 0.5 (or 50 percent). The probabilities of all possible outcomes should add up to 1 (or 100 percent), which it does.

Answer:6.25

Step-by-step explanation:1.25x5=6.25

Answer:

$6.25

Step-by-step explanation:

1.25 × 5 = 6.25

hope this helps...

Answer:

it is correct I think it's right

Step-by-step explanation:

Answer:

(-1,2)

Step-by-step explanation:

Write out the system in a matrix

3  5     7

2(6  -1    -8 ) Multiply row two by five and add to row one.

1  0  -1 Multiply row 1 by -6 and add it to row two.

6  -1  -8

1 0 -1

0 -1 -2 Multiply bottom row by -1

1 0 -1

0 1 2

x=-1, y=2