When solving the linear equation, ax + b = 0 where a≠ 0, what is the answer of the equation x = -b/a referred as?

Answer:

-30

Step-by-step explanation:

0 is greater the -30 and -1 but less then 29

29 is greater then 0, -30, and -1

-1 is less the 0 and 29 but greater then -30

-30 is less then 0, 29, and -1

from greatest to smallest

29, 0, -1, -30

-30 is the smallest integer

Sue's total pay for the year given the salary, bonus and share of profit is  £38,110.

Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.

Salary for the year = monthly salary x number of months in a year

£1410 x 12 = £16,920

The next step is to determine the profit last year

Profit = total revenue - total cost

£549,000 - £473,500 = £75,500

Now determine the share of profit that Sue would earn.

Share of profit = 26% x  £75,500

0.26 x  £75,500 = £19,630

Now determine the total bonus she would earn : 4 x £390 = £1560

Total salary = £1560 +  £19,630 +  £16,920 = £38,110

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The situation can be represented by the above diagram

7 students play basketball, that is,

x + y = 7 (eq. 1)

13 students play baseball, that is,

y + z = 13 (eq. 2)

10 students who play neither sport.

x + y +z = 26 - 10

x + y +z = 16

Substituting with equation 2,

x + 13 = 16

x = 16 - 13

x = 3

Substituting with equation 1,

3 + y = 7

y = 7 - 3

y = 4

Then there are 4 students that play both sports. Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is: 4/26 = 2/13

Answer:

8

Step-by-step explanation:

First, let’s say the number is x

Then follow the steps

12x+6

36x+18

36x+9

12x+3=99

So x=8

Answer:

x = 14

Step-by-step explanation:

3 (x - 3) + 8x = 5 (2x + 1)​

FOIL: 3x - 9 + 8x = 10x +5

Move all the x terms to one side and all the constants to the other:

3x + 8x - 10x = 5 + 9

Combine like terms: x = 14

The combined amount of raisin cookies and oatmeal cookies sold was 78.

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

Given:

At a bake sale,

48 raisin cookies were sold.

8:5 is the ratio of raisin cookies sold to oatmeal cookies sold.

Let n number of oatmeal cookies were sold.

So, 8/5 = 48/x

1/5 = 6/x

x = 30

The combined amount of raisin cookies and oatmeal cookies sold was,

= 48 + x

Substitute the value of x to the above equation,

we get,

= 48 + 30

= 78

Therefore, a total number of 78 cookies were sold.

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Answer:

x is the variable

Step-by-step explanation:

The variable is 6 and division arithmetic operation is present in algebraic expression.

A variable is a quantity that could change depending on the context of an experiment or mathematical question.

The given expression is 6/x,

in the given expression, 6 is constant and x is a variable.

And the division operation is given between 6 and x.

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Answer:

7606.62

Step-by-step explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)

Now just equate this to a time 0 payment at the same rate

\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.

Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

Answer: f(3) = 145 ==> 1st option

Step-by-step explanation:

f(p) = 7p³ - 5p² + 1/3p

f(p) = 7p³ - 5p² + p/3

f(3) = 7(3)³ - 5(3)² + (3)/3

f(3) = 7(27) - 5(9) + 1

f(3) = 189 - 45 + 1

f(3) = 144 + 1

f(3) = 145 ==> 1st option

Answer:

9.8 inches

Step-by-step explanation:

C = 2\(\pi\)r

61.544 = 2(3.14)r

61.544 = 6.28 r  Divide both sides by 6.28

9.8 = r

The measure of angle DCE in this problem is given as follows:

m < DCE = 22.5º.

The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.

The three trigonometric ratios are given as follows:

The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:

cos(38º) = DB/12.2

DB = 12.2 x cosine of 38 degrees

DB = 9.6 cm.

BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:

DE = 1/4 x 9.6

DE = 2.4 cm.

Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:

tan(x) = 2.4/5.8

x = arctan(2.4/5.8)

x = 22.5º

m < DCE = 22.5º.

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Answer:

x = 22.5°

Step-by-step explanation:

The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.

The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.

SA = 2(lw + lh + hw), where:

The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:

The surface area to be covered = surface area of the box - area of the bottom rectangular face

The surface area to be covered = 2(lw + lh + hw) - (l)(w)

l = 26

w = 15

h = 8

Substitute

The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =

The surface area to be covered = 1436 - 390 = 1,046 cm

Area of one tile = 1 cm square

Number of tiles needed = 1,046/1

Number of tiles needed = 1,046 tiles.

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Answer:

Option C

Step-by-step explanation:

I just graphed on my TI-84

Hope this helps!

Answer:

sorry I hope I could help u :(

Answer:

10 is answer

Step-by-step explanation:

because minos minos = plus

Answer:

Westbound = x;

Eastbourne = x-20;

So they will have the common rate: 360/2 = 180;

x+x-20 = 180

2x = 200;

x = 100;

So Eastbourne will be 100-20 = 80 miles per an hour;

Answer: The perimeter is 20 cm

Step-by-step explanation: The top and bottom are same length, so 6+6, and the sides are the same length, so 4+4 don’t forget it’s cm and it becomes 20 cm.

PERIMITER = ADDING ALL SIDES

AREA = MULTIPLYING

Answer:

41.60

Step-by-step explanation:

\(\sqrt{108}\)=10.39230485=10.40

10.40+10.40+10.40+10.40=41.60

10.40*2=20.80

\(20.80^{2}\)=432.64

Now we can see that our fraction is 30/100, which means that 12/40 as a percentage is 30%.

hope this helps if so then please mark em brainliest

If not then i am very sorry

Answer:

Step-by-step explanation:

By the center angle theorem:

WE get:

Angle ABC = 0.5 * Angle AOC

Angle ABC = 28 degrees

Hope that helps

The amount Stefan spent originally to buy the bike is; $100.91.

The amount Stefan made in profit by selling the bicycle and helmet to Jin is; $10.09.

According to the task content;

Stefan sold the bicycle and helmet for a total of;

104 + 17 = $111.

Also, since the total cost ($111) for Jin is 110% of what Stefan spent to buy the bicycle and helmet, x originally; we have

110% × x = 111

x = (111 × 100) / 110

x = $100.91.

Therefore, Stefan spent $100.91 originally to buy the bike and helmet.

Consequently, the money Stefan made by selling the bicycle and helmet to Jin is; 111 - 100.91 = $10.09.

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Answer: The initial cost on rent on your first year living there is 1100. Supposing you live there for another 11 years your rent would be 2200 per month.

Step-by-step explanation:110x11=1100 1100+1100=2200

Answer: I think it's 1,100

Step-by-step explanation: We know that the apartment costs $1100 per month during the first year but if it goes up 110 dollars per year how much would total be in 11th year?

First we need to multiply 1100 and 110 which equals 121,000

Secondly, of course we need to make sure that our anwser is correct, now we divide 121,000 with 11 years (which equals 1100)

But of course if it is not correct, I'm very sorry. But Have a nice day/night!

Hope it helped!

-GreenteaStudys

The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol

The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.

The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.

The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.

The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.

The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.

To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.

Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.

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Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?