The sum of the interior angles of the 10-sided polygon on the left is ____

We can write the quadratic in standard form as:

y = x² -18x - 1053

For a quadratic equation whose solutions are:

x = x₁

x = x₂

We can write it as:

y = (x - x₁)*(x - x₂)

Here the solutions are:

x = 9 + 9√13

x = 9 - 9√13

Then we can write the quadratic as:

y = (x - 9 - 9√13)*(x - 9 + 9√13)

Expanding that:

y = x² -18x - 81*13

y = x² -18x - 1053

Learn moer about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

Answer:

[tex] \frac{210}{360} = \frac{7}{12} [/tex]

This figure represents 7/12 of the circle.

Answer:

The points that are on the line given by the equation y = x are:

A. (3, 3)

B. (2, 2)

D. (-1, -1)

E. (1, 1)

To check if a point is on the line, you can substitute its coordinates into the equation and see if the equation is true. For example, for point (3, 6), we have:

y = x

6 = 3

This is not true, so the point (3, 6) is not on the line. Repeat this process for each point to determine which points are on the line.

Answer:

G^-1(t)=t/7+4

Step-by-step explanation:

G(t) = 7(t - 4)

y = 7(x - 4)

x = 7(y - 4)

x/7 = y - 4

y = x/7 + 4

G^-1(t) = t/7 + 4

Answer: G^-1(t)=t/7+4

The mean of brothers and sisters = 3

From the attached data set of brothers and sisters we can write the data values (frequency) as:

1, 5, 4, 2

We need to find the mean of brothers and sisters,

We know that the formula for the mean of data.

mean([tex]\bar{x}[/tex]) = sum of all data values / total number of data values

First we find the sum of all data values.

1 + 5 + 4 + 2 = 12

and the total number of data values = 4

Using above formula of mean,

mean([tex]\bar{x}[/tex]) = sum of all data values / total number of data values

mean([tex]\bar{x}[/tex]) = 12 / 4

mean([tex]\bar{x}[/tex]) = 3

Therefore, the required mean is: 3

Learn more about the mean here:

https://brainly.com/question/30891252

#SPJ1

Find the complete question below.

Answer:

A

Step-by-step explanation:

the domain is the values of x covered by the graph

on the left the graph → - ∞

on the right the graph tends to + ∞

there are no excluded values of x on the domain , so

domain is - ∞ < x < ∞

Answer:

C

Step-by-step explanation:

cos x and sin(90 - x) are cofunctions and are equal , then

cos x = [tex]\frac{1}{3}[/tex] , then sin(90 - x) = [tex]\frac{1}{3}[/tex]

For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

To learn more about domain and range click on,

https://brainly.com/question/15136070

#SPJ1

Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

The number of mugs that Maggie made with the left over clay that she had would be = 23 mugs

The total quantity of clay that Maggie bought = 50lbs

The quantity she used for sculpture = 15.6lbs

The quantity of clay she used for mug = 0.84 lbs

The quantity of clay left = 19.28 lbs

If 0.84 = 1 mug

19.28 = X

make X the subject of formula:

X = 19.28/0.84

= 23 mugs

Learn more about weight here:

https://brainly.com/question/29892643

#SPJ1

Answer:

Here's a cost statement for the year 2021:

Production of 1,500 units

Cost of raw materials = Rs. (20,000 x 1.2) = Rs. 24,000

Labour cost = Rs. (12,000 x 1.1) = Rs. 13,200

Fixed overheads = Rs. (8,000/2) = Rs. 4,000

Variable overheads = Rs. (8,000/2 x 1.5) = Rs. 6,000

Office overheads = Rs. 4,000

Selling expenses per unit = Rs. (1,000 x 0.8 / 1,500) = Rs. 0.53

Total cost per unit = Rs. (24,000 + 13,200 + 4,000 + 6,000 + 4,000) / 1,500 = Rs. 28.80

Profit = 25% of selling price

Selling price per unit = (28.80 / (1 - 0.25)) = Rs. 38.40

Total profit = (1,500 x 38.40 x 0.25) = Rs. 14,400

Therefore, the cost statement for the year 2021 shows a total profit of Rs. 14,400 and a selling price per unit of Rs. 38.40.

Jill's annual earnings can be calculated by multiplying her weekly pay by the number of weeks in a year: $298/week x 52 weeks/year = $15,496/year. Her earnings to date are $14,900, so she has earned an additional $596 in the current week.

Social Security is taxed at 6.2%, so the amount deducted from her pay each week is 6.2% of her gross weekly pay. That's 0.062 x $298 = $18.48.

The probability that a person has the virus given that they have tested positive find the P(A/B)=0.0045

We can use Bayes' theorem to find the probability that a person has the virus given that they have tested positive:

P(A | B) = P(B | A) * P(A) / P(B)

where P(B | A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus (1/300), and P(B) is the total probability of testing positive.

To find P(B), we can use the law of total probability, which states that:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

where P(B | not A) is the probability of testing positive given that the person does not have the virus. This is the false positive rate, which is 5% or 0.05 in this case. P(not A) is the complement of P(A), which is 299/300.

Substituting the values, we get:

P(B) = 0.85 * 1/300 + 0.05 * 299/300

= 0.059

Now we can plug in the values into Bayes' theorem:

P(A | B) = 0.85 * 1/300 / 0.059

= 0.0045 or 0.45%

Therefore, the probability that a person has the virus given that they have tested positive is 0.45% or 0.0045 (rounded to the nearest tenth of a percent).

To learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

Answer: Themba needs a total of 7.5  cups of yogurt to make 5 bowls of fruit dip, so 0.75 cup(s) will be needed

Step-by-step explanation:

your welcome.

Answer: Given b=2√14 and c=9,

a = 5

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : a₁ = 7

Step-by-step explanation:

a recursive formula allows a term in the sequence to be found from the preceding term.

the sequence here has a common ratio between consecutive terms

[tex]\frac{21}{7}[/tex] = [tex]\frac{63}{21}[/tex] = 3

thus to find a term in the sequence multiply the previous term by 3, that is

[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : first term a₁ = 7

Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.

A general exponential decay is:

f(x) = A*(b)^x

Where A is the initial value, b is the rate of decay, x is the variable.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

Learn more about exponential decays at:

brainly.com/question/27822382

#SPJ1

Answer:

The place value of 4 in 265 473 is 40,000

Answer:

Step-by-step explanation:

Order:

3 is in the ones place and has a value of 3

7 is in the tens place and has a value of 70

4 is in the hundreds place and has a value of 400

5 is in the thousands place and has a value of 5000

6 is in the ten thousands place and has a value of 60,000

2 is in the hundred thousands place and has a value of 200,000

Answer:

Step-by-step explanation:

T+4 = -7

T = -7 -4

T = -11

Answer:

Here is a Venn diagram that illustrates the information:

```

           ___________

          |           |

          |    N      |

          |_____  ____|

          |\    ||    /|

          | \   ||   / |

          |  \  ||  /  |

          |   \ || /   |

          |  C \||/ T  |

          |_____\v/____|

              A

```

In the diagram, N represents the set of students who read the novel, C represents the set of students who read the comics, and T represents the set of students who read the textbook. The region labeled A represents the set of students who read all three.

Using the Venn diagram, we can find the number of students who read:

a. comics and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for comics and novel, but not for textbook. This region has 9 students.

b. textbook and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for textbook and novel, but not for comics. This region has 1 student.

c. none of the 3: This corresponds to the region of the diagram that is outside of all three circles. This region has 13 students.

Therefore, the number of students who read a. comics and novel only is 9, b. textbook and novel only is 1, and c. none of the 3 is 13. Answer: a. 9, b. 1, c. 13.

Answer:

AB = 90° , AC = BC = 135°

Step-by-step explanation:

the arc AB is equal to the measure of the central angle it subtends, then

AB = 90°

the sum of the arcs in a circle = 360° , then since AC and BC are congruent

AB + AC + BC = 360° ( since AC = BC ), then

90° + 2AC = 360° ( subtract 90° from both sides )

subtract 90° from both sides

2AC = 270° ( divide both sides by 2 )

AC = 135°

since AC = BC , then

AC = BC = 135°

The value of the variable x in the equation 6 / -4.5 = 8 / 4x is - 3 / 2.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Therefore, let's solve the equation.

The variable in the equation is x . A variable is a number represented with letter in an equation.

Therefore,

6 / -4.5 = 8 / 4x

cross multiply

6(4x) = -4.5(8)

24x = - 36

divide both sides of the equation by 24

Therefore,

x = -36 / 24

x = - 3 / 2

learn more on equation here: brainly.com/question/13737751

#SPJ1

Answer:131290

Step-by-step explanation:13129*100/10=131290

Answer:

56 cm

Step-by-step explanation:

have a good day God bless :)

Answer:A,D

Step-by-step explanation:

y = [5.3, 27]

x= [-1,3]

The horizontal distance the ball travelled is 2.73 m.

A projectile is any object that is moving in space under the influence of gravity and its momentum. The horizontal distance covered by a projectile from its point of projection is called range. It can be determined by;

R = U[tex]\sqrt{\frac{2H}{g} }[/tex]

where u is the initial speed of the object, H is the height of projection and g is the gravitational constant.

So that in the information given, we can determine the range as;

R = U[tex]\sqrt{\frac{2H}{g} }[/tex]

  = 35[tex]\sqrt{\frac{2*0.39}{10} }[/tex]

  = 35*0.078

  = 2.73

R = 2.73 m

The horizontal distance the ball has travelled is 2.73 m.

Learn more about projectiles at https://brainly.com/question/30297855

#SPJ1

The solution of the each given equations:

(1) x = 9

(2) x = -2

(3) x = -2

(4) x = 26

(5) x = 3/5

(6) x = 13/12

(7) x = 15

(8) x = 26

(9) x = 7/3

(10) x = 5/8

We have to solve this given equation in on variable.

(1) Given equation is,

x - 7 = 2

x = 2 + 7 = 9

Hence, the solution is, x = 9

(2) Given equation is,

3x + 4 = -2

3x = -2 -4

3x = -6

x = -6/3 = -2

Hence, the solution is, x = -2

(3) Given equation is,

2x + 7 = x + 5

2x - x = 5 - 7

x = -2

Hence, the solution is, x = -2

(4) Given equation is,

x/2 = 13

x = 2*13 = 26

Hence, the solution is, x = 26

(5) Given equation is,

5(2 + x) = 13

10 + 5x = 13

5x = 13 - 10

5x = 3

x = 3/5

Hence, the solution is, x = 3/5

(6) Given equation is,

6(2x - 1) = 7

12x - 6 = 7

12x = 7 + 6 = 13

x = 13/12

Hence, the solution is, x = 13/12

(7) Given equation is,

2x/5 = 6

2x = 6*5 = 30

x = 30/2 = 15

Hence, the solution is, x = 15

(8) Given equation is,

x/2 = 13

x = 2*13 = 26

Hence, the solution is, x = 26

(9) Given equation is,

(x - 1)3 = 4

3x - 3 = 4

3x = 4 + 3 = 7

x = 7/3

Hence, the solution is, x = 7/3

(10) Given equation is,

(2x - 1)4 = 1

8x - 4 = 1

8x = 1 + 4

8x = 5

x = 5/8

Hence, the solution is, x = 5/8

To know more about equations here

https://brainly.com/question/22688504

#SPJ1

The standard error is 0.0912.

The standard error (SE) is a measure of the precision of the sample mean estimate compared to the true population mean. To calculate the SE, we use the formula SE = standard deviation / square root of sample size.

In this scenario, the population parameter is 0.7, and the sample size is 30. If we assume that the sample mean is an unbiased estimator of the population mean, then the SE can be calculated using the above formula. However, we do not know the standard deviation of the population, so we use the sample standard deviation as an estimate.

Assuming the sample is large enough to assume normality, the formula becomes SE = [tex]\sqrt{(0.7*0.3)/30}[/tex]   = 0.0912. Therefore, the standard error for a sample size of 30 is 0.0912. This means that if we were to take multiple samples of size 30 from the same population, the standard deviation of the means of those samples would be around 0.0912 away from the population parameter of 0.7 on average.

To learn more about standard error here:

https://brainly.com/question/13179711

#SPJ1

The second job offer is better by $21,840.

We have :

An employee is considering two job offers.

First offer: $57,000 yearly salary with an 8% matching 401k

Second offer: $63,000 yearly salary with a 4% matching 401k

Let's calculate the total value of the second offer after 4 years:

Yearly salary is : $63,000

Total gross income after 4 years: $63,000 x 4 = $252,000

The company matches 5% of the employee's salary.

So, the employee contributes 5% of $63,000 = $3,150 per year

After 4 years,

Company matches: $3,150 x 4 = $12,600

Employee contributions: $3,150 x 4 = $12,600

Total 401k contributions: $12,600 + $12,600 = $25,200

The total value of the second offer after 4 years is:

Total value: $252,000 + $25,200 = $277,200

Now, let's compare this to the total value of the first offer, which is : $255,360.

Therefore, the second job offer is better by:

$277,200 - $255,360 = $21,840

Hence, The second job offer is better by $21,840.

Learn more about Salary at:

https://brainly.com/question/14371457

#SPJ1

The probability that a statistics teachers do not know the true meaning of life is 46.8%

From the question, we have the following parameters that can be used in our computation:

53.2% of Americans say they believe that statistics teachers know the true meaning of life.

This means that

P(Believe) = 53.2%

For the required probability, we have

P(Not believe) = 1 - P(Believe)

So, we have

P(Not believe) = 1 - 53.2%

Evaluate

P(Not believe) = 46.8%

Hence, the probability that a statistics teachers do not know the true meaning of life is 46.8%

Read more about probability at

https://brainly.com/question/24756209

#SPJ1

The percentage of the sodas that was served which were regular would be = 18%

The quantity of regular sodas served = 18

The quantity of diet soda served = 82

The total number of soda served = 18+82 = 100

Therefore the percentage of soda that were regular would be;

= 18/100 × 100/1

= 18%

Learn more about percentage here:

https://brainly.com/question/24339661

#SPJ1