From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.

Answer:

  ∡BOA ≅ ∡DOC

Step-by-step explanation:

Given a circle O with congruent chords BA and DC, you want the relation between angles BOA and DOC.

All of the radii of circle O are congruent. That means BO≅AO≅DO≅CO. The chords BA and DC are marked as congruent. This means ∆BOA and ∆DOC are congruent by the SSS postulate.

Corresponding parts of congruent triangles are congruent, so ...

  ∡BOA ≅ ∡DOC

In order to calculate the area of carpet needed to cover the entire floor, we just need to calculate the area of the room.

The area of a rectagle is calculated by the product of its dimensions, so we have:

So the area of carpet needed is 132 square feet.

Answer: B.

Step-by-step explanation: First, you find the difference between 2 and 5  =( 3 ), and 54 and 45 ( -9 ). Meaning the unit rate is -3. (-9/3 = -3)

The difference between 12:00 am and 2:00 am is 2 hours meaning 2 x 3 is 6. 54 + 6 = 60 meaning at 12:00 am it was 60 degrees Fahrenheit.

Answer:

y = 24x + 17 20

Step-by-step explanation:

Firstly, let's say that 153 and 17 are both the y-intercepts of their respective equations, while 22 and 24 are the slope. With this we can create the following set of equations:

y = 24x + 17

y = 22x + 153

So your answer would be y = 24x + 17

Now let's find the sales answer!

Since we know that Ida made 4 more sales than Wade this week, we could say:

y = 24(x+4) + 17

y = 22x + 153

Now since we know that they earned the same amount we can do the following:

24(x+4) + 17 = 22x + 153

Simplify...

24x + 96 + 17 = 22x + 153

Simplify again:

24x + 113 = 22x + 153

subtract 22x and 113 from both sides...

2x = 40

Then:

x = 20

So this means that Wade made 20 sales this week!

So let's check if we are right:

Now that we know that x = 20, we need to plug it into Wade's equation!

y = 22(20) + 153

y = 440 + 153

y = 593

Wade made $593 this week!

To check if we are right, let's plug it into Ida's equation:

y = 24x + 113

y = 24(20) + 113

y = 480 +113

y = 593

Ida also made $593 this week!

MEANING we are right!

I hope I helped :P

Consider that the Alternate Exterior Angles are always equal for a transversal passing through two parallel lines.

The given diagram depicts two incline parallel lines and the vertical line acts as a transversal to them.

Now, angle 1 and angle 8 are alternate exterior angles so they must be equal,

So the measure of the angles is given by,

Thus, both the angles measure 149 degrees.

The given expression is

Since sec is the opposite of cosine, then

Since the value of cos(3pi/2) is 0, then

Since 1/0 is an undefined value, then

The answer is undefined

We are asked to express 952 in scientific notation

The scientific notation is given by

The number 952 has the decimal point at the end, so we move this decimal point to the left until there is only one digit is left (9 in this case) and then count the number of times we moved.

In this case, we moved 2 times so the exponent (power) is 2

The sign of exponent is positive when we move to the left (like in this case)

The sign of exponent is negative when we move to the right.

We have the following:

Since it is a square, the sides are equal, and the perimeter is the sum of all the sides, therefore it would be

The answer is 8n - 12

One option is to use the distance formula.

In this case, this is what Julie would be working with:

[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(x-w)^2+(y-z)^2}\\\\[/tex]

If Julie knew the values of x, y, w, and z, then she could find a numeric result for the distance (d).

Answer:

10 divided by 3 1/3 is;

Explanation:

We want to divide 10 by 3 1/3;

Firstly, let us convert the mixed fraction to improper fraction;

Then we can proceed to divide;

Therefore, 10 divided by 3 1/3 is;

The milestones at which we will be profitable in terms of the number of consumers serviced are going to be (20, $170), and (130, $60).

In several aspects of commerce and finance, a break-even point is an important concept to understand. In the context of finance and accounting, it is a reference to the level of output at which the total production income matches the entire production expenses.

When it comes to financing, the moment at which an investment is considered to have broken even is known as the "break-even point."

When the market price of an underlying asset hits the level at which a buyer will not incur a loss, this is referred to as the break-even point in the options trading market.

In contrast, the point at which a buyer will not incur a loss.

The following will serve as examples of the model:

n - n1 = m(p - p1)

n - 50 = -1(p - 140)

n = -p + 190

Where

Revenue = price * quantity

Revenue = p * n

Revenue = (190 - n) * n

[tex]Revenue= 190n - n^2[/tex]

Cost = 40n +2600

At break-even, revenue = cost

[tex]190n - n^2 = 40n + 2600[/tex]

[tex]n^2 - 150n + 2600 = 0.[/tex]

n = 20 p = 170

n = 130 p = 60

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The quotient of 7.7 x 10^8 and 5.5 x 10^2 expressed in scientific notation is 1.4x10^6.

What is quotient?

A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is used to describe the integer component of a division (when Euclidean division), as well as a fraction or a ratio (when proper division). A quotient in the second sense is only the proportion of a dividend to its divisor.

Lets calculate the quotient for the value given in question:

[tex]7.7 \times 10^8[/tex]

[tex]5.5 \times 10^2[/tex]

Now we divide the 7.7 by 5.5

[tex]\frac{7.7}{5.5} = 1.4[/tex]

we get value 1.4.

on dividing  [tex]\frac{10^8}{10^2}[/tex] we get, [tex]10^6[/tex]

Combining both the value, we get

quotient = [tex]1.4 \times 10^6[/tex]

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Let 'a' represent the unknown side of the triangle.

To solve for the unknown side, we will apply the Pythagoras theorem.

Let solve for cscθ

Let us solve for cosθ

Let us solve for tanθ

The annual percentage rate (APR) for the loan of $3,600 at 8% add-on interest for 3 years is 15.6%.

The annual percentage rate is the nominal or effective interest rate charged on a loan for a year, unlike the Monthly Percentage Rate (MPR), which is a monthly rate.

The annual percentage rate can be calculated by using the formula:

APR = 2Nr/N + 1

N = number of payments

r = the add-on interest rate

N = 3 years = 36 months (12 x 3)

r = 8% or 0.08 (8/100)

APR = (2 x 36 x 0.08)/(36 + 1)

= 5.76/37

= 0.15.57

= 15.57%

= 15.6%

Thus, with an 8% interest rate for 3 years, the APR is 15.6%.

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Based on the concept of multiplication, the amount of molecules consumption of water does a person drink in a year is 1.32 x 10²⁸.

Molecules:

A molecules is the group of two or more atoms linked together by sharing electrons in a chemical bond

Given,

There are about 6 x 10²⁴ molecules in a liter of water. it is estimated that a person drinks about 2.2 x 10³ liters of water a year.

Here we have to find the amount of molecules consumption of water does a person drink in a year.

To find the total amount of molecules consumption for the year we have to use the following formula,

Total molecules consumption per year = amount of water x molecules.

Here we know the values of the following,

Water consumption per year = 2.2 x 10³ liters

Molecules of one liter water = 6 x 10²⁴

Apply the values on the formula, then we get,

=> total molecules consumption = (2.2 x 10³) x (6 x 10²⁴)

=> (2.2 x 6) x (10³ x 10²⁴)

=> 13.2 x 10³⁺²⁴

=> 13.2 x ²⁷

It can be further simplified as,

=> 1.32 x 10²⁸

Therefore, the amount of molecules consumption of water does a person drink in a year is  1.32 x 10²⁸.

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For the new price to be 28% less than the original price then, therefore, the original price is definitely more than the new price

Let the original price be

the new price given is

It means that the percentage decrease is

The formula for percentage decrease is

By substitution, we will have

Therefore,

The original price = $775

The required solution of the inequality on  the number line is represented as x>20 .

Any monotonically rising function can, by definition, be applied to both sides of an inequality without destroying the inequality connection (provided that both of the expressions are in the domain of that function).

–3(2x – 5) < 5(2 – x)

-6x+30 < 10-5x

-6x+5x<-20

-x<-20

x>20 (x∈R)

The inequality relation is flipped when a monotonically decreasing function is applied to both sides of an inequality. In the equations for the adding inverse and multiple inverse for positive numbers, a monotonically decaying function is utilized.

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The equation of the line whose slope is 1/6 passing through the point (-9, 3) is -x - 6y - 27 = 0

To determine a line's inclination or steepness, use the slope formula. By calculating the ratio of the change in the y-axis to the change in the x-axis, it may be used to calculate the slope of any line. A line's slope is determined by how its "y" coordinate changes in relation to how its "x" coordinate changes.

Given slope of equation m =[tex]\frac{1}{6}[/tex]

A point on line (x₁,y₁) = (-9,3)

(y-y₁)= m (x-x₁)

(y-3) = [tex]\frac{1}{6}[/tex] ( x − (-9))

y-3= [tex]\frac{1}{6}[/tex] (x+9)

6(y-3) = x+9

6y - 18 = x +9

-x - 6y - 27 = 0

This is the equation of line

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No solution

y = 4x + 5

y = 4x - 2

Solving algebraically:

equate both equations

y = y

4x + 5 = 4x - 2

collect like terms:

4x - 4x = - 2 - 5

0 = -7

When the right hand side is not the same as the left hand side equation, it is a no solution.

Their intersection point gives no solution

The critical value of tα/2 for a 90% confidence interval for the sample size 15 is 1.761.

Given, sample size=15

Confidence interval= 90%.

To find the critical value we have to first find alpha, by subtracting 90 from 100.

= 100%-90%

=1-0.9

=0.1

α=0.1

α/2=0.05

Next, we have to find the degrees of freedom(df) by using the formula n-1.

=15-1

df=14

Calculate tα/2 by using t-distribution with degrees of freedom 14 and α/2 = 0.05 as right-tailed area.

From the table we get the critical value for tα/2 as 1.761.

Therefore, the critical value for a 90% confidence interval with sample size 15 is 1.761.

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The required sample size of the given estimate is 3030.65.

Given that,
The population standard deviation is approximately σ = 50.2. You would like to be 90% confident that your estimate is within 1.5 of the true population mean.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
For the 90% confidence the value of the z = 1.645
Now the sample size is given as,
n = [z × σ/1.5]²
Substitute values in the above equation,
n = [1.645×50.2/1.5]²
n = 3030.65

Thus, the required sample size of the given estimate is 3030.65.

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We are asked to determine probabilities from a population of high school graduates. Let's remember that probability is defined as the quotient of desired events and the number of total events.

a) what is the probability that a 2001 graduate of City High School was accepted into college

To determine the probability we need to find the quotient of the number of students that were accepted into college and the total number of students. The total number of students accepted into college is 145 female plus 100 males, therefore, the probability is:

Therefore, the probability is 65.3%.

b)what is the probability that 2001 graduate of City high School was not a female

To do this we will use the fact that the sum of the probabilities that a student is a female plus the probability that the student is not a female must be equal to 1.

Therefore, solving for the probability that the student is not a female we get:

The probability that the student is female is the quotient between the number of female students and the total number of students, therefore:

Therefore, the probability that the student is not a female is 53.9%.

c) what is the probability that a 2001 graduate of City high School was accepted into college or male

To determine this probability we need to have into account that the probability of event A or event B happening is the sum of both probabilities minus the probability of both events happening at the same time, therefore:

Replacing the probabilities we get:

Solving the operations:

Therefore, the probability that a student is accepted or male is 91.6%

d) what is the probability of being a female given you were accepted into college.​

The probability of event A given event B is given by the following formula:

In this case, we have:

Replacing the probabilities:

Therefore, the probability is 60%.

The translation of two units right of the graph of y = x is graphed at the end of the answer.

Translation is a transformation to the graph of a function or of a figure that keeps everything such as orientation and inclination stable, changing only the position of the graph.

The translations are movements to left, right, up or down, and each movement is represented as follows:

In this problem, the definition of the translation is given as follows:

y = f(x - 2).

Hence a = 2, and the function is shifted right 2 units.

Considering function y = x, the translated function is:

y = f(x - 2) = x - 2.

(each instance of x in the function is replaced by x - 2).

The graph of the two functions is shown at the end of the answer, which x - 2 being a shift right of 2 units of f(x).

The function is not given, hence we suppose that it is of y = x.

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Following the instructions provided, we shall use a graphing calculator (Desmos) to determine the equation of the circle shown by the "colorful people."

The first step is to determine the radius which we can observe from the circle itself, whose diameter spans from 0 units to 10 units along the x-axis. The radius therefore is 5 units (half of the diameter).

Observe also that the center has now moved away from the origin (0, 0), and if we move the slider very carefully for h, that would be 5 units away from the origin towards the right (along the x-axis), andk would be 7 units away from the origin) towards the bottom (along the y-axis).

After following these steps, we can replicate the circle given in the question and if we now substitute the values of h, k and r into the equation of a circle, we would end up with;

Answer:

x-intercept is at (18, 0)

y-intercept is at (0, 360)

Given:-

To find the volume of cone.

So the volume formula for cone is,

Substituting we get,

So the required solution is 190.76

Step 1

The selection formula is;

Answer; 252 groups