Consider the line y=4x-4.
Find the equation of the line that is parallel to this line and passes through the point (3, 6).
Find the equation of the line that is perpendicular to this line and passes through the point (3, 6).

The dimensions of the given right triangle would be 5.66 inches and 11.31 inches.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Let the legs of the triangle be x and y

Using the Pythagorean theorem:

c² = a²+b²

So the hypotenuse will be:

x² + y² = 8²

x² + y² = 64

x² = 64 - y²

So the area of the triangle is:

A = 1/2bh

A = 1/2xy

⇒16 = 1/2xy

32 = xy

x = 32/y

x² = 1024/y²

Substitute the above value in x² = 64 - y² and solving for y we get:

1024/y² = 64 - y²

1024 = 64y²- y⁴

This can be written as:

y⁴ - 64y² + 1024 = 0

Thus y = 4√2 = 5.66

x = 64/(4√2)= 16/√2 = 8√2 = 11.31

Therefore, the dimensions of the given right triangle would be 5.66 inches and 11.31 inches.

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Answer:

3rd quadrant

Step-by-step explanation:

Given:

Point (-2, -9)

Computation:

In 1st quadrant (+ , +)

In 2nd quadrant (- , +)

In 3rd quadrant (- , -)

In 4th quadrant (+ , -)

So given point (-2, -9) is in 3rd quadrant.

Answer:

\(f(8) = 81\)

\((g\ o\ f)(x) = x^2 + 2x -4\)

Step-by-step explanation:

Solving (a):

\(f(x) = x^2 + 2x +1\)

\(g(x) = x - 5\)

Solve for f(8)

We have:

\(f(x) = x^2 + 2x +1\)

Substitute 8 for x

\(f(8) = 8^2 + 2*8 +1\)

Solve

\(f(8) = 64 + 16 +1\)

\(f(8) = 81\)

Solving (b):

\((g\ o\ f)(x)\)

This is solved by:

\((g\ o\ f)(x) = g(f(x))\)

So, we have:

\(g(x) = x - 5\)

\(g(f(x)) = f(x) - 5\)

Substitute: \(f(x) = x^2 + 2x +1\)

\(g(f(x)) = x^2 + 2x + 1 - 5\)

\(g(f(x)) = x^2 + 2x -4\)

Hence:

\((g\ o\ f)(x) = x^2 + 2x -4\)

Answer:

125

Step-by-step explanation:

All the work is in picture attat

Answer:

26 and 27

Step-by-step explanation:

Let the numbers be x and y

x + y = 53

xy = 702

x = 702/y

702/y + y = 53

Multiply through by y

702 + y^2 = 53y

y^2 - 53y + 702 = 0

y^2 - 27y - 26y + 702 = 0

y(y - 27) - 26(y - 27) = 0

(y - 27) (y - 26) = 0

y = 26 or 27

Solve for x in x + y = 53

if y = 26,

x = 53 - 26 = 27

if y = 27,

x = 53 - 27 = 26

The numbers are 26 and 27

k= 2.5.

To find the slope of a line, let's refer to the slope formula:

\(m=\frac{y_2-y_1}{x_2-x_1}\).

(Check the attched image below).

Point 1: (0, 5)

Point 2: (2, 10)

\(m=\frac{5-10}{0-2}=\frac{-5}{-2}=2.5\)

k= 2.5.

The approximate difference in the maximum heights achieved by the two projectiles is 3.7 feet .

Given that :

f(x) = -16x^2 + 42x + 12,

f'(x) = -32x + 42 = 0 ,

so x = 42/32

= 21/16

= 1.3125

Then its max height is:

f(x) = f(21/16) = -16(21/16)2 + 42(21/16) + 12

f(x) = [-(21)2 + 42(21) + 12(16)]/16

= [-441 + 882 + 192]/16 = 633/16

= 39.563

= 39.6 rounded

g(0) =  -9 =  C

g(1) =  33 =  A + B + C = A + B -9,  so A = 33 + 9 -B = (42 - B)

g(2) =  25 = 4A + 2B - 9

25 = 4(42 - B) + 2B -9 = (168 - 9) -2B,

so  2B = -25 + 159 = 134  

B = 67

Then A = 42 - B

= 42 - 67

= - 25

Thus g(x) = -25x2 + 67x - 9,

and its derivative or slope is g'(x) = -50x + 67 = 0 for the peak height

x  = -67/-50 = 1.34,

g(x) = -25(1.34)2 + 67(1.34) - 9

= -44.89 + 89.78 - 9

= 35.89

= 35.9 rounded

Finally, the difference in peak or max height = 39.6 - 35.9

=  3.7 feet

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Answer:

Excuse me?

Step-by-step explanation:

Put your question DB and I'll gladly answer!

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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9514 1404 393

Answer:

  (b) dilation by 2, reflection in y-axis

Step-by-step explanation:

Each of the dimensions of ΔA'B'C' is double the corresponding dimension of ΔABC, so dilation by a factor of 2 has occurred.

The sequence of vertices in ΔA'B'C' is CCW, opposite that of ΔABC. Hence, a reflection has taken place. (Rotation keeps the same order.)

The transformation is a dilation by a factor of 2 and a reflection across the y-axis.

The range of the graph of the exponential function is (b) {y | y > 0}

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

The graph of the exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

From the graph, the constant term is 0

So, the range is y > 0

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Answer:

Step-by-step explanation:

When the digit in the thousands place is < 5, the thousandths place and following digits are replace by 0.

2. When the digit in the thousands place is = or > 5, the digit in the hundredths places is increased by 1 and the following digits become 0.

Answer:

36 women

Step-by-step explanation:

28 divided by 7 is 4 then times the 4 by 9 and you get 36

Answer:

It is 36

Step-by-step explanation:

The value of numbers are 71 and 35.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The difference between two numbers = 36

And, Five time the larger is 11 times the smaller.

Now,

Let the larger number = x

And, The smaller number = y

So, We can formulate;

The difference between two numbers = 36

⇒ x - y = 36  ..(i)

And,  Five time the larger is 11 times the smaller.

⇒ 5x = 11y

⇒ 5x - 11y = 0  ..(ii)

Multiply by 5 in (i), we get;

⇒ 5x - 5y = 210  ..(iii)

Subtract above equation from (ii), we get;

⇒ 6y = 210

⇒ y = 35

And, From (i);

⇒ x - y = 36

⇒ x - 35 = 36

⇒ x = 36 + 35

⇒ x = 71

Thus, Two numbers are 71 and 35.

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Answer:

7/2 = 35/10

3/5 = 6/10

Step-by-step explanation:

To get a common denominator of 10, simply multiply the current denominator by any number to equal 10. The first fraction has a denominator of 2. If we divide 10 by 2, we get the answer 5. This means 2 can be multiplied by 5 to get a denominator of 10. However, what we do to the denominator we must also do to the numerator (multiply by 5).

7/2

7 × 5 / 2 × 5

35/10

3/5

3 × 2 / 5 × 2

6/10

Answer:

7/2 = 35/10

3/5 = 6/10

Step-by-step explanation:

\(\frac{7}{2}\cdot \frac{5}{5}=\frac{35}{10}\)

\(\frac{3}{5}\cdot \frac{2}{2}=\frac{6}{10}\)

The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901

The amount of money gained after an investment is compounded is given by:

\(A=P(1+\frac{r}{n} )^{nt}\)

Where P is principal, A is the final amount, r is the rate, n is the number of times compounded per period and t is the time

Given that P = $1689, t = 4, r = 3% = 0.03, n = 1, hence:

\(A=P(1+\frac{r}{n} )^{nt}\\\\A=1689(1+\frac{0.03}{1} )^{4*1}\\\\A=\$1901\)

The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901

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Answer:

the probability that the two committees have at least one member in common is approximately 0.3622.

Step-by-step explanation:

To find the probability that two committees have at least one member in common, we can use the complement rule, which states that the probability of an event happening is 1 minus the probability of the event not happening.

Let A be the event that the two committees have no members in common. To calculate the probability of A, we can first find the number of ways to choose three people out of 20 without any overlap, and then use this to find the total number of ways to choose two committees of three people each without any overlap:

Number of ways to choose 3 people out of 20 without overlap:

C(20,3) = (201918)/(321) = 1140

Number of ways to choose 3 people out of 20 with overlap:

C(20,3) - C(2,1)C(17,2) = 1140 - 2(2*136) = 680

The first term is the total number of ways to choose 3 people out of 20, and the second term is the number of ways to choose 3 people out of 20 such that one particular person is included. We multiply by 2 because there are two committees.

The total number of ways to choose two committees of three people each without any overlap is:

C(20,3) * C(17,3) = (1140*680) = 775200

Therefore, the probability that the two committees have no members in common is:

P(A) = 775200 / (C(20,3)*C(17,3)) = 0.6378

So the probability that the two committees have at least one member in common is:

P(at least one member in common) = 1 - P(A) = 1 - 0.6378 = 0.3622

Therefore, the probability that the two committees have at least one member in common is approximately 0.3622.

thirty-five thousand, three hundred twenty-six.

Answer:

Thirty-five thousand Three Hundred and twenty-six

Step-by-step explanation:

You can also just look it up on google.

Hope This Helps :)

The electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

In the analogy of a circuit with resistance, we can compare it to an obstacle race. Here's how we can relate the different elements:

Circuit: The entire obstacle race course represents the circuit itself. It includes all the components and paths that the participants will go through.

Obstacles: The obstacles in the race represent the resistors in the circuit. Just like resistors impede the flow of electrical current in a circuit, obstacles in the race impede the progress of the participants.

People/Participants: The people participating in the race represent the flow of electric current in the circuit. They are the "charge" moving through the circuit, encountering and overcoming obstacles (resistors) to reach the finish line.

The goal of the participants (people) is to navigate through the obstacles (resistors) and complete the race (circuit) by reaching the finish line.

Similarly, in an electrical circuit, the goal is for the electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

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Answer:

94%

Step-by-step explanation:

We need to look at the graph. Olive wants the probability that 20 or more of the 50 babies were female. Looking at the graph, the x-axis is "number of females born out of 50 babies". We want to find the sum of all the ones that are at least 20, or 20 and above.

The numbers above the bars represents how many of each case there are. Above the bar labelled 20, there is the number 11, and so on. So, our sum is:

11 + 17 + 14 + 23 + 16 + 29 + 16 + 23 + 14 + 6 + 9 + 3 + 1 + 2 + 1 + 1 + 1 = 187

In total, there are 200 cases, so our probability is 187 / 200 = 93.5% ≈ 94%.

The answer is thus A.

Step-by-step explanation:

Step 1:  Count up how many babies are more than 20

\(11 + 17 + 14 + 23+16+29+16+23+14+6+9+3+1+2+1+1+1\)

\(187\)

\(187 / 200\) ← Will give us percentage of the probability that 20 or more of the 50 babies were born female.

0.935 * 100

93.5%

Answer:  Option A, 94%

Statement (A) is true, Statement (B) is false, Statement (C) is true, Statement (D) is true and Statement (E) is false.

The given information is that P(odd) = 1/3

where odd numbers are 3 and 5, and there are two odd-numbered sections out of six equal sections.

(A) The probability of landing on an odd-numbered section is not exactly 33.33%, but approximately equal to 33.33% or 1/3.

So, statement (A) is true.

(B) The probability of landing on an even-numbered section is not exactly 66.67%, but approximately equal to 66.67% or 2/3.

So, statement (B) is false.

(C) The probability of landing on an odd-numbered section is given as 1/3, which is less than the probability of landing on an even-numbered section, which is 2/3. Therefore, statement (C) is true.

(D) It is given that one of the sections is numbered 6. So, it is not impossible to land on 6. Therefore, statement (D) is false.

(E) To determine if the spinner is fair, we need to know the probability of each outcome, which is not provided in the given information. Therefore, we cannot determine if the spinner is fair or not based on the information given. So, statement (E) is uncertain.

Therefore, the true statements about this game are (A), (C), and (D).

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The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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Answer: (0.79, 3.05 )

Step-by-step explanation:

Confidence interval for the population mean:

\(\overline{x}\pm z^c\dfrac{\sigma}{\sqrt{n}}\)

, where \(\overline{x}\) = Sample mean

\(\sigma\) = population standard deviation

n= sample size.

\(z^c\) = Critical z value for confidence interval c.

As per given:

n= 10

\(\overline{x}=1.92\)

\(\sigma=1.83\)

Critical z-value for 95% confidence = 1.96

A 95% confidence interval for the mean opinion in the population of all licensed drivers:-

\(1.92\pm (1.96)\dfrac{1.83}{\sqrt{10}}\\\\=1.92\pm1.134\\\\= (1.92-1.134,\ 1.92+1.134)\\\\\approx(0.79,\ 3.05 )\)

Hence, a 95% confidence interval for the mean opinion in the population of all licensed drivers = (0.79, 3.05)

Answer:

6666

Step-by-step explanation:

Answer:

4in²

Step-by-step explanation:

area of rectangle = l x b = 4 x 1 = 4in²

Answer:

4 in²

Step-by-step explanation:

4x1 is 4 so the answer is 4

The percentile of 6.2 in the given data set is 40%.

To determine the percentile of 6.2 in the given data set, we can use the following steps:

Arrange the data set in ascending order:

4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2

Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.

Calculate the percentile using the formula:

Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100

In this case, the percentile of 6.2 can be calculated as:

Percentile = (4 / 10) × 100 = 40%

The percentile of 6.2 in the sample data set is therefore 40%.

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Answer:

The answer is 4(3x² + 1)(x - 5).

Step-by-step explanation:

First, you have to take out all the common ratios :

12x³ - 60x² + 4x - 20

= 4(3x³ - 15x² + x - 5)

Next, you have to factorize the inner brackets :

3x³ - 15x² + x - 5

= 3x²(x - 5) + (x - 5)

= (3x² + 1)(x - 5)

Answer:

4(3x² + 1)(x - 5)

Step-by-step explanation:

Given

12x³ - 60x² + 4x - 20 ← factor out 4 from each term

= 4(3x³ - 15x² + x - 5)

Factor the first/second and third/fourth terms inside the parenthesis

= 4[ 3x²(x - 5) + 1(x - 5) ] ← factor out (x - 5) from each term

= 4(3x² + 1)(x - 5)

In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.

The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."

When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.

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