the length of a rectangle is 2 feet more than the width. Find the minimum dimensions if the perimeter is more than 16 feet and the length and width are integers.

The 95% confidence interval for the proportion of respondents who say yes is of:

(0.5562, 0.6176)

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters, which are the sample size and the estimate, are given as follows:

[tex]n = 990, \pi = \frac{581}{990} = 0.5869[/tex]

The lower bound of the interval is of:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 - 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.5562[/tex]

The upper bound of the interval is of:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 + 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.6176[/tex]

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Answer:

20 slices

Step-by-step explanation:

If there were 11 large pizzas with 8 slices per pizza, that would mean that there are a total of 88 slices of pizza.

If there are four classrooms, that means that if each classroom had 20 slices, there would be enough for everyone with 8 pieces leftover.

20 x 4 = 80

Answer:

3x  + 12

Step-by-step explanation:

3(x+1)+9

= 3x  + 3 + 9

= 3x  + 12

Answer:

1

Step-by-step explanation:

Perpendicuar lines have slopes that are opposite reciprocals: 6 ==> -1/6

y=mx+b

y=-x/6 + b ==> plug in slope -1/6 into slope equation

1 = -6/6 + b ==> plug in x and y values into slope equation

1 = -1 + b

1 + 1 = -1 + 1 + b

b = 2 ==> solve for b

y = -x/6 + 2 ==> plug in the value of b into the equation

y - 1 = -x/6 + 2 - 1

y - 1 = -x/6 + 1

y - 1 = -(x/6-1) ==> answer: 1

They should charge for its premium in order to have an expectation of $0 for the policy is $85.

Given that, the probability that a 50-year-old male in the U.S. will die within one year is about 0.00142.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, probability of alive 100-0.00142

= 0.99858

P(A)=0.99858A+0.00142(A+60000)

Put A=0, in the obtained function, we get

P(0)=0.99858(0)+0.00142(0+60000)

=0.00142×(60000)

=$85.2

= $85

Therefore, they should charge for its premium in order to have an expectation of $0 for the policy is $85.

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The probability that 3 of the 6 children of this parents has the genes would be 0.1318

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

The total number of children from the family is n = 6

and the probability of those with the cystic fibrosis is x = 3,

Probability of the disease = 0.25

We have the formula as

[tex]^{6} C_{x} *P^{x} *(1-p)^{n-x}[/tex]

The probability is 1/4 = 0.25

This is then written as

6C3 x 0.25³ x (1 - 0.25)⁶⁻³

= 20 x 0.015625  0.421875

= 0.1318

The probability that 3 out of the 6 children would have this gene is 13.18%

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The pattern is that two larger numbers differ by 2 and the smaller is the root of twice the sum of the larger two.

The given formula gives rise to the above observations. it tells you

a = 2x

b = x^2 -1

c = x^2 +1

This is a special case of Euclid's formula ...

a = 2mn

b = m^2 -n^2

c = m^2 +n^2

for n=1.

Since m and n can be any integer values, there are certainly many other. Pythagorean triples that do not match the formula given in the problem. Using n=2, for example, the triples are:

a = 4x

b = x^2 -4

c = x^2 +4

Some triples from this set of formulas are (5, 12, 13), (20, 21, 29), (28, 45, 53), (36, 77, 85).

It should bm be noted that triples from this set of formulas will not match directly those from the formulas in the problem statement, but triples from both lists may reduce to the same primitive triple.

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Complete question

Examine this set of Pythagorean triples from part C. Look for a pattern that is true for each triple regarding the difference between the three values that make up the triple.

Describe this pattern. Then see if you can think of another Pythagorean triple that doesn’t follow the pattern you just described and that can’t be generated using the identity (x2 − 1)2 + (2x)2 = (x2 + 1)2. Explain your findings.

x-value Pythagorean Triple

3 (6,8,10)

4 (8,15,17)

5 (10,24,26)

6 (12,35,37)

Based on the number of people present, the total number of combinations of Chairperson and Vice Chairperson is 240 combinations.

In order for us to find out the total possible combinations, we will use the formula as:

Total possible combinations = Number of possible chairpersons * Number of possible vice chairpersons

We are given that;

Number of possible chairpersons = 16

Number of possible vice chairpersons = 15 (This is because a chairperson is chosen first and leaves 15 people.)

Thus, we can say that;

Total possible combinations = 16 * 15

Total possible combinations = 240 combinations

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Answer:

100.86

Step-by-step explanation:

8.2*8.2+0.5(8.2)*8.2

The only equation given that represents the Exponent Property of Logs is; Option A: log(A^r) = r*log(A)

The  exponent property of logarithm says that the log of a power is the exponent times the logarithm of the base of the power. For example;

logₐ(MN) = logₐM + logₐN

logₐ(M/N) = logₐM - logₐN

logₐ(3²) = 2logₐ3

The first example above shows the product rule of logarithms

The second example shows the quotient rule of logarithms

The third rule shows the power rule

Now, looking at the options, the only one that shows the correct pattern of exponent property of logarithm is;

Option A: log(A^r) = r*log(A)

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The sum of first 50 terms of the sequence a(n) = 3n + 2 is  3925

In this question, we have been given a sequence a(n) = 3n + 2

We need to find the sum of the first 50 terms of the sequence

a(1) = 3 + 2

      = 5

a(2) = 6 + 2

      = 8

a(3) = 9 + 2

      = 11

a(4) = 12 + 2

      = 14

...

Given sequence is arithmetic sequence with common difference d = 3 and the first term a = 5

Using the formula for the sum of first n terms of AP

Sum of n terms of A.P. = n/2[2a + (n - 1)d]

For n = 50

S(50) = (50/2) * [2(5) + (50 - 1)3]

S(50) = 25 * [10 + (49 * 3)]

S(50) = 25 * 157

S(50) = 3925

Therefore, the sum of first 50 terms of the sequence a(n) = 3n + 2 is  3925

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Answer:

B. 10

Step-by-step explanation:

[tex]\rm \implies 28 \div 7 + 2 \times 3 \\ \\ \rm \implies 4 + 2 \times 3 \\ \\ \rm \implies 4 + 6 \\ \\ \rm \implies 10[/tex]

Perimeter meaning: the continuous line forming the boundary of a closed geometric figure.

side length: 15

perimeter: 368

Answer:

Step-by-step explanation:

Equation of circle is, (x-h)^2+ (y-k)^2=r .......(eqn1)

where, (h,k) is the center and r is the radius.

therefore, from the question by rearranging the equation,

x² + y² + 4x − 6y + 12=0

viz, (x² +4x+4) + (y²-6y+9)-1=0  

(x+2)^2 + (y-3)^2=1

therefore from eqn1, (-2,3) is the center and radius is 1

From the graph of the given function , the value of f(1) = -1.

As given in the question,

From the graph of the given function,

Two coordinates from the graph are as follow:

( x₁ , y₁) = (1, -1)

( x₂ , y₂ ) = ( 0, -3 )

Equation of the line representing the function is given by:

(y - y₁) /(x-x₁) = ( y₂ -y₁)/ (x₂ -x₁)

⇒(y +1)/ (x-1) = (-3 +1)/ (0-1)

⇒ (y +1)/ (x-1) = 2

⇒y +1 = 2x -2

⇒ y = 2x -3

To get the value of x we have,

  y = f(x)

⇒f(x) = 2x -3

⇒f(1) = 2(1) -3

⇒f(1) = -1

Therefore, from the graph of the given function , the value of f(1) = -1.

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The value of 2/5 divided by 8/15 is 3/4

A fraction can be defined as the he or portion of a whole set or element

There are different types of fractions, which includes;

Some examples include;

Simple fractions; 1/ 2, 1/3

Proper fractions; 1/ 4, 2/ 3

Improper fractions; 3/ 2, 5/3

Mixed fractions; 2 1/ 6

We have that;

2/ 5 ÷ 8/15

Take inverse of divisor and multiply

2/ 5 × 15/ 8

Divide through

3/4

Hence, the value is 3/4

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The required percentage of height of 34 and 54 inches are 85% and 135%.

Given that,
The percentage of the height of 34 inches and 54 inches against the height of 40 inches is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,

a,
percentage = 34/40 × 100%
Percentage = 85%

b,
percentage = 54/40 × 100%
Percentage = 135%

Thus, the required percentages of height of 34 and 54 inches are 85% and 135%.

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The dimensions of the rectangular window that gives a maximum area are as follows;

Width = [tex]\dfrac{12}{2+\pi }[/tex] feet and length = 3 feet

The maximum value of a function is given by the point at which the graph of the function has the highest value.

The parameters of the window are;

Length of the framing material available = 12 ft.

The shape of the window = A semicircle on top of a regular rectangular window

Required; The dimension of the rectangular part of the Norman window that allows the most light

Solution;

Diameter of the semicircular part of the window = The width of the rectangular part

Let x represent the width of the window, we have;

Perimeter of the semicircle = π·x/2

Side length of the rectangular window = (12 - π·x/2 - x)/2

Area of the rectangular part of the window, A = x × (12 - π·x/2 - x)/2

Area of the semicircle = π·x²÷4

Area of the window, is therefore;

[tex]A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} +\dfrac{ \pi \cdot x^2}{4}[/tex]

At the maximum area, of the rectangular part, we have;

[tex]A_r' =\dfrac{d}{dx}\left( A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} \right) = -\dfrac{x\cdot \pi +2\cdot x-12}{2} = 0[/tex]

x·π + 2·x - 12 = 0

The width, x = [tex]\dfrac{12}{2+\pi }[/tex] feet

The length of the rectangle is therefore;

[tex](12 - \pi \cdot \dfrac{6}{2+\pi } - \dfrac{12}{2+\pi })/2 = 6 - \pi \cdot \dfrac{3}{2+\pi } - \dfrac{6}{2+\pi } = 3[/tex]

The length of the rectangular window = 3 feet

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(A) and (E) are the true statement.

Given,

In the question:

Jake and Liana make and sell wooden birdhouses. Jake spent $150 buying supplies. He sells each birdhouse for $15. The equation P = 12x - 120 represents the profit, P, Liana earns for selling x birdhouses. Jake and Llana each made 50 birdhouses.

To find the which statement is true?

Now, According to the question:

Jake's Profit: J = 15x - 150

Liana's Profit : P = 12x - 120

(A) when x = 0, P = -120, J = -150

then, 150 - 120 = $30

So, Jake spent $30 more than Liana

So, A is true, B is wrong.

(C) when x = 50 , J = 15 x 50 - 150 = $600

P = 12 x 50 - 120 =$480

Since, 600> 480

(D) when J = P

then, 15x - 150 = 12x = 120

3x = 30

x = 10

x = 10 not equal to 20

So, D is wrong

(E)  when P> -0 , and J > 0

then, 12x -120 > 0 and 15x - 150 > 0

=> x > 10

So, the minimum is 11, E is true .

Hence, Above the solution (A) and (E) are the true statement.

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The graph of the linear equation can be seen in the image at the end.

We start by defining the variables we will use:

x = number of weeks.

y = money that Anika has.

We assume that Anika starts with $0, and then she wins $5 each week, so after x weeks she has:

y = $5*x

To graph this linear equation we need to find two points on the line, if x = 0 we get:

y = $5*0 = $0

So we have the point (0, 0)

if x = 1

y = $5*1 = $5

So we have the point (1, 5)

Now we can graph these two points and connect them with a line, the graph can be seen below.

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The winner of the race among the friends would be Leslie.

The person who has the highest average speed will win the race. Average speed is the total distance travelled per time.

Average speed = total distance / total time

Carolina's average speed = 7/8 ÷ 1/2

7/8 x 2 = 7/4 = 1 3/4 miles per hour

Leslie's average speed = 1 ÷ 1/3

1 x 3 = 3 miles per hour

Bryan's average speed = 3/4 ÷ 3/4

3/4 x 4/3 = 1 mile per hour

Javier's average speed = 1 ÷ 2/3

1 x 3/2 = 1 1/2 miles per hour

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The terms which are equivalent to the slope in a proportional relationship include:

Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope formula is the rise over run formula, where the fraction consists of a rise, whether the line is going up or down, divided by the run.

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Complete question

Select all the terms which are equivalent to the slope in a proportional relationship.

Constant of proportionality

Origin

Inverse

Rise over run

Unit rate

Answer: h = 22.5

Step-by-step explanation:

Total angle area of a 12 sided polygon is 1800

1. One angle would be 1800/12= 150

2. Add 30 one each side to cancel out and only leave 8h.

3. To get rid of the 8 we divide the the other side by 8.

The answer is 22.5

Answer: D 22.5 i got it right on the exam

Step-by-step explanation:

Two times or Twice the sum of a number and 3 is 8. The value of the number will be 1.

Let the value of the unknown number or variable be c.

Given,

"Two times the sum of a number and 3 is equal to 8", which means when you add the unknown number with 3 and then multiply it by 2, then the final answer will come as 8.

If we form the statement into an equation, then finding the value of the unknown variable will be a lot easier.

The equation will be:

    2(c + 3) = 8

=> 2c + 6 = 8

=> 2c = 8- 6

=> 2c = 2

=> c = 2/2

=> c = 1.

Hence, the value of the unknown number c will be 1.

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The slope of the side connecting (0,−2) and (-2, 3) is: -5/2.

The slope of the side connecting (6, 0) and (4, 5) is: -5/2.

The slope (m) of a side connecting two points with given coordinates can be calculated using the slope formula shown below:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Slope of the side connecting (0,−2) and (-2, 3):

Slope (m) = change in y / change in x = (3 - (-2)) / (-2 - 0)

m = 5/-2

Slope (m) = -5/2.

Slope of the side connecting (6, 0) and (4, 5):

Slope (m) = change in y / change in x = (5 - 0) / (4 - 6)

m = 5/-2

Slope (m) = -5/2.

Therefore, the slope of both sides are the same, which is: -5/2.

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For 10m long ladder whose foot is leaning against a vertical wall and from the base of the wall it is 6m away then height of the wall at a point ladder reaches is equal to 8m.

As given in the question,

Wall , ladder and base forms a right angled triangle

Length of the ladder leaning against the wall is hypotenuse = 10m

Distance between the ladder and base of the wall is base= 6m

Let us consider 'h' be the height of the wall is altitude.

Wall , ladder and base forms a right angled triangle

Using Pythagoras theorem we have,

(Hypotenuse)² = (Base)² + (altitude)²

⇒10² = 6² + h²

⇒100 =36 +h²

⇒h² =100 -36

⇒h² =64

⇒h = 8m

Therefore, for 10m long ladder whose foot is leaning against a vertical wall and from the base of the wall it is 6m away then height of the wall at a point ladder reaches is equal to 8m.

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The percent of loads of clothes are washed in an extra large washer is 75%.

It was stated that out of the 600 loads of clothes washed at a cleaners in one week.450 of those loads are washed in an extra large- washer

Therefore, the percentage that are washed in extra large washer will be:

= Number washed in extra large washer / Total number of clothes × 100

= 450/600 × 100

= 3/4 × 100

= 75%

The percentage is 75%.

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Answer:

y = 2(x - 1)^2 - 9

Step-by-step explanation:

The vertex form of a parabola is y = a(x - h)^2 + k

(h, k) is the vertex, aka (1, -9)

(x, y) is the point that is passed through aka (2, -7)

Using this, we can substitute these values into the equation.

First, let's work with the vertex

We know that h = 1 and k = -9:  y = a(x - 1)^2 - 9

Now, let's substitute in the point that was given: -7 = a(2 - 1)^2 - 9

Now, we can find the a-value by simplifying: -7 = a - 9   -->  a = 2

Finally, we can make the equation by taking our equation that we made with the vertex but just putting the a-value in since we know it.

y = 2(x - 1)^2 - 9 is the equation of the parabola in vertex form

I hope this helps! Let me know if it is wrong

Answer:

1.3% decrease

Step-by-step explanation:

% change = (9.69 - 9.56) / 9.69) x 100 = 1.3% decrease

9.69-9.56 = 0.13

0.13/0.69= 0.0134158972

Multiply by 100 and you get 1.34158927

Round to nearest tenth and you get = 1.3%

Therefore, the percentage decrease is 1.3