Find the equation of the line passing through the points 3, 3 and 4, 5

a) The 90% confidence interval for the proportion of adults that have blue eyes is given as follows: (0.087, 0.133).

b) As the interval does not contain 0.08, the belief that 8% of people have blue eyes is misguided.

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

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

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

The confidence level is of 9%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.9}{2} = 0.95\), so the critical value is z = 1.645.

The parameters for this problem are given as follows:

\(n = 500, \pi = \frac{55}{500} = 0.11\)

The lower bound of the interval is given as follows:

0.11 - 1.645 x sqrt(0.11 x 0.89/500) = 0.087.

The upper bound of the interval is given as follows:

0.11 + 1.645 x sqrt(0.11 x 0.89/500) = 0.133.

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Answer: f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Step-by-step explanation: Using the given recursive formula:

f(1) = 0

f(n) = f(n-1) + 2

We can find the values of f(n) for different values of n:

f(1) = 0

f(2) = f(1) + 2 = 0 + 2 = 2

f(3) = f(2) + 2 = 2 + 2 = 4

f(4) = f(3) + 2 = 4 + 2 = 6

f(5) = f(4) + 2 = 6 + 2 = 8

And so on.

We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:

f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Answer: 3n + 15 ≤ 7

n = number

hope this helped! :D

The two lines never intersect (are parallel lines) thus the equation:

6 - x = 3 - x

Has no solutions.

Here we have the equation:

6 - x = 3 - x

And (supposedly) a graph of the two lines:

y = 6 - x

y = 3 - x

Notice that the part on the linear equations that depens of x is equal to the ones in the equation above.

So basically we have a system of equations:

y = 6 - x

y = 3 - x

Because "y" is the same thing in both equations, we can rewrite:

6 - x = y = 3 - x

If we remove the part in the middle, we return to the original equation:

6 - x = 3 - x

Now, the solution of that equation is given by the point where the two graphs of the linear equations intersect, it will never happen, because both linear equations are parallel (have the same slope) which means that the equation:

6 - x = 3 - x

Has no solutions.

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Answer:

its smthing about no solutions. Just pick the answer that says no solution satifies it

Step-by-step explanation:

i got it right on imagine math :))) (i dont have the screen shot)

Answer:

9(4-n)

Step-by-step explanation:

Hope this helps

Tell me if I'm wrong

Answer:

the 2nd one i think hope it is,please ,please

Answer:

the third one.

Step-by-step explanation:

1/2 is half a number and +7 is 7 more so 7 more than half a number.

Answer:

Since it is growing at 5% per year, at the end of each year the population will be 1.05 times what is was at the start of the year.

Start with 110,000 and multiply by 1.05 a total of 16 times to get the population at the end of 16 years.

P = 110,000 x 1.0316 ≅ 176,518

Step-by-step explanation:

Answer:

7857

Step-by-step explanation:

The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

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Answer:

8a×64

Step-by-step explanation:

This is right because you have to add the two numbers with the variable and add the regular numbers

The rate at which the depth of the liquid is increasing when it reaches one-third of the height of the bowl is (7/3)π cm³/s.

To ascertain the rate at which the liquid's depth rises, let's find the derivative of the depth function with respect to time.

Let;

The rate of change of the volume of the liquid with respect to time is constant and equal to 7π cm³/s.

To determine the height of the bowl, we can evaluate the curve y = [-4 / (8 - x)] - 1 when x = 4 and y = 7.6 and then find the absolute difference between the values.

h = |[-4 / (8 - 4)] - 1 - [-4 / (8 - 7.6)] - 1|

Let's calculate the rate at which the depth rises when it reaches one-third of the bowl's height.

D = depth of bowl

Using this relationship from the question given;

D = (1/3) * h

In order to determine the rate at which D will change with respect to time, let's differentiate both sides of the equation.

dD/dt = (1/3) * dh/dt

Since dh/dt is the rate at which the depth of the liquid is changing, which is constant and equal to 7π cm³/s, we can substitute it into the equation:

dD/dt = (1/3) * (7π)

Simplifying, we have:

dD/dt = (7/3)π cm³/s

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The  difference in the account balances at the end of the loan terms is, $1770.87. So option B is correct

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

Given that,

Offer 1-  5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer

Offer 2-  3.75% annual interest compounded monthly for a 66-month term

In offer 1,

Total amount A  = $32487.50

In offer 2,

Total amount =

\(A = P[ 1 + r/n]^{nt}\)

\(A = 25000[ 1 + 0.0375/12]^{12*5.5}\)

A = $30,716.63

Difference = 32487.50 - 30716.63

                  = $1770.87

Hence, the difference in account balance is $1770.87

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\(f(x)=7\cos(2x)\hspace{5em}f\left( -\frac{\pi }{4} \right)=7\cos\left( -\frac{\pi }{4} \right) \\\\\\ f\left( -\frac{\pi }{4} \right)=7\left( \frac{\sqrt{2}}{2} \right)\implies f\left( -\frac{\pi }{4} \right)=\cfrac{7\sqrt{2}}{2}\)

Answer:

y= -1/3x + -5

Step-by-step explanation:

y= mx + b

b= y-intercept, which is -5. (x-value where the lines goes through the y-axis)

To find the slope, you take the

Change of y/ Change of x

Take two points (I did, (0,-5) and (3, -6) ).     (x,y)

-6 - (-5)= -1

3 - 0= 3

-1/3= m

The statement is true because 4 × 30%=120

In the first month, the price of the avocado is said to have been raised by 30 percent.

While already raised by 30 percent, another 30 percent raise would make the increase to be 60 percent.

While is at 60 percent, the third month the raise would be = 90 percent because 30 * 3 = 90

Then at 90 percent if there is another raise of 30 percent, the increase would grow to be 120 percent.

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After evaluating the integral answer is 85/4. thus, option A is the answer.

The given transformation is a change of variables from (x, y) to (u, v). To evaluate the integral using the transformation, we need to use the Jacobian determinant. The Jacobian determinant is the absolute value of the determinant of the matrix of partial derivatives of the transformation.

du/dx = 1, du/dy = 1

dv/dx = -2, dv/dy = 1

The determinant of the matrix of partial derivatives is det(J) = du/dx * dv/dy - du/dy * dv/dx = (1)(1) - (1)(-2) = 3

So the Jacobian determinant is |J| = |3| = 3.

The integral becomes:

R\int \int 5y dx dy = (1/3) R\int \int 5v du dv

where R is the region in the uv-plane that corresponds to the region in the xy-plane bounded by the lines y= -x+1, y=-x+4, y= 2x+2, y= 2x+5

The integral evaluates to (1/3) R\int \int 5v du dv = (1/3) * 85/2 = 85/6 = 85/4

Therefore the correct answer is 85/4

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Answer:

height = 5 cm

Step-by-step explanation:

a cube has congruent sides (s)

the volume (V) of a cube is calculated as

V = s³

given V = 125 , then

s³ = 125 ( take cube root of both sides )

\(\sqrt[3]{s^3}\) = \(\sqrt[3]{125}\) = \(\sqrt[3]{5^3}\)

s = 5

then height = 5 cm

Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

We can see that Natalie is reducing the amount she owes by $18 every two weeks.

Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.

This means that after n weeks, the amount she still owes is:

$180 - $18n

Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:

$180 - P

After two weeks, she will owe:

($180 - P) - P = $180 - 2P

After four weeks, she will owe:

($180 - 2P) - P - P = $180 - 4P

After six weeks, she will owe:

($180 - 4P) - P - P = $180 - 6P

And after eight weeks, she will owe:

($180 - 6P) - P - P = $180 - 8P

We can set up an equation using the information we have:

$180 - 8P = $108

Solving for P, we get:

P = $9

Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

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The complete question:

Natalie borrowed money from her parents to pay for a trip. ​Natalie will ​pay her parents in equal amounts every week until she pays back the ​entire amount she borrowed. ​ ​The table below shows the amount of ​money Natalie still owes her parents at the end of every two weeks for ​the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?

Week 0 = $180

Week 2 = $162

Weeks 4 = $144

Week 6 = $126

Week 8 = $108

Answer:

its 10

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

9-3÷1/3+ 2

9-3/ (1/3)+2

∵3/(1/3)= 9

so,

9-9 +2

0+2= 2

Answer:

A) \(\frac{d}{9} + \frac{d}{6} = 240\)

B) 864 feet

Step-by-step explanation:

The bee has been away  for a total of 17 minutes from the hive but since it rested at the flowerbed for 13 minutes, the total travel time is 17-13 = 4 minutes. Since units are expressed in feet per second, we have to convert 4 minutes to seconds which works out to 240 seconds

The basic equation for distanced  traveled by an object traveling at speed of s is given by d = st  where t is the time taken to traverse distance d

Alternatively we can write this equation as    

\(t = \frac{d}{s}\)

Travel time from hive to flowerbed at 9 feet/sec = \(\frac{d}{9}\) seconds

Travel time from flowerbed to hive at 6 feet/sec =  \(\frac{d}{6}\) seconds

Total travel time is the sum of the above and can be expressed by the equation

\(\bold{\frac{d}{9} + \frac{d}{6} = 240}\)     ( Answer A)

To solve this equation multiply by the least common multiple of 9 and 6 which is 18

\(18(\frac{d}{9} + \frac{d}{6}) = 18(240) \text{ seconds}\)

2d + 3d = 4320 seconds

d = 4320/5 = 864 feet  (Answer B)

To solve this equation multiply by the least common multiple of 9 and 6 which is 18

We can verify our answer using the distance computed

Total travel time = 864/9 + 864/6 = 96 + 144 =240 which matches our equation and resultant value

\(\\\)Answer:

m = - 4

Step-by-step explanation:

Slope Formula: \(m=\frac{y_{2}- y_{1} }{x_{2}- x_{1} }\)

Substitute (-2,9) and (3,-11) into m = \(\frac{y_{2} -y_{1} }{x_{2} x_{1} }\)

=  \(m=\frac{-11-9}{3-(-2)}\)

m = -4

Answer:

Slope (m) = -4

Step-by-step explanation:

Given :-

Points (-2, 9) and (3, -11)

To Find :-

Slope (m)

Solving :-

m = y₂ - y₁ / x₂ - x₁

= -11 - 9 / 3 + 2

= -20 / 5

= -4

Solution :-

Slope (m) = -4

Answer:

Area = ½* height(a+b)

Where;

a=4units

b=8units

h=6units

Therefore Area= ½*6(4+8)

= ½*6*12

=36sq.un

Answer:

24sq²

Step-by-step explanation:

Area = ( b1 + b2) x h

          ---------------------

                     2

Area =   (8 + 4) x 6

          ---------------------

                     2

Area =     (12) x 6

          ---------------------

                     2

A = 72/2

A = 36

A = 1/2 * b * h

A = (1/2) * 4 * 6

A = (1/2) * 24

A = 12

36 - 12 = 24sq²

I hope this helps!

The values of x and y are given as follows:

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases for this problem are given as follows:

2 and x.

The altitude is given as follows:

6.

Hence the length x is given as follows:

2x = 6²

2x = 36

x = 18.

Applying the Pythagorean Theorem, the length y is given as follows:

y² = 18² + 6²

y² = 360

\(y = \sqrt{36 \times 10}\)

\(y = 6\sqrt{10}\)

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Answer:

3/4 teaspoon of pepper is needed for 9 potatoes

Step-by-step explanation:

Set up a proportion. 1/4 teaspoon to 3 potatoes is equal to ? to 9 potatoes

x= amount of pepper for 9 potatoes

(1/4)/3= x/9 cross multiply

(3 * x)= (1/4 * 9)

3x= 9/4

multiply both sides by 4

12x= 9

divide both sides by 12

x= 9/12

simplify by 3

x= 3/4 teaspoon

Answer:

3/4 teaspoon of pepper is needed for 9 potatoes

Step-by-step explanation:

Set up a proportion. 1/4 teaspoon to 3 potatoes is equal to ? to 9 potatoes

x= amount of pepper for 9 potatoes

(1/4)/3= x/9 cross multiply

(3 * x)= (1/4 * 9)

3x= 9/4

multiply both sides by 4

12x= 9

divide both sides by 12

x= 9/12

simplify by 3

x= 3/4 teaspoon

Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

Answer:

A2 x average range

Step-by-step explanation:

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

Answer:

Step-by-step explanation:

x + x + 1 + x + 2 + x + 3 = 274

4x + 6 = 274

4x = 274 - 6

4x = 268

x = 268/4

x =  67

===========

The numbers are 67, 68, 69, 70

Answer: A

Step-by-step explanation:

If pllot the point -1 on x-axsis and 4 on y. Quadrant || on the top left corner :)