Michelle rents a movie for a flat fee of $1.50 plus an additional $1.25 for each night she keeps the movie. Choose the cost function that represents this scenario if x equals the number of nights Michelle has the movie.

c(x) = 1.50 + 1.25x
c(x) = 1.50x + 1.25
c(x) = 2.75
c(x) = (1.50 + 1.25)x

Answer: 5 + 5 is indeed 10, in the same since that 479 + 2 is 481. Just like how 5 x 2 is 10. Just like how 8 x 8 is 64.

Step-by-step explanation: Yes.

The perimeter and area of a rectangle are (5,6) and (6,5).

The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.

A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.

The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.

The perimeter of the rectangle:

P=2l+2w=22

divide 2 into both sides

l+w=11 -------------> (1)

w=11-l

Area of the rectangle:

l*w=30

l(11-l)=30

11l-l^2-30=0

l^2-11l+30=0

By factor method,

(l-5)(l-6)=0

l=5,6.

Substitute this value in w,

l=5 implies w=6

l=6 implies w=5

There we have two solutions.

The length and breadth of the rectangle is

(5,6) and (6,5).

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Answer: D.

hope this helps

In equilateral triangle, the length of side x is,

⇒ x = 5.8

Since, A triangle is a 3 - sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We know that;

The given triangle is equilateral.

Hence, Its all sides are equal.

Hence, By Pythagoras theorem , we get;

⇒ x² = 5² + (x/2)²

⇒ x² = 25 + x² / 4

⇒ x² - x²/4 = 25

⇒ 3x²/4 = 25

⇒ 3x² = 100

⇒ x² = 100 / 3

⇒ x² = 33.33

⇒ x = √33.33

⇒ x = 5.8

Thus, In equilateral triangle, the length of side x is,

⇒ x = 5.8

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The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer:

Step-by-step explanation:

The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.

As per the given data, the given formula is:

\($T=2 \pi \sqrt{\left(\frac{L}{32}\right)}\) gives the time it takes in seconds.

Where,

T is the time it takes for a pendulum to make one full swing back and forth (in seconds).

L is the length of the pendulum, in feet.

Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.

Substitute the given parameters into the formula will give;

\($1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}\)

Now divide both sides by 2π.

\($ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\\)

\($ 0.3024=\sqrt{\left(\frac{L}{32}\right)}\)

Then taking square on both sides.

\($ (0.3024)^2=\frac{L}{32} \\\)

0.09144576 = \($\frac{L}{32}\)

Later multiply both sides by 32.

2.9262 = L

The approximate value of the length of a pendulum:

L ≈ 3

Therefore, the length of a pendulum is about 3 feet.

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The sample space for the two mornings at the stop light would be D. {red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}.

In probability theory, the sample space constitutes the collection of all potential results that could ensue from an experiment. Symbolized by S, it encompasses every plausible outcome that can arise when such a test is conducted.

The sample space would therefore be :
{red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}

This includes all the possible lights that could be seen on the two mornings by Julie.

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Answer:

qualitative

Step-by-step explanation:

Breed of dog does not involve numbers: it's qualitative since dogs can have categories like "poodle" or "dachshund."

Refer to the attached photos. I would appreciate a rate :)

Answer:

the answer is------------ 1/4.4.4

Answer:

3/7

Step-by-step explanation:

The null hypothesis (H0) can be expressed as H0: p = 71%. and The alternative hypothesis (H1) can be expressed as H1: p > 71%.

In the given problem, we need to express the null and alternative hypotheses in symbolic form.

The null hypothesis (H0) is that the percentage of workers indicating they are mildly satisfied with their job is equal to 71%. This can be expressed as: H0: p = 71%.

The alternative hypothesis (H1) is that the percentage of workers indicating they are mildly satisfied with their job is greater than 71%. This can be expressed as H1: p > 71%.

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Answer:

81

Step-by-step explanation:

Suppose 43% of the population has a retirement account. If a random sample of size 774 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3%?

Answer:

the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082

Step-by-step explanation:

Given that:

sample size n = 774

Let P be the population proportion for having a retirement account  = 0.43

Also

Let consider \(\hat p\) be the sample proportion of having a retirement account.

However; as n is > 30 ; we can say:

\(\mathbf{\mu_{\hat p} = 0.43}\)  ;  

 \(\mathbf{\sigma_{\hat p^2} = \dfrac{p(1-p)}{n}}\)  

⇒   \(\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(1-0.43)}{774}}\)

⇒ \(\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(0.57)}{774}}\)

So; we need  P( the sample proportion will differ from 'p' by less than 3% i.e 0.03)

\(=P(| \hat p- p|< 0.03)\)

\(=P(| \hat p- \mu _p|< 0.03)\)

\(= P ( |\dfrac{\hat P - \mu_p}{\sigma_{\hat p}}|< \dfrac{0.03}{\sqrt{ \dfrac{0.43*0.57}{774} }})\)

\(= P(|Z|<1.6859)\ \ \ \ [Z=(\dfrac{\hat P - \mu_{\hat P}}{\sigma_{\hat P}}) \sim N(0,1)]\)

\(= P(-1.6859 <Z<1.6859) \\ \\ = \Phi(1.6859)- \Phi (-1.6859) \\ \\ = \Phi (1.6859) - (1- \Phi(1.6859) \\ \\ = 2 \Phi (1.6859)-1\)

From Normal Cumulative Distribution Function Table

\(= 2*0.9541 -1\)

= 1.9082 - 1

= 0.9082

Thus; the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082

Answer:

\(y=5x^2-80x+324\)

Step-by-step explanation:

The number of square feet needed to cover the hole is 44ft²

To find this, we need to find the area of the green region and subtract the little square that it has inside.

Remember that for a rectangle, the area is the product between the dimensions, then the area of the green region is:

A = 12ft*4ft = 48ft²

The little square has an area:

a = 2ft*2ft = 4ft²

Then the area needed is:

area = 48ft² - 4ft² = 44ft²

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Given the model for the height of a ball:

To hit the ground, the height must be h(t) = 0. Then:

We use the general solution for a quadratic equation:

From the problem, we identify:

Using the formula:

We only take the positive value (because the time is always positive!). Then, the answer is:

Hello there. To solve this question, we have to remember some properties about arithmetic sequences.

Given the first term of an arithmetic sequence and its common difference, we can determine the n-th term of the sequence using the following formula:

We know that a1 = 3 and d = 4, hence

Is the general formula for the n-th term of the sequence.

Plugging n = 22, we find

This is the 22nd term of this sequence.

The answer of the given question based on the compound interest is  the balance after 6 years is $14,162.62 (option a).

Amount refers to total value of something, usually in terms of a money. It can also be used in  context of a quantity of something, such as an amount of the  time or an amount of the material.

formula for the compound interest is :

A = P(1 + r/n)^(nt)

Where,

A = final amount

P = principal amount

r = annual interest rate

n = the number of times interest is to be compounded per year

t = time in years

In this case, we have:

P = $1,000

r = 3.75% = 0.0375 (annual interest rate as a decimal)

n = 12 (monthly compounding)

t = 6 years

Substituting the  values into  formula, we will get:

A = 1000(1 + 0.0375/12)⁽¹²*⁶⁾

A = $1,4162.62

Therefore, the balance after 6 years is $14,162.62 (option a).

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Answer:

120

Step-by-step explanation:

we know if the arc measures 120, we know that its 1/3 of the circle, so ABC will also be 120

-- i have attached a picture of the graph

- in order to graph, plug in values for x and find y

- this would create order pairs which you will plot.

some order pairs:

(0,0)

(1,3)

(2,6)

Answer: Plot the two points (0,0) and (1,3). Draw a straight line through them. The graph is shown below.

===========================================================

Explanation:

When x = 0, we have y equal to...

y = 3x

y = 3*0

y = 0

So this means (x,y) = (0,0) is one point on the line

Let's follow those steps for x = 1

y = 3x

y = 3*1

y = 3

So the point (x,y) = (1,3) is also on the line.

You can repeat this process for any x value you want; however, we only need two points to form the line. Plot (0,0) and (1,3). Then draw a straight line through both points. Extend the line as far as you can in either direction. This forms the graph of y = 3x.

You can use a graphing calculator (eg: TI83) to get the job done. Or you can use a free online resource such as GeoGebra or Desmos. I prefer GeoGebra as it offers more options. The graph shown below was made with GeoGebra.

Note that moving from point A(0,0) to B(1,3) has us move up 3 and over to the right 1. This is due to the slope of 3 = 3/1.

y = 3x is the same as y = 3x+0. It is of the form y = mx+b with m = 3 = 3/1 as the slope and b = 0 as the y intercept.

Answer:

The answer is x=-5

Step-by-step explanation:

Step 1: Divide both sides by 4.

4x /4  =  −20/4

x=−5

Step-by-step explanation:

Let breadth be x,

then length is 2x cm,

perimeter of rectangle=2(l+b),

48=2(2x+x),

48÷2=3x

24=3x

24÷3=x

8cm =x,

B=8cm

L=2×8=16cm

Answer:

length =2x

breadth= let x be breadth

Perimeter = 48cm

now

Perimeter = 2 (l+b)

or, 48 cm = 2 (2x+x)

or, 48cm= 4x + 2x

or, 48 cm = 6x

or, 48cm÷6 =x

x = 8 cm

breadth= 8cm

length = 8 ×2 =16cm