12. Phillip deposited $450 in an account that earns
5% interest, compounded yearly. If he makes
no further deposits, how much will be in the
account after 2 years?
A. $472.50
B. $491.14
C. $496.13
D. $512.24

Answer:

The factory makes 12,000 (12k) hats each day

Step-by-step explanation:

4000

× 3

--------

12,000

The predicted values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350, therefore, the correct option is IC.

Given,

Mean of X = 600

Standard deviation of X = 10

Mean of Y = $5000

Standard deviation of Y = 1000

Correlation r= 0.9

Future value of X = 595

Z score of X = (X- Mean of X) / Standard deviation of X= (595-600) / 10 = -0.5

Using the formula, Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (-0.5) * 1000 = $4750

The predicted value of Y for X = 595 is $4750.

Now, to find the values of A, B, C, and D; we need to calculate the Z score of X = 615 and find the corresponding predicted value of Y.

Z score of X = (X- Mean of X) / Standard deviation of X= (615-600) / 10 = 1.5

Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (1.5) * 1000 = $6350

The predicted value of Y for X = 615 is $6350.

Hence, the values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350

Therefore, the correct option is IC.

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Step-by-step explanation:

see attached. I hope this helps.

Answer:

Perpendicular.

Step-by-step explanation:

To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form

y = 2/3x - 4 ==> slope = 2/3

y = -3/2x - 7 ==> slope = -3/2

Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1

(2/3) * (-3/2) = -1

Since the product of the slopes is -1, the two lines are perpendicular.

Therefore, the answer is: perpendicular.

Answer:

98

Step-by-step explanation:

147/3=49x2=98

The final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them.

Let's clarify the itinerary for the 15-day tour visiting 5 national parks.

You have a 15-day tour, and you plan to visit 5 national parks. Each park will have a stay of two days.

When you multiply the number of parks (5) by the number of days spent in each park (2), you get a total of 10 days allocated for staying in those 5 parks.

However, there seems to be a discrepancy in the calculation because allocating 10 days for park stays leaves only 5 days remaining, not 15.

To resolve this issue and ensure a 15-day tour, we need to reevaluate the itinerary. Let's assume you want to spend two days at each park, which gives you a total of 10 days for park stays.

To fill the remaining 5 days, you have a few options:

1. Travel Days: You can allocate a day for travel between each park, which would require an additional 4 days. This accounts for the transportation time and allows you to enjoy the journey between the parks.

2. Additional Park Visits: If there are other nearby national parks or attractions in the area, you can extend your tour to include visits to these places. This would allow you to explore more diverse locations and make the most of your 15-day tour.

3. Rest and Relaxation: Alternatively, you might choose to use the extra days for relaxation or leisure activities. You can spend some time enjoying the amenities and attractions available near the parks, such as hiking trails, wildlife observation, or local cultural experiences.

Ultimately, the final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them. Make sure to consider travel times, desired activities, and any additional locations you wish to explore when creating your 15-day tour.

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Answer:

The angle corresponding to angle 4 is angle 8

Answer:

One

Step-by-step explanation:

Line of symmetry of a figure is an imaginary line about which the figure can be divided into two equal halves.

In other words, a line passing the center of the figure about which we can fold the figure into two halves overlapping each other.

For the trapezoid given in the figure, line of symmetry will be a vertical line perpendicular to the parallel sides.

Therefore, The figure has 1 line of symmetry.

Answer: 3

Step-by-step explanation:  When you translate that formula to f(0)=-2x+3 you can see it much clearer the number without a variable tied to it is the y-intercept.

Answer:

A) 23

Step-by-step explanation:

Let's divide the total number of cupcakes by the different option choices, and see what works and what doesn't:

A) 23/ 23 = 1

   This works, everyone will get one cupcake

B) 23 / 12 ≈ 1.91666667

   This doesn't work, we have a decimal / remainder, and you normally would not split 2/3s of a cupcake with someone at a party

C) 23 / 6 ≈ 3.8333334

   This doesn't work, we have a decimal / remainder, and you normally would not split 2/3s of a cupcake with someone at a party

D) 23 / 12 ≈ 5.75

   This doesn't work, we have a decimal / remainder, while this is a nicer remainder, it still is incorrect

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

$7.02

Step-by-step explanation:

without tax

The inference from given boxplot is : The visiting team had more variability in the number of shots taken.

In this question we have been given two boxplots.

For the boxplots that the coach made,

for the home team:

Whiskers range is:16 to 32

So, the minimum value = 16

the maximum value = 32

the box ranges from 20 to 23. A line divides the box at 22.

so, the first quartile = 20

the third quartile = 23

the Median = 22

interquartile range(IQR) = 23 - 20

                                      = 3

And for the visiting team

Whiskers range :14 to 32

This means, the minimum value is 14 and the maximum value = 32

As the box ranges from 16 to 24 and a line divides the box at 18,

the first quartile is 16, the third quartile = 24 and the median = 18

So, the interquartile range (IQR) = 24 - 16

                                                   = 8

From above data analysis the inference is that the visiting team had more variability in their shots, because their distribution has a higher interquartile range (8 > 3)

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Given question is incomplete.

The complete question is:

A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games. He displayed the results in the box plots below.A box plot titled Number of Shots Taken by home team players. The number line goes from 10 to 32. The whiskers range from 16 to 32, and the box ranges from 20 to 23. A line divides the box at 22.

Number of Shots Taken by Home Team Players

A box plot titled Number of Shots Taken by visiting team players. The number line goes from 10 to 32. The whiskers range from 14 to 32, and the box ranges from 16 to 24. A line divides the box at 18.

Number of Shots Taken by Visiting Team Players

Which describes an inference that the coach might make after comparing the medians of the two data sets?

Answer:

SA =12.

Step-by-step explanation:

In a parallelogram the diagonals bisect each other , so:

2x - 1 = x + 7

2x - x = 7 + 1

x = 8.

QS = x + 4 = 8 + 4

= 12.

But QS = SA, so SA =12.

9514 1404 393

Answer:

  3/4

Step-by-step explanation:

f(-2) = 3·2^-2 = 3/2^2

f(-2) = 3/4

_____

The applicable rule of exponents is ...

  a^-b = 1/a^b

Answer:

5x + 35 = 175

$28

Step-by-step explanation:

She paid 35 for 1 pair of skis. She paid a certain amount(x) for 5 hours (5x + 35). Therefor making the expression 5x + 35 = 175.

Then, solve the equation with inverse operations.

5x + 35 = 175

Step 1: Subtract 35 from both sides.

5x = 140

Step 2: Divide 5 from both sides.

x = 28

Therefore, Kylie paid $28 each hour of the group skiing lessons.

Answer:

7

Step-by-step explanation:

To find the maximum number of turning points of any polynomial function, subtract one from the degree.

Since the degree is 8, subtract 1 from this:

8 - 1

= 7

So, the maximum number of turning points is 7.

Answer:

Step-by-step explanation:

Solution : Given that, n = 363 x = 171 = x / n =171 / 363 = 0.471 1 - = 1 - 0.471 = 0.529

Answer:

Step-by-step explanation:

The slope is determined with two points.

Take the pairs (0, - 9) and (1, - 5).

The slope is:

Answer:

Slope = 4

Step-by-step explanation:

Formula we use,

→ Slope = (y2 - y1)/(x2 - x1)

Then required slope will be,

→ (y2 - y1)/(x2 - x1)

→ (-5 -(-9))/(1 - 0)

→ (-5 + 9)/(1 - 0)

→ 4/1 = 4

Therefore, the slope is 4.

Factors other than independent variables which may act on the dependent variable , when these factors vary systematically with independent variable they are known as confounds variables or extraneous variable.

Therefore, factors which vary systematically with the given independent variable is called  confounds variables or extraneous variable.

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120 ways can the letters in the word spoon be arranged. So, The correct option is d) 120.

The word "spoon" has five letters, and we need to find the number of ways to arrange these letters. This can be done using the permutation formula, which is n!/(n-r)!, where n is the total number of items and r is the number of items being selected. In this case, we have five items and we need to arrange all of them, so r = 5. Therefore, the number of arrangements is 5!/(5-5)! = 5!/0! = 5x4x3x2x1 = 120.

To understand this concept better, consider that the first letter of "spoon" can be any of the five letters. Once we choose a letter for the first position, there are four letters left to choose from for the second position, three for the third position, two for the fourth position, and only one letter left for the fifth position. Multiplying these numbers gives us the total number of arrangements. Therefore, there are 120 ways to arrange the letters in the word "spoon". So the correct answer is d) 120.

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angle R = 180 - 109 - 47.5

= 23.5 ( B )

Answer:

565.7 cubic units

Step-by-step explanation:

Volume of cylinder=2πrh

                               =2x(22/7)(10)(9)

                               =180x(22/7)

                               =565.7

Answer:

25.35

Step-by-step explanation:

Area of the shaded portion = Area of semicircle - Area of the right triangle

Area of semicircle = πr²/2

Area of semicircle = 3.14(6)²/2

Area of semicircle = 3.14 * 18

Area of semicircle = 56.52

Area of triangle = 1/2 * base * height

Get the height using the SOH CAH TOA identity

sin 60 = H/12

H = 12sin60

H = 12(0.8660)

H = 10.39

Get the base

12² = b²+10.39²

144 = b²+108

b² = 144 - 108

b² = 36

b = 6

Area of triangle = 1/2 * 6 * 10.39

Area of triangle = 3 * 10.39

Area of triangle = 31.17

Area of shaded portion = 56.52 - 31.17

Area of shaded portion = 25.35

Answer:

Hello There!!

Step-by-step explanation:

Firstly,select three ordered pairs from the table. Secondly,substitute the first pair of values in to the form of the quadratic equation: f(x) = ax^2 + bx + c and then solve for a.

hope this helps,have a great day!!

~Pinky~

Yes, it showed you the fomula

Answer: 64x^6y^3

Answer:

The conversing factor is \(\dfrac{1}{1000}\ km\).

Step-by-step explanation:

The average speed of a person is 18 km/h.

We need to convert the speed to meters/hour.

We know that,

1 km = 1000 m

or

\(1\ m=\dfrac{1}{1000}\ km\)

So,

\(18\ \dfrac{km}{h}=18\times \dfrac{1000\ m}{h}\\\\=18000\ m/h\)

So, the conversing factor is \(\dfrac{1}{1000}\ km\).

The expression \(\(\left(\frac{1}{32}\right)^x \cdot \left(\frac{1}{2}\right)^{9x-5}\)\)can be rewritten as\(\(\left(\frac{1}{2}\right)^{f(x)}\) where \(f(x) = 14x\).\)

To rewrite the expression \(\left(\frac{1}{32}\right)^x \cdot \left(\frac{1}{2}\right)^{9x-5}\) as \(\left(\frac{1}{2}\right)^{f(x)}\), we need to determine the value of \(f(x)\) in terms of \(x\) that corresponds to the given expression.

Let's break down the given expression and find the relationship between \(f(x)\) and \(x\):

1. \(\left(\frac{1}{32}\right)^x\)

  This term can be rewritten as \(\left(\frac{1}{2^5}\right)^x\) since 32 is equal to \(2^5\).

  Using the property of exponents, we have \(\left(\frac{1}{2}\right)^{5x}\).

2. \(\left(\frac{1}{2}\right)^{9x-5}\)

  This term can be rewritten as \(\left(\frac{1}{2}\right)^{9x} \cdot \left(\frac{1}{2}\right)^{-5}\).

  Simplifying \(\left(\frac{1}{2}\right)^{-5}\), we get \(\left(\frac{1}{2^5}\right)^{-1}\), which is equal to \(2^5\).

  Therefore, \(\left(\frac{1}{2}\right)^{-5} = 2^5\).

  Substituting this back into the expression, we have \(\left(\frac{1}{2}\right)^{9x} \cdot 2^5\).

Now, let's combine the simplified terms:

\(\left(\frac{1}{2}\right)^{5x} \cdot \left(\frac{1}{2}\right)^{9x} \cdot 2^5\)

Using the laws of exponents, we can add the exponents when multiplying powers with the same base:

\(\left(\frac{1}{2}\right)^{5x + 9x} \cdot 2^5\)

Simplifying the exponent, we get:

\(\left(\frac{1}{2}\right)^{14x} \cdot 2^5\)

Finally, we can rewrite this expression as:

\(\left(\frac{1}{2}\right)^{f(x)}\)

where \(f(x) = 14x\) and the overall expression becomes \(\left(\frac{1}{2}\right)^{f(x)} \cdot 2^5\).

In summary, the expression \(\left(\frac{1}{32}\right)^x \cdot \left(\frac{1}{2}\right)^{9x-5}\) can be rewritten as \(\left(\frac{1}{2}\right)^{f(x)}\) where \(f(x) = 14x\).

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