The scale for a model car is 2 inches : 2 feet. What is the height of the
actual car in feet?



​

The present value, or initial investment, needed to grow to $70,000 for the child's education at age 17 with continuous compounding at 6% is approximately $25,260.21.

To calculate the initial investment, or present value, needed to grow to $70,000 for the child's education at age 17 with continuous compounding at an interest rate of 6%, we can use the formula for continuous compound interest. The formula is:

PV = FV / e^(rt)

Where PV is the present value, FV is the future value, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time period.

In this case, we have:

FV = $70,000

r = 6% or 0.06

t = 17 years

Using the formula, we can calculate the present value:

PV = 70000 / e^(0.06 * 17)

By plugging in the values into the formula and solving, we find:

PV ≈ 70000 / e^(1.02)

PV ≈ 70000 / 2.7696

PV ≈ 25260.21

Therefore, the initial investment, or present value, required to grow to $70,000 for the child's education at age 17 with continuous compounding at 6% is approximately $25,260.21.

The total of 280 makes no sense because it tries to combine unrelated measurements and counts, such as library dimensions with the count of items like bookshelves and computers. Dimensions and counts are separate numerical categories and should be considered independently.

The library dimensions, bookshelves, and computers are individual elements that depict various characteristics of the library. The sum provided i.e., 280, cannot portray any sensible information about the library because it mistakenly incorporates unrelated physical dimensions (length and width in feet) with the count of items (bookshelves and computers). This is like adding apples and oranges which, conceptually, makes no sense.

The dimensions of the library, the number of bookshelves, and the number of computers are distinct items that aren't inter-convertible or comparable as they belong to different quantitative categories. They should be considered independently to provide meaningful information about the library.

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Answer:

78949

Step-by-step explanation:

v = Bh = πr²h = 3.14 x (3x - 4)² x (11x + 10)             x = 7

  = 3.14 x (21 - 4)² x (77 + 10)

  = 3.14 x 289 x 87

  = 78949

Answer:

c

Step-by-step explanation:

Answer:

It is C

Step-by-step explanation:

I took the quiz.

Answer:

  16 minutes

Step-by-step explanation:

The number of minutes is expected to be proportional to the number of walls and inversely proportional to the number of minutes. Relative to the effort given, the number of walls is a factor of 4/9, and the number of people is a factor of 7/4. Hence the number of minutes will be ...

  (63 min)×(4/9)×1/(7/4) = (63 min)×(16/63) = 16 min

It will take 16 minutes for 7 people to paint 4 walls.

Answer:

The anwer is v

Step-by-step explanation:

Answer:

Measure of [tex]\angle A = \angle D =60[/tex] and [tex]\angle B=\angle C=120[/tex] in degrees.

Step-by-step explanation:

Given:

A parallelogram where angles A and D measures same also, C and B measures same.

According to the question:

Measure of angle C is twice the measure of angle A.

Let the measure of angle A be "x" degree.

Accordingly :

Measure of each angle C and B = "2x"

Measure of each angle A and D ="x"

Note:

The sum of the measures of the angles of a parallelogram is​ 360°.

⇒ [tex]x+x+2x+2x=360[/tex]

⇒ [tex]6x=360[/tex]

⇒ [tex]x=\frac{360}{6}[/tex]

⇒ [tex]x=60[/tex]

So,

Measure of angle A and D be 60 degrees each.

Measure of angle B and C is 120 degrees each.

The measure of angles A and D in the parallelogram is 60° each, while the measure of angles C and B is 120° each.

The question is about finding the measure of each angle in a parallelogram. Given that the sum of the angles in a parallelogram is 360° and that the measure of angle C is twice the measure of angle A, we can set up equations to solve the problem.

Let's denote the measure of angle A as 'a'. Since angles A and D are of the same measure, the measure of angle D will also be 'a'. The measure of angle C and B are each twice the measure of angle A, so they will be '2a'.

The sum of the measures of all angles in a parallelogram is 360°, we can write the equation: a + 2a + a + 2a = 360°. Simplifying it you get: 6a = 360°. Solve this equation by dividing both sides by 6, you will get a = 60°.

Therefore, in the parallelogram, the measure of angles A and D is 60°, while the measure of angles C and B is twice as much, namely 120°.

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Answer:

y=25x-500

Step-by-step explanation:

25 is positive with the x because its the slope and 500 is the cost so you subtract is. 500 is the y intercept

Answer:

$3.1

Step-by-step explanation:

7.75/2.5 = 3.1

Answer:3.1

Step-by-step explanation:

7.75/2.5=3.1

Answer:

by taking a survey

Step-by-step explanation:

Answer:

4[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Answer:

7 is greater than 5 so round up

4.75 is rounded to 5

Step-by-step explanation:

to round to a place look to the place right after it, to round to the nearest whole number look at the tenth place, right after the decimal place

you see 7

Final answer:

The probability that Alex applies for his first sick leave on the fifth day is approximately 0.049, assuming that the likelihood of taking a sick day is consistent and independent across all days.

Explanation:

The probability that Alex applies for his first sick leave on the fifth day can be determined using the information given about the second day and the independent nature of the sick leave events. Since the probability of Alex taking his first sick leave on the second day is 0.21, and it is given that the probability of taking a sick day is the same for each day and is independent, we can infer that the probability of not taking a sick leave on any given day is 1 - 0.21 = 0.79. Therefore, for Alex to take his first sick leave on the fifth day, he must not take sick leave on the first four days and then take leave on the fifth, so the probability is calculated as:

(0.79 x 0.79 x 0.79 x 0.79) x 0.21 ≈ 0.049

Here, (0.79)^4 represents the probability that Alex does not take sick leave for the first four days, and 0.21 represents the probability that he takes his first sick leave on the fifth day.

The probability that Alex applies for his first sick leave on the fifth day is 0.0729.

To find this, we need to follow these steps:

1. The probability that he applies for sick leave for the first time on the second day is 0.21. This means he must have been at work on the first day and then applied for sick leave on the second day. Since the events are independent, the probability that he does not apply for sick leave on any day is [tex]\(1 - P(\text{sick leave})\)[/tex]. Therefore, we have [tex]\( P(\text{work on first day}) \times P(\text{sick leave on second day}) = 0.21 \)[/tex].

2. Let ( p ) be the probability that Alex applies for sick leave on a given day. We then have [tex]\( (1-p) \times p = 0.21 \)[/tex].

3. To solve for ( p ), we can find the square root of 0.21, since [tex]\( p^2 = 0.21 \) if \( p = 1-p \)[/tex], which is true when [tex]\( p < 0.5 \)[/tex].

4. The probability that Alex applies for his first sick leave on the fifth day is [tex]\( (1-p)^4 \times p \)[/tex]. We calculate [tex]\( (1-p)^4 \)[/tex] using the ( p ) we found from the square root of 0.21 and then multiply by ( p ).

Let's calculate \( p \) and then use it to find the probability for the fifth day.

There seems to be a mistake in the calculation. I incorrectly assumed that the probability of not taking a sick leave (\(1 - p\)) squared would be equal to the probability of taking the first sick leave on the second day, which isn't necessarily true given that \( p \) is less than 0.5 but not necessarily \( p = 1 - p \).

Let's go through the calculations again step by step:

1. Let ( p ) be the probability that Alex applies for sick leave on a given day. The probability that he does not apply for sick leave on any day is therefore(1 - p).

2. Since the events are independent, the probability that Alex applies for his first sick leave on the second day (having worked on the first day) is the product of the probability that he did not take a sick leave on the first day and the probability that he did take a sick leave on the second day, which can be represented as ( (1 - p) times p ).

3. Given that the probability for the second day is 0.21, we can set up the equation ( (1 - p) times p = 0.21 \) and solve for( p ).

4. Using the value of ( p ) found from the equation, we can then calculate the probability that Alex applies for his first sick leave on the fifth day, which would be [tex]\( (1 - p)^4 \times p \).[/tex]

( p ) from the equation and then determine the probability for the fifth day.

The probability that Alex applies for his first sick leave on the fifth day is exactly [tex]\( 0.07203 \)[/tex]. This was calculated by first determining the daily probability of taking sick leave, which is [tex]\( 0.3 \)[/tex], and then using it to calculate the probability of not taking a sick leave for the first four days and then taking one on the fifth day.

Answer:

d. x= 10^6.4

Step-by-step explanation:

[tex] log_{10}(x) = 6.4 \\ x = {10}^{6.4} \\ [/tex]

Question not well presented.

See correct question presentation below

A plane with equation (x/a) + (y/b) + (z/c) = 1, where a,b,c > 0 together with the positive coordinate planes form a tetrahedron of volume V = (1/6)abc. Find the plane that minimizes V if the plane is constrained to pass through the point P(2,1,1).

Answer:

The plane is x/6 + y/3 + z/3 = 1

Step-by-step explanation:

Given

Equation: (x/a) + (y/b) + (z/c) = 1 where a,b,c > 0

Minimise, V = (1/6) abc subject to

the constraint g = 2/a + 1/b + 1/c = 1

First, we need to expand V

V = (abc)/6

Possible combinations of V taking 2 constraints at a time; we have

(ab)/6, (ac)/6 and (bc)/6

Applying Lagrange Multipliers on the possible combinations of V, we have:

∇V = λ∇g

This gives

<bc/6, ac/6, ab/6> = λ<-2/a², -1/b², -1/c²>

If we equate components on both sides, we get:

(a²)bc/12 = -λ = a(b²)c/6 = ab(c²)/6

Solving for a, b and c;

First, let's equate:

(a²)bc/12 = a(b²)c/6 -- divide through by abc, we have

a/12 = b/6 --- multiply through by 12

12 * a/12 = 12 * b/6

a = 2 * b

a = 2b

Then, let's equate:

(a²)bc/12 = ab(c²)/6 -- divide through by abc, we have

a/12 = c/6 --- multiply through by 12

12 * a/12 = 12 * c/6

a = 2 * c

a = 2c

Lastly, we equate:

a(b²)c/6 = ab(c²)/6 -- divide through by abc, we have

b/6 = c/6 --- multiply through by 6

6 * b/6 = 6 * c/6

b = 2

Writing these three results, we have

a = 2b; a = 2c and b = c

Recalling the constraints;

g = 2/a + 1/b + 1/c = 1

By substituton, as have

2/(2c) + 1/c + 1/c = 1

1/c + 1/c + 1/c = 1

3/c = 1

c * 1 = 3

c = 3

Since a = 2c;

So, a = 2 * 3

a = 6

Similarly, b = c

So, b = 3

So, the plane: (x/a)+(y/b)+(z/c)=1;

By substituton, we have

x/6 + y/3 + z/3 = 1

Hence, the plane

So the plane is x/6 + y/3 + z/3 = 1

The equation of the plane that minimizes the volume of the tetrahedron and passes through the point (2,1,1) is x + z = 1.

To find the plane that minimizes the volume of the tetrahedron, we need to find the equation of the plane that passes through the point P=(2,1,1) and has coefficients a, b, and c. We can substitute the coordinates of the point into the equation of the plane and solve for the a, b, and c.

Substituting the coordinates of P into the equation of the plane gives 2a + b + c = 1. Since a, b, and c are all greater than 0, we can set a = 1, b = 0, and c = 1.

Therefore, the equation of the plane that minimizes the volume of the tetrahedron is x + z = 1.

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Answer: 135 days

Step-by-step explanation:

Since the amount of time it takes her to arrive is normally distributed, then according to the central limit theorem,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 21 minutes

σ = 3.5 minutes

the probability that her commute would be between 19 and 26 minutes is expressed as

P(19 ≤ x ≤ 26)

For (19 ≤ x),

z = (19 - 21)/3.5 = - 0.57

Looking at the normal distribution table, the probability corresponding to the z score is 0.28

For (x ≤ 26),

z = (26 - 21)/3.5 = 1.43

Looking at the normal distribution table, the probability corresponding to the z score is 0.92

Therefore,

P(19 ≤ x ≤ 26) = 0.92 - 28 = 0.64

The number of times that her commute would be between 19 and 26 minutes is

0.64 × 211 = 135 days

Answer:

135

Step-by-step explanation:

Under S would be 1 and 9 under E would be 2 6 8 10 and 12 and 4 goes in the middle

Answer and Step-by-step explanation:

First, from this set of numbers determine which ones are square numbers. Remember that square numbers are those that can be written in the form of k^2, where k is a number.

Square numbers: 1 (because 1^2 = 1), 4 (because 2^2 = 4), and 9 (because 3^2 = 9)  ⇒  There are 3 square numbers

Next, find the number of even numbers.

Even numbers: 2, 4, 6, 8, 10, and 12  ⇒  There are 6 even numbers

Place all the 3 square numbers inside the S circle and all the 6 even numbers in the E circle. However, notice that one number, 4, is both a square number and an even number, so put 4 in the shared portion.

Hope this helps!

Answer:

69%

Step-by-step explanation:

Since we only have two options, rain or not rain, they have to add to 100%

100 -31 = 69

So not raining is 69%

Answer:

69%

Step-by-step explanation:

Answer:$70

Step-by-step explanation: if there are 3 seeds in each pot, you start by dividing 42 by 3. This equals 14. This shows how many pots you will need to use up all of the seeds. So to find how much it will cost, you multiply the amount of pots by the cost of each pot. So 14 times 5, which equals 70.

Answer:

Y < -1/4x + 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The tens place because 3746 rounded to nearest hundred is 3700 and 3746 rounded to the nearest ten is 3750

Final answer:

3,746 rounded to the nearest ten is 3,750, which is greater than 3,746 rounded to the nearest hundred, which is 3,700.

Explanation:

When comparing which is greater, 3,746 rounded to the nearest hundred or to the nearest ten, it's important to understand the concept of rounding. Rounding to the nearest hundred, we consider the tens digit, which is 4, and since it's less than 5, we round down to 3,700. When rounding to the nearest ten, we look at the ones digit, which is 6, and since it's 5 or greater, we round up to 3,750.

Therefore, 3,750 (rounded to the nearest ten) is greater than 3,700 (rounded to the nearest hundred).

Answer:

7x +1 = 22

7x = 21

x = 3

Step-by-step explanation:

Answer:

D) -3/2

Step-by-step explanation:

x intercept is when y = 0

(2x + 3)/(x + 4) = 0

2x + 3 = 0

x = -3/2

Answer:

C) 250 feet

Step-by-step explanation:

Let the diameter of the circle be d feet.

[tex] \therefore \: C = \pi d \\ \therefore \: 250\pi = \pi d \\ d = \frac{250\pi}{\pi} \\ d = 250 \: ft[/tex]

Answer:

84cm^2

Step-by-step explanation:

Area of a parallelogram is Base times Height

Area = BxH

plug in

B = 14

H = 6

Answer:

The bullet reaches its final velocity after 0.1 second.

Step-by-step explanation:

Velocity: The ratio of distance to the time that needs to cover the distance.

Acceleration: The change of velocity per unit time is called the acceleration of the object.

[tex]Acceleration=\frac{\textrm{Final velocity- initial velocity}}{Time}[/tex]

S.I unit is m/s².

C.G.S unit is cm/s².

Dimension: [LT⁻²]

An accelerometer is used to measure acceleration of an object.

Given that

The bullet accelerates from a stop to 1000 m/s to the east.

It accelerates at 10,000 m/s² in the same direction.

The initial velocity of the object is = 0 m/s

The final velocity of the object is = 1000 m/s

[tex]\therefore 10000=\frac{1000-0}{Time}[/tex]

[tex]\rightarrow Time = \frac{1000}{10000}[/tex]

[tex]\rightarrow Time = \frac1{10}[/tex]

[tex]\rightarrow Time = 0.1[/tex]

The bullet reaches its final velocity after 0.1 second.

Answer:

[tex]\pi r^2 h[/tex]

Step-by-step explanation:

[tex]\text{Area of the circle: Area of the Square =}\dfrac{\pi r^2}{4r^2}:1=\dfrac{\pi}{4}:1[/tex]

Height of the cylinder =h

Radius of the Cylinder=r

Base Length of the Prism=2r

Therefore:

Volume of the Prism =[tex](2r)^2h=4r^2h[/tex]

[tex]\text{Volume of the Cylinder =} \frac{\pi}{4}(\text{the volume of the prism)}\\=\frac{\pi}{4}(4 r^2 h) \\=\pi r^2 h[/tex]

Answer:

D

Step-by-step explanation:

i took the test

Answer:

Step-by-step explanation:

2,3 and 5

Answer:2,3,5

Step-by-step explanation:

Answer:

It i s 6

Step-by-step explanation:

Very six

We will see that the line that best fits the data is the one in the first graph (top left one).

To know which line is the best one, what we need to do is:

I know that it is hard to do it with these graphs, as these are kinda small and the measure may be hard to take, so you can just estimate.

By doing that estimation you can see that (only for the two better graphs, I ignored the bottom two).

The first one has a total distance of near 10 units.

The second one has a total distance of near 11 units.

So the graph that fits best the data is the first one (top left).

If you want to learn more about fitting lines, you can read:

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Answer:

This is nonlinear.

Step-by-step explanation:

Answer:

There  are two real solutions to this equation, representing the number of seconds elapsed between the dolphin exiting and reentering the water.

Step-by-step explanation: