A car is bought for $45, 200. The insurance company decided to calculate the depreciation each year as 14.5% of the book value at the beginning of the year. Determine the value of the car at the end of 6 years.

Answer:

√25 + 2

Step-by-step explanation:

Only the first expression, √25 + 2, is rational. To be rational, an expression must be able to be written as the ratio of two integers. In this case, we can rewrite the expression as 5 + 2, which is equal to 7, which is a ratio of 7/1.

Answer:

x < 21

Step-by-step explanation:

Let x = the number of grapes James has left

x + 4 < 25

x < 21

Answer:  35

Step-by-step explanation:

The semi-annual net cash flow the company must achieve in order for the purchase to be made is $2500.

Number of period = 6 × 2 = 12

Rate = 4% / 2 = 2%

Annual cash flow × PVIFA × (2% × 12) + $7500 × PVIF(2%,12) - $32348 = 0

Annual cash flow × 10.5753 = $32348 - $7500 × 0.7885

Annual cash flow × 10.5753 = $32348 - $5914

Annual cash flow × 10.5753 = $26434

Annual cash flow = 26434/10.5753

Annual cash flow = $2500

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Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

By a change of units, we will get that 108 mi/h = 158.4 ft/s

Here we want to transform 108 mi/h to feet per second.

Then we will use two relations:

Then we can just transform as:

108mi/h = (108*5,280 ft)/h = 570,240 ft/h

570,240 ft/h = 570,240 ft/(3,600 s) = 158.4 ft/s

So we have:

108 mi/h = 158.4 ft/s

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\(x^2 + 4x + (\frac{4}{2})^2 = x^2 + 4x + 4\)

Answer is 4

Answer:

48

Step-by-step explanation:

(a)  the probability of generating 999999 is \((1/10)^6\)

(b) the probability of generating 703928 is \((1/10)^6\)

(c) the probability of generating a sequence of six identical digits is \((1/10)^6\)

(d)  the probability of generating a sequence with no identical digits is  15,120/1,000,000.

(e)  the probability of generating a sequence with exactly one repeated digit is\(10 * 6 * (9^4).\)

Probability is described as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

The probability of generating a sequence with no identical digits is calculated as  (10/10) * (9/10) * (8/10) * (7/10) * (6/10) * (5/10) = 15,120/1,000,000.

We start by choosing  the digit to be repeated, which can be done in 10 ways and the next thing is to choose the position of the repeated digit, and can be done in 6 ways.

We then see that remaining four positions can be filled out with any of the other 9 digits and this can also be   done in \(9^4\) ways.

So we can conclude that the number of possibilities in this case is \(10 * 6 * 9^4.\)

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Answer:

1. distance = 275 ft

2. rate = 55 miles/hour

Step-by-step explanation:

April travels at the rate of 25 ft per seconds and the time she spent traveling is 11 seconds. How far she traveled is the distance she covered. The rate or the speed unit is given as ft per seconds. Therefore, the distance covered can be expressed as follows.

rate = distance/time

where

rate = 25 ft/sec

time = 11 secs

rate = distance/time

25 = distance/11

cross multiply

distance = 25 × 11

distance = 275 ft

Isaac drove for 3 hours and he covered a distance of 165 miles. The rate of travel can be expressed as follows

rate = distance/time

distance = 165 miles

time = 3 hours

rate = 165/3

rate = 55 miles/hour

Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

Answer:

21°

Step-by-step explanation:

Let smaller angle be x

Bigger angle = 2x + 27

Since they are complementary they all sum up to 90°

Therefore 2x + 27 + x = 90

3x = 90 - 27

3x = 63

x = 21, therefore the smaller angle is 21°

Answer:

constants

Step-by-step explanation:

That is, they're the terms without variables. We call them constants because their value never changes, since there are no variables in the term that can change its value.

The term or number with no variable attached is called a constant as in the polynomial or expression.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

A number consists of the expression with no variable.

As we know, the expression is a combination of numbers, variables, and operators.

If we take an example of the polynomial.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

\(\rm p(x) = a_0+a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)

Here a₀ is a constant because the term a₀ has no variables.

Thus, the term or number with no variable attached is called a constant as in the polynomial or expression and the constant value does not change.

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Answer:

dilation and rotation

Step-by-step explanation:

The equation has no solution for the variable w

The equation is given as

v = -3x + s

In the above equation, there is no occurrence of the variable w

This means that it is not possible to solve the equation for w

Hence, the equation has no solution for the variable w

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The quotient of the given expression is 68.

What is the quotient?

A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

For the given problem,

To find out the estimation of the quotient, we first round the dividend and the divisor to the closest tens, hundreds, or thousands, and then divide the rounded figures to approximate the quotient.

Given, 3411 divided by 53

So, the rounding value becomes 3400 divided by 50,

then, 3400/50 = 68

Hence, the quotient is 68.

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Answer:

28

Step-by-step explanation:

I guess bicause that is te variable.

Therefore, a)= (x^ n+ y^ n) is bounded.
b)  limn→ ∞ I n f (x^ n+ y^ n)  ≥  limn→ ∞ I n f(x ^ n)+  limn→ ∞ I n f(y^ n)                                          

Step-by-step explanation:

a) Let (x^ n) and (Y^ n) be bounded sequences, so
∃M>0 such that |x^ n|≤ M ∀n ∈ N
∃M>0 such that |Y^ n|≤ M ∀n ∈ N

Consider
|x^ n| ≤ |x^ n|+|Y^ n|
≤M +M'
=P          (Take p=M+M'>0)

Thus, |x^ n + y^ n|≤p,  ∀n ∈ N.
Therefore, (x^ n+ y^ n) is bounded.


b) Let (x) be a bounded sequence so ( x^ n) is bounded below by k.
Then for each n ∈ N, the set x^ n=(x^ n,x^n+1,....) is bounded below by k.
By completeness axion X^ n has infimum m^ n and the sequence (m^ n) being a increasing sequence is either convergent or divergent to ∞
If(m^ n) is convergent then limn→ ∞m^ n is called the limit infimum of (x^ n).

Thus, limn→ ∞I n f( x^ n)=limn→ ∞ I n f (x^ n,x^n+1,...)
∴
Similarly, m'^ n=I n f (y^ n, y^ n+1...)
Consider
I n f (x^ n+ y^ n, x^n+1 +y^n+1..) ≥ I n f (x^ n, x^ n+1...)+I n f ( y^ n, y^ n+1..)
I n f(x^ n+ y^ n, x^n+1 +y^n+1...) ≥ m^ n+ m'^ n
We have
= limn→ ∞ I n f (x^ n+ y^ n)= limn→ ∞ ( x^ n +y^ n, x^n+1 +y^n+1...)
=≥ limn→ ∞(m^ n+ m')
= limn→ ∞m^ n+ limn→ ∞m'^ n
= limn→ ∞ I n f (x^ n) + limn→ ∞ I n f (y^ n)
∴Therefore
 limn→ ∞ I n f (x^ n+ y^ n)  ≥ limn→ ∞ I n f(x ^ n)+  limn→ ∞ I n f(y^ n)



INCOMPLETE QUESTION:

Let {xn} and {yn} be bounded sequences. a) Show that {xn +yn} is bounded. b) Show that (lim n→∞inf xn) + (lim n→∞ inf yn) ≤ lim n→∞inf (xn +yn). Hint: Find a subsequence {xni + yni } of {xn + yn} that converges. Then find a subsequence {xnmi } of {xni } that converges. Then apply what you know about limits. c) Find an explicit {xn} and {yn} such that (lim n→∞ inf xn) + (lim n→∞infyn) < lim n→∞ inf (xn +yn). Let {xn} and {yn} be bounded sequences (from the previous exercise we know that {xn +yn} is bounded). a) Show that (lim sup n→∞ xn) + (lim sup n→∞ yn) ≥ lim sup n→∞ (xn +yn). Hint: See previous exercise. b) Find an explicit {x n} and {yn} such that (lim sup n→∞ xn) + (lim sup n→∞ yn) > lim sup n→∞ (x n +yn).


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The statements that are true regarding the expression with the exponents -1, -3, and 1 are;

An exponent is a quantity or power to which a value, expression or number is to be raised.

The specified expression can be presented as follows;

8⁻¹ × 8⁻³ × 8

Therefore; 8⁻¹ × 8⁻³ × 8 = 8⁽⁻¹ ⁺ ⁻³ ⁺ ¹⁾ = 8⁻³ = 1/8³

1/8³ = 1/512

Similarly, we get; 8⁷ × 8⁻¹⁰ = 8⁽⁷ ⁻ ¹⁰⁾ = 8⁻³ = 1/8³

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9514 1404 393

Answer:

  yes, no, no

Step-by-step explanation:

The triangle will be a right triangle if the sum of the squares of the two short sides, less the square of the long side, is zero. (This is what the Pythagorean theorem tells you.) The angle where the radius meets the circle must be a right angle if the line is to be a tangent.

__

a) 3^2 +4^2 -5^2 = 9 + 16 -25 = 0 . . . . AB is a tangent

__

b) 9^2 +15^2 -18^2 = 81 +225 -324 = -18 . . . . AB is not a tangent

__

c) 10^2 +48^2 -52^2 = 100 +2304 -2704 = -300 . . . . AB is not a tangent

Answer:

4.00 pls give brainliest

Step-by-step explanation:

Hello turkshcutie11!

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

Find the value of x.

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

It's given that the triangle in the figure is a right triangle (a triangle with one angle as 90°). So, we can use the pythagoras property to solve this question.

__________________

Given sides :-

__________________

Using pythagoras property...

Hypotenuse ² = Base² + Altitude ²

x² = 5² + 3²

x² = 25 + 9

x² = 34

x = √34

x = 5.83 units (1st option).

__________________

Hope it'll help you!

ℓu¢αzz ッ

Answer:

a) The null and alternative hypothesis are:

\(H_0: \mu=35.1\\\\H_a:\mu< 35.1\)

b) The 95% confidence interval for the mean stocks traded in 2014 in millions is (21.13, 29.07).

c)  D. Reject the null hypothesis because μ= 35 1 million shares does not fall in the confidence interval.

Step-by-step explanation:

The claim is that 2014 stock volumes are significantly different from 2011 stock volumes (35.1 millions).

Then, the null and alternative hypothesis are:

\(H_0: \mu=35.1\\\\H_a:\mu< 35.1\)

We can test this by calculating a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=25.1.

The sample size is N=40.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

\(s_M=\dfrac{s}{\sqrt{N}}=\dfrac{12.4}{\sqrt{40}}=\dfrac{12.4}{6.32}=1.961\)

The degrees of freedom for this sample size are:

\(df=n-1=40-1=39\)

The t-value for a 95% confidence interval and 39 degrees of freedom is t=2.023.

The margin of error (MOE) can be calculated as:

\(MOE=t\cdot s_M=2.023 \cdot 1.961=3.966\)

Then, the lower and upper bounds of the confidence interval are:

\(LL=M-t \cdot s_M = 25.1-3.966=21.13\\\\UL=M+t \cdot s_M = 25.1+3.966=29.07\)

The 95% confidence interval for the mean is (21.13, 29.07).

The value 35.1 is not included in the interval, so we can conclude that there is significant difference from the 2011 stock volume.

0.015  in fraction

=\(\frac{15}{1000}\)

Simplified is

=\(\frac{3}{200}\)

Answer:\(\frac{3}{200}\)

The equation of the parallel line will be y = (2/3)x - 8/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y - 4 = 2/3 (x - 3)

The equation of the line that is parallel to the given line will be written as,

y = (2/3)x + c

The equation of the line that passes through (1, -2), then we have

- 2= (2/3)(1) + c

- 2 = 2 /3 + c

c = - 8 / 3

Then the equation of the parallel line will be y = (2/3)x - 8/3.

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The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

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Conditional probability formula:

Given situation:

probability that a randomly selected student is male, given that the student speaks French

M= Student is male

F=Student speaks Frenc

Answer: 132

Step-by-step explanation:

negative times negative equals positive

Answer:

Explanation: