can someone give me the answers in order please


A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.
A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.

B) What is the correct answer to part A written in percentage form?
r=------------%

C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.

Answer:

no solution

Step-by-step explanation:

The space taken up by the table is 24 feet².

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Kitchen table = 6 feet by 4 feet

This means,

The table is a rectangle.

The area of the table.

= 6 x 4

= 24 feet²

Thus,

The area of the rectangle is 24 feet².

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Answer:

Step-by-step explanation:

So what you need to do is mark to points on the graph. For example (9,4) and (18,8). The run would be 9 and the rise would be 4. Gradient = rise/run which is 4/9. So that's the gradient. Now it asks for the equation. The formula for an equation is y=mx+c m= the gradient and c = the y-intercept (the y intercept is where the line meets the axis so it would be 0) so the answer is: y=4/9x+0.

Hope this helped !!

Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 2x^2 + x -3 \qquad \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0} \\\\\\ \cfrac{[2(2)^2 + (2) -3]~~ - ~~[2(0)^2 +(0) -3]}{2}\implies \cfrac{7-(-3)}{2}\implies \cfrac{7+3}{2}\implies \text{\LARGE 5}\)

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The function is given below.

f(x) = 2x² + x - 3

The rate of change of the function for the interval between 0 to 2 is calculated as,

Average rate = [f(2) - f(0)] / [2 - 0]

Average rate = [(2(2)² + 2 - 3) - (2(0)² + 0 - 3)] / 2

Average rate = 10 / 2

Average rate = 5

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

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Answer:

3π/4 radians

Step-by-step explanation:

arctan(tan(x/3))=1

x/3=π/4 rad

x = 3π/4 radians

The differential equation

\(ay'' + by' + c = 0\)

has characteristic equation

\(ar^2 + br + c = 0\)

with roots \(r = \frac{-b\pm\sqrt{b^2-4ac}}{2a} = \frac{-b\pm\sqrt{D}}{2a}\).

• If \(D>0\), the roots are real and distinct, and the general solution is

\(y = C_1 e^{r_1x} + C_2 e^{r_2x}\)

• If \(D=0\), there is a repeated root and the general solution is

\(y = C_1 e^{rx} + C_2 x e^{rx}\)

• If \(D<0\), the roots are a complex conjugate pair \(r=\alpha\pm\beta i\), and the general solution is

\(y = C_1 e^{(\alpha+\beta i)x} + C_2 e^{(\alpha-\beta i)x}\)

which, by Euler's identity, can be expressed as

\(y = C_1 e^{\alpha x} \cos(\beta x) + C_2 e^{\alpha x} \sin(\beta x)\)

The solution curve in plot (A) has a somewhat periodic nature to it, so \(\boxed{D < 0}\). The plot suggests that \(y\) will oscillate between -∞ and ∞ as \(x\to\infty\), which tells us \(\alpha>0\) (otherwise, if \(\alpha=0\) the curve would be a simple bounded sine wave, or if \(\alpha<0\) the curve would still oscillate but converge to 0). Since \(\alpha\) is the real part of the characteristic root, and we assume \(a>0\), we have

\(\alpha = -\dfrac b{2a} > 0 \implies -b > 0 \implies \boxed{b < 0}\)

Since \(D=b^2-4ac<0\), we have

\(b^2 < 4ac \implies c > \dfrac{b^2}{4a} \implies \boxed{c>0}\)

The solution curve in plot (B) is not periodic, so \(D\ge0\). For \(x\) near 0, the exponential terms behave like constants (i.e. \(e^{rx}\to1\)). This means that

• if \(D>0\), for some small neighborhood around \(x=0\), the curve is approximately constant,

\(y = C_1 e^{r_1x} + C_2 e^{r_2x} \approx C_1 + C_2\)

• if \(\boxed{D=0}\), for some small neighborhood around \(x=0\), the curve is approximately linear,

\(y = C_1 e^{rx} + C_2 x e^{rx} \approx C_1 + C_2 x\)

Since \(D=b^2-4ac=0\), it follows that

\(b^2=4ac \implies c = \dfrac{b^2}{4a} \implies \boxed{c>0}\)

As \(x\to\infty\), we see \(y\to-\infty\) which means the characteristic root is positive (otherwise we would have \(y\to0\)), and in turn

\(r = -\dfrac b{2a} > 0 \implies -b > 0 \implies \boxed{b < 0}\)

The fallacy in the given statement "oak trees are shady, shady things are not to be trusted, therefore oak trees are not to be trusted" is equivocation. So, second option is accurate.

Equivocation is a type of fallacy in logic and rhetoric where a word or phrase is used with multiple meanings or ambiguous terms, leading to misleading or false conclusions. It occurs when a word or phrase is used in different senses within the same argument or context, resulting in confusion or deception.

Equivocation often involves exploiting the ambiguity of words or phrases to create a deceptive or misleading impression. It can occur in various forms, including:

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The reading that separates the rejected thermometers from the others is given as follows:

1.175 ºC.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for this problem are given as follows:

\(\mu = 0, \sigma = 1\)

The 12% higher of temperatures are rejected, hence the 88th percentile is the value of interest, which is X when Z = 1.175.

Hence:

1.175 = X/1

X = 1.175 ºC.

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Answer:

x = 9

Step-by-step explanation:

To solve the equation 2x - 7 + 3x = 4x + 2 for x, you can follow these steps:

Combine like terms on both sides of the equation. Add the x terms together and move the constant terms to one side of the equation:

2x + 3x - 4x = 2 + 7

Simplifying the left side: x = 9

Simplify the right side of the equation:

x = 9

Therefore, the solution to the equation is x = 9.

Answer:

631

Step-by-step explanation:

4x105=420

102*102=204

Rewrite the equation:

420+204+7= 631

Answer:

i think that the answers is -16x + 5

Amelia would have to multiply the number 7/10 on the price on the tags that she has to pay.

Percentage is a part of the whole number. It is denoted by % sign.

1 %= 1/100.

Given that,

The discount on new camera bought by Amelia = 30%.

To find the number that Amelia should multiply to pay,

Let The required number be x,

and total price of the camera is 100%

So after discount the price of camera = 100 - 30 = 70%

Implies that,

100 × x = 70

x = 70 / 100

x = 7 / 10

So the required number is 7/10 that Amelia should multiply the price she would have to pay.

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The height of the cylinder is 11cm. Option C

The formula for the volume of a cylinder is expressed as;

V = πr²h

Given that the parameters are;

Now, substitute the values given from the diagram shown, we have;

99 × 3.14  = 3.14 × (3)² × h

find the value of the square

99 × 3.14 = 3.1 4 × 9 × h

multiply the values

99 × 3.14  = 28. 26h

Make 'h' subject

h = 11cm

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Answer:

Answer is D

Step-by-step explanation:

Answer:

The answer would be D.

Step-by-step explanation:

Answer:

95% of confidence intervals are

(31.5215 , 53.4785)

Step-by-step explanation:

Explanation:-

Given sample size 'n' =24

Mean of the sample  x⁻ = 42.5

Standard deviation of the sample 'S' = 26

95% of confidence intervals are determined by

\((x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} })\)

Degrees of freedom

                ν =n-1 = 24-1 =23

\(t_{0.05} = 2.0686\)

95% of confidence intervals are

\((42.5 - 2.0686 \frac{26}{\sqrt{24} } , 42.5+ 2.0686 \frac{26}{\sqrt{24} })\)

( 42.5 -10.9785 ,42.5 +10.9785)

(31.5215 , 53.4785)

Answer:

a

Step-by-step explanation:

edge

Answer:

15:24, 20:32 and 40:64.

Step-by-step explanation:

hope this helps

Answer:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Step-by-step explanation:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Answer:

Step-by-step explanation:

The angles marked 1 and 2 share the vertical line as a common side, so they are "adjacent" angles. Each is the sum of an acute angle and a right angle, so is "obtuse."

None of the other descriptors apply.

Answer:

(4, -1)

Step-by-step explanation:

Given:

C(1, -6)

D(7, 4)

Required:

Midpoint of CD using \( M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) \)

SOLUTION:

\( M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) \)

Let \( C(1, -6) = (x_1, y_1) \)

\( D(7, 4) = (x_2, y_2) \)

Thus:

\( M(\frac{1 + 7}{2}, \frac{-6 + 4}{2}) \)

\( M(\frac{8}{2}, \frac{-2}{2}) \)

\( M(4, -1) \)

Answer:

\(x \leqslant - 4\)

Answer:

its C

Step-by-step explanation:

Answer:

\(\displaystyle k = \frac{34}{3}\)

Step-by-step explanation:

We are given the polynomial:

\(\displaystyle P(x) = 3x^3 - kx^2 + 5x + k\)

And we want to determine the value of k such that (x - 2) is a factor of the polynomial.

Recall that the Factor Theorem states that a binomial (x - a) is a factor of a polynomial P(x) if and only if P(a) = 0.

Our binomial factor is (x - 2). Thus, a = 2.

Hence, by the Factor Theorem, P(2) must equal zero.

Find P(2):

\(\displaystyle \begin{aligned} P(2) &= 3(2)^3 - k(2)^2 + 5(2) + k \\ \\ &= 3(8) - 4k + 10 + k \\ \\ &= 34 - 3k \end{aligned}\)

This must equal zero. Hence:

\(\displaystyle \begin{aligned} 34 - 3k &= 0 \\ \\ -3k &= -34 \\ \\ k = \frac{34}{3} \end{aligned}\)

In conclusion, k = 34/3.

Answer:

20

Step-by-step explanation:

you just divid the number of points earned (14), by the percent earned (70). This gives you the total becuase you would divid 14 by the total to get 70.

The equation that represent the gross pay is y = 0.12x + 1760. The commission was $10896 and gross pay was $12656

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the gross pay for x total sales.

Donald Simmons a $1760 monthly salary plus a 12% commission on merchandise he sells each month, hence:

y = 1760 + 12% of x

y = 0.12x + 1760

Donald's sales were $90,800 for last month. Hence:

a) Commission = 0.12 * $90800 = $10896

b) Gross pay:

y = 10896 + 1760 = $12656

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Answer:

Hence, n 3 −n=n(n+1)(n−1) is divisible by 6.

Step-by-step explanation:

The condition for any number to be divisible by 6 is that the number must be individually divisible by 3 and 2.

Check whether n 3−n is divisible by 3.

n3−n=n(n+1)(n−1)

When a number is divided by 3 then by the remainder theorem, the remainder obtained is either 0 or 1 or 2.

n=3p or n=3p+1 or n=3p+2, where p is some integer.

If n=3p, then the number is divisible by 3.

If n=3p+1, then n−1=3p+1−1=3p. The number is divisible by 3.

If n=3p+2, then n+1=3p+2+1=3(p+1). The number is divisible by 3.

So, any number in the form of n

3

−n=n(n+1)(n−1) is divisible by 3.

Check whether n

3

−n is divisible by 2.

When a number is divided by 2, the remainder obtained is either 0 or 1 by the remainder theorem.

n=2p or n=2p+1, where p  is some integer.

If n=2p, then the number is divisible by 2.

If n=2p+1 then n−1=2p+1−1=2p. The number is divisible by 2.

So, any number in the form of n

3

−n=n(n+1)(n−1) is divisible by 2.

Since, the given number n

3

−n=n(n+1)(n−1) is divisible by both 3 and 2. Therefore, according to the divisibility rule of 6, the given number is divisible by 6.

Answer:

Step-by-step explanation:

Let's simplify the equation first:

(n-3)(n+2)-(n-3)(n+8)

= n² - n - 6 - (n² + 5n - 24)

= n² - n - 6 - n² - 5n +24

= -6n - 18

Divisible means that the equation can be divided by 6 with no remainder.

If I divide the equation by 6, I get (-n-3)

It goes in evenly, therefore it is divisible by 6

Answer:

2x^3 + 17x^2 + 25x - 50

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

Answer: 39?

Step-by-step explanation: is it integers?