Consider the function f(x) = 1/x on the interval [2,7]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (2, 7) such that f'(c) is equal to this mean slope. For this problem, there is only one that works. Find it.

Answer:

b = 72

Step-by-step explanation:

Since AB and AC are congruent then Δ ABC is isosceles with base angles also congruent, that is

∠ ACB = ∠ ABC = b

the sum of the 3 angles in the triangle is 180° , then

b + b + 36 = 180

2b + 36 = 180 ( subtract 36 from both sides )

2b = 144 ( divide both sides by 2 )

b = 72

The  answer is:Karen would have $1000000 in the second account when she is 23 years old.

In order to calculate at what age Karen would have $1000000 in the second account, we need to calculate the future value of her investment in the first account, and then use that as the present value for the second account.Let us complete the tables given:

First Account PV: $0 FV: $0 Periods: 144 Rate: 5.75% Payment: $500 PMT/yr: 12 CMP/yr: 4Second Account PV: $163474.72 FV: $1000000 Periods: 23 Rate: 7% Payment: $0 PMT/yr: 1 CMP/yr: 1.

In the first account, Karen invested $500 a month for 12 years.

The total number of periods would be 12*4 = 48 (since it is compounded quarterly). The rate of interest per quarter would be (5.75/4)% = 1.4375%.

The PMT/yr is 12 (since she is investing $500 every month). Using these values, we can calculate the future value of her investment in the first account.FV of first account = (500*12)*(((1+(0.014375))^48 - 1)/(0.014375)) = $162975.15

Rounding off to the nearest cent, the future value of her investment in the first account is $162975.15.

This value is then used as the present value for the second account, and we need to find out at what age Karen would have $1000000 in this account. The rate of interest is 7% compounded annually.

The payment is 0 since she does not make any further investments in this account. The number of periods can be found by trial and error using the formula for future value, or by using the NPER function in Excel or a financial calculator.

Plugging in the values into the formula for future value, we get:FV of second account = 162975.15*(1.07^N) = $1000000Solving for N, we get N = 22.93. Rounding off to the nearest year, Karen would have $1000000 in the second account when she is 23 years old.

Therefore, the main answer is:Karen would have $1000000 in the second account when she is 23 years old.

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Thomas's total commission for last month is $1,255.

Thomas sold merchandise worth $13,000. He earns 3.5% on the first $3,000, which is $105. He earns 9% on the next $5,000, which is $450. The remaining amount is $5,000, and he earns 14% on it, which is $700. Therefore, his total commission is $1,255. WORD COUNT: 69.
To calculate Thomas's total commission on his $13,000 worth of merchandise sales, we will use the commission rates provided. He earns 3.5% on the first $3,000, 9% on the next $5,000, and 14% on sales over $8,000.
First $3,000: $3,000 * 0.035 = $105
Next $5,000: $5,000 * 0.09 = $450
Sales over $8,000: $13,000 - $8,000 = $5,000; $5,000 * 0.14 = $700
Now, add the commission amounts: $105 + $450 + $700 = $1,255.
Thomas's total commission for last month is $1,255.

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The rate of increase of area when the diagonal of the square is 14 m is 4√2x m²/min.

Given, The length of the diagonal of a square is increasing at a rate of 4 m/min.The diagonal length of the square when the area is increasing is 14 m each.
Let the side of the square be 'x' units.Diagonal of the square = √2x
The area of the square = x²
From the above details, we can relate the diagonal and the area of the square in terms of 'x' units.
Diagonal of the square, d = √2x ... (1)
Area of the square, A = x² ... (2)
Now differentiate the equation (1) and (2) with respect to time t.
d/dt (d) = d/dt (√2x)4 = d/dt (√2x) => d/dt (d) = 2(√2) (dx/dt) ... (3)
Differentiating (2) with respect to time t, we get
d/dt (A) = d/dt (x²)=> d/dt
(A) = 2x(dx/dt) ... (4)
From equations (1) and (3), we get:
dx/dt = 4 / (2√2)dx/dt = 2√2 m/min
From equations (2) and (4), we get:
d/dt (A) = 2x(dx/dt)
d/dt (A) = 2(x) (2√2)
d/dt (A) = 4√2x
The area of the square is increasing at a rate of 4√2x m²/min when the diagonal length is 14 m each.

So, the rate of increase of area when the diagonal of the square is 14 m is 4√2x m²/min.

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Answer:

angle e = 64

angle d =141

Step-by-step explanation:

for angle e

add 77 to 39 and you'll get 116

subtract 116 from 180

you'll get 64

angle e = 64

for angle d

subtract 39 from 180

and you'll get 141 which is the value of angle d

F(x) = 18 es un ejemplo de una función constante. En matemáticas, una función constante es aquella cuya salida no varía independientemente del valor de entrada. En este caso, no importa qué valor de "x" se utilice, el resultado siempre será 18.

Estas funciones son importantes en álgebra, cálculo y análisis matemático, ya que representan situaciones en las que no hay cambios en el resultado a pesar de las variaciones en las entradas. Algunos ejemplos de aplicaciones de funciones constantes incluyen tasas de interés fijas, velocidades constantes y temperaturas constantes.

Una característica clave de una función constante es que su derivada, que representa la tasa de cambio, es igual a cero. Esto se debe a que la salida no cambia, independientemente de cómo cambie la entrada. En el caso de F(x) = 18, la derivada sería F'(x) = 0.

En resumen, F(x) = 18 es un ejemplo de función constante, en la cual la salida siempre es 18, independientemente del valor de entrada "x". Estas funciones son útiles para modelar situaciones en las que no hay cambios en el resultado a pesar de las variaciones en las entradas, y tienen derivadas iguales a cero.

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Given:

Point = (1,-4), Slope - 8

Point = (1,5), Slope =1

To find:

The slope-intercept forms of the given lines.

Solution:

The slope intercept form of a line is:

\(y=mx+b\)

The point slope form is:

\(y-y_1=m(x-x_1)\)

where, m is the slope of the line.

We have, Point = (1,-4), Slope - 8. So, the equation of the line is:

\(y-(-4)=-8(x-1)\)

\(y+4=-8x+8\)

\(y=-8x+8-4\)

\(y=-8x+4\)

Therefore, the correct option is B.

We have, Point = (1,5), Slope =1. So, the equation of the line is:

\(y-5=1(x-1)\)

\(y-5=x-1\)

\(y=x-1+5\)

\(y=x+4\)

Therefore, the correct option is D.

Answer: La compañera de Eduardo, Francisca, está equivocada.

Step-by-step explanation:

Para determinar quién tiene la razón, es necesario conocer la cantidad de pegamento necesaria para cubrir todos los tarugos. Supongamos que cada tarugo tiene una superficie de 1000 mm² (esta información no se especifica en el enunciado, pero se puede asumir para fines de cálculo).

Entonces, la superficie total de los 20 tarugos sería:

20 tarugos x 1000 mm²/tarugo = 20,000 mm²

Para cubrir completamente esta superficie, Eduardo necesita una cantidad de pegamento igual a 20,000 mm².

Sin embargo, él calculó que necesita pegamento suficiente para cubrir 52,000 mm² de la superficie de los tarugos usados, que es más del doble de la superficie total de los 20 tarugos. Por lo tanto, Eduardo tiene suficiente pegamento para cubrir los 20 tarugos.

Answer:

  an = 5n -7

Step-by-step explanation:

Try the offered formulas with n= 1 and see which gives you the first term of the sequence.

an = -2n +3

  -2(1) +3 = 1 . . . . not -2

an = -2n +7

  -2(1) +7 = 5 . . . . not -2

an = 5n +3

  5(1) +3 = 8 . . . . not -2

an = 5n -7

  5(1) -7 = -2 . . . . this is the formula you want

_____

If you recognize the common difference of the sequence to be 5, then you can automatically eliminate any formulas that don't contain 5n.

Answer:

$96

Step-by-step explanation:

Using translation concepts, a stretch of a decay exponential function is given by:

\(f(x) = 5\left(\frac{1}{5}\right)^x\)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

An exponential decay function is given by:

\(y = ab^x\)

In which |b| < 1.

A stretch means that the function is multiplied by a factor with absolute value greater than 1, hence the function would be given by:

\(f(x) = 5\left(\frac{1}{5}\right)^x\)

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The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

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An annual payment is found approximately $617.34. The correct option is e.. $617.34.

To find the size of your payments, you can use the formula for calculating the equal installments on a loan.

First, calculate the annual payment by dividing the borrowed amount ($2,000) by the present value factor of an annuity due with 4 periods at a 9% interest rate.

Using a financial calculator or spreadsheet, the present value factor of an annuity due with 4 periods at 9% interest rate is 3.2403.

Dividing $2,000 by 3.2403 gives us an annual payment of approximately $617.34.
Therefore, the correct answer is e. $617.34.

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The correct option is Option A

The minimum value of D is 2, while the maximum value of C is -3.

The minimum value of D is 5 more than the maximum value of C

The hexadecimal expression of decimal integer -100 in the 8-bit signed binary integer system is "9C". The decimal integer expression of the signed binary number 11010111 is -41. The 8-bit fixed point binary number expression of decimal real number -3.47 is 10111011.

To obtain the hexadecimal expression of decimal integer -100 in the 8-bit signed binary integer system, we first need to represent -100 in binary form. Since the 8-bit signed binary integer system uses two's complement representation, we can find the binary representation of -100 by taking the two's complement of the binary representation of 100. The binary representation of 100 is 01100100, so the two's complement of this number is 10011100. Therefore, the binary representation of -100 is 10011100, and its hexadecimal expression is 9C.

To find the decimal integer expression of the signed binary number 11010111, we first need to determine its sign bit. Since the leftmost bit is a 1, the number is negative. To obtain its binary value, we can take the two's complement of the binary representation of 00101001, which is the binary representation of the absolute value of 11010111. The two's complement of 00101001 is 11010111, so the binary representation of -41 is 11010111 in the 8-bit signed binary integer system.

To obtain the 8-bit fixed point binary number expression of decimal real number -3.47, we first need to represent -3.47 in binary form. To do this, we can convert the integer part and the fractional part separately. The integer part of -3.47 is -3, which has a binary representation of 11111101 in the 8-bit signed binary integer system. The fractional part of -3.47 can be converted using the binary fraction representation method. Multiplying 0.47 by 2 yields 0.94, which has an integer part of 0. Multiplying 0.94 by 2 yields 1.88, which has an integer part of 1. Continuing in this way, we can obtain the binary fraction 01101101. Therefore, the binary representation of -3.47 is 11111101.01101101. To obtain the 8-bit fixed point binary number expression, we need to shift the binary point to the left by 4 bits, yielding 11010111.

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Hi there!

\(\large\boxed{a = 6 m/s^{2}}\)

Use the kinematic equation to solve for acceleration:

\(a = \frac{v_{f}-v_{i}}{t}\)

Where:

vf = final velocity

vi = initial velocity

t = time

Plug in the given values:

\(a = \frac{65-35}{5}\\\\a = 30 / 5 \\\\=6 m/s^{2}\)

We are given the relationship:

a. It's required to find a relationship where r is a function of t. To do that, we need to solve the equation for r.

Subtract 4t:

Divide by 7:

b. We use the function found in part a and evaluate it for t=-7:

Thus, f(-7) = 6

c. Solve f(t) = 18

Again, we use the function from part a and solve the equation:

Multiplying by 7:

Subtract 14 and then divide by -4:

t = -28

Answer:

Volume = 9900 ft2

Step-by-step explanation:

To find the volume of the pool, we can use the base as the trapezoid, and then we need to calculate the base area and multiply by the height.

The trapezoid has a bigger base of 8 and a smaller base of 3, with a height of 60, so the area is:

Area = (8+3)*60/2 = 330 ft2

Now, to find the volume, we just need to multiply the base area by the height of 30 feet:

Volume = Area * Height = 330 * 30 = 9900 ft2

Answer:

they are diffrent coins so that means theyy have diffrent valus.

Step-by-step explanation:

Answer: y ≤ 22-x

Y ≥36 - 5/2x

Step-by-step explanation:

VARIABLE DEFINITIONS:

X= the number of quarters

Y= the number of dimes

“at most 22 counc” -> 22 or fewer coins

Use the ≤ symbol

Therefore the total number of coins, x+ y, must be less than or equal to 22:

x+y ≤22

“no less than $3.60” -> 3.60 or more use the ≥ symbol

One quarter is worth $0.25, so x quarters are worth 0.25x. One dime is worth $0.10, so y dimes are worth 0.10y. The total 0.25x + 0.10y must be greater than or equal to $3.60:

0.25x+0.10y ≥3.60

Sole each inequality for y:

x+y ≤22 0.25x+0.10y ≥3.60

y ≤22-x 0.10y ≥3.60-0.25x

y ≥3.60-0.25x / 0.10

y ≥36-5/2x

Graph y ≤ 22 - x by shading down the graph

y ≥36 - 5/2x by shading up:

Since the point (16,2) is inside the double shaded region, one possible solution to the system of inequalities would be:

Sadie could have 16 quarters and 2 dimes

Answer:

Step-by-step explanation:

diameter d=18 m

r=18/2=9 m

circumference=2πr=2π×9=18π square meters.

Answer:

139°

Step-by-step explanation:

By definition, the measure of an exterior angle is the sum of the two interior angles not supplementary to the exterior one.

Here, we see that the two interior angles not supplementary to ∠2 are valued at 75° and 64°, so our exterior angle is the sum of these:

∠2 = 75 + 64 = 139°

Answer:

e

Step-by-step explanation:

There are three a's, we can write a³ instead of a×a×a. This gives us d×b×c×a³

To simplify the expression d×b×c×a×a×a, we can rewrite it using exponents. Since there are three a's, we can write a³ instead of a×a×a. This gives us:

d×b×c×a³

This is the simplified expression using single variables raised to exponents. We can read this as "d times b times c times a to the power of 3".

It's important to note that when we have multiple variables multiplied together, we can simplify the expression by combining them using exponents. This makes it easier to work with and to manipulate algebraic equations.

In this case, we were able to simplify the expression by replacing three instances of a with a³. We could continue to simplify further if we had additional like terms, but in this case, this is the simplest form of the expression.

Overall, simplifying expressions using exponents is a common technique in algebra and can help make solving equations more manageable.

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Answer:

57 liters

Step-by-step explanation:

Answer

1.0/5

0

MrRoyal

Ace

9K answers

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MISSING DETAILS

Yoko's fish tank has 17 liters of water in it. She plans to add 5 liters per minute until the tank has at least 57 liters. What are the possible numbers of minutes Yoko could add water?

Answer:

Minutes = 8 minutes

Step-by-step explanation:

Topic: Inequality

Given:

Available Size of water = 17 liters

Increment = 5 liters/minute

Size of water needed = At least 57 liters

Putting the above together, as have

17 + 5m > 57

where m represents total minutes and > represent at least

Solving the Inequality

5m > 57 - 17

5m > 40 ------ Divide through by 5

5m/5 > 40/5

m > 8

So, Yoko will need to add water for at least 8 minutes before she fills her tank to 57 liters.

The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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Answer:

5% = 1/20

15% = 3/20

6.5% = 0.065

25% = 0.25

7% = 0.07

Step-by-step explanation:

I hope this helps! Just ask me if you have any questions.

Have a nice dayy! :)

Answer:

.05  25%  .15  7% .065  100% 2000% .25

Step-by-step explanation:

Percentages to decimals :

example  

5% = .05

First remove the % sign: 5

Where is the decimal? Here : 5.00

Now move the decimal to the left two places. Fill the gaps with zeros : .05

Another way to do it is by divide the number by 100. Use a calculator if necessary.

Example 2: 6.5%

Move decimal two places to left: .065

Example 3: .56%

Move decimal to places to the left:  .0056

Decimals to percentages. Do the exact opposite. Move decimal to places to the right then add the % sign.

Example: .25 becomes 25%

                .07 becomes 07% or just 7%

Given the point (1, 3) lies on the graph of y = f(x) and the slope of the tangent line at this point is m = 2.To find the function f(x) .we need to use the slope-point form of a line.

Let the tangent line be y = mx + b where m = 2 and (x, y) = (1, 3) is a point on the line.

Therefore,y = 2x + b3

= 2(1) + bb

= 3 - 2b

= 1.

Thus the equation of the tangent line is given byy = 2x + 1 .

The slope of the tangent line at the point (1, 3) is m = 2, therefore the graph of the function f(x) at the point (1, 3) has a slope of 2.

Hence, the derivative of f(x) at x = 1 is 2.

Answer: The point (1, 3) lies on the graph of y = f(x), and the slope of the tangent line through this point is m = 2. The function f(x) is y = 2x - 1, and the derivative of f(x) at x = 1 is 2.

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Answer:

C. Obtuse

Step-by-step explanation:

 An obtuse triangle is a triangle with one obtuse angle and two acute angles.