four times daphne's age plus five times isaac's age adds up to 57. also, isaac's age is 11 less than twice daphne's age. how old is isaac?

The numerical value of cosh(ln5) is 2.55, obtained by using the hyperbolic cosine function definition and the properties of exponential and logarithmic functions.

The question asks you to find the numerical value of cosh (ln5). This involves using hyperbolic trigonometry functions, specifically the hyperbolic cosine function.

The hyperbolic cosine, represented by 'cosh', is a mathematical function whose definition is similar to the ordinary trigonometric cosine function. However, it is defined using exponential functions rather than angular measure. The general definition is cosh(x) = (e^x + e^(-x))/2.

Using this formula and substituting ln5 for x results in cosh(ln5) = (e^(ln5) + e^(-ln5))/2.

The expression e^(ln5) simplifies to 5 since e and ln are inverse functions.

For the second term, e^(-ln5), we can use the fact that a negative exponent signifies taking the reciprocal, so this simplifies to 1/5.

Therefore, cosh(ln5) = (5 + 1/5)/2 = 5.1/2 = 2.55.

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The solution to cosh (ln5) is obtained by substituting ln5 in the formula of hyperbolic cosine function, which simplifies it to (5 + 1/5)/2 yielding a result of 2.6.

To find the numerical value of cosh (ln5), we need to know the definition of cosh. It is a hyperbolic function defined as cosh(x) = (e^x + e^-x)/2 where e is Euler's number (approximately 2.71828).

So, to find cosh (ln5), we substitute ln5 in place of x in the formula cosh(x) = (e^x + e^-x)/2.

This gives us cosh(ln5) = (e^ln5 + e^-ln5)/2. However, e and ln are inverse functions, so e^ln5 simplifies to 5. Similarly, for e^-ln5, we need to use the property a^-b = 1/a^b to simplify it to 1/5.

Then we just add and divide, yielding cosh(ln5) = (5 + 1/5)/2 = 2.6.

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Answer:

The correct answer is D. The simplified form of the expression 7^4 is 2,401.

Step-by-step explanation:

7 ^ 4, that is, the exponentiation of 7 to the fourth power, implies the continuous multiplication of the number 7 for 4 times. Therefore, this number will appear 4 times in a multiplication, whose result will be said number exposed to the fourth power.

Simplified, this operation translates into 7x7x7x7, whose result is 2,401.

Final answer:

To calculate the value of the car in 8 years with a constant yearly depreciation rate of 5.1%, we can use the formula for compound interest.

Explanation:

To calculate the value of the car in 8 years, we can use the formula for compound interest: A = P(1 - r/n)^(nt), where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the initial amount is $9,250, the interest rate is 5.1%, and the number of times interest is compounded per year is 1. Plugging these values into the formula, we get:

A = 9250(1 - 0.051/1)^(1*8) = $6630.27

Therefore, the car will be worth approximately $6,630.27 in 8 years.

The graph will show exponential decay and The domain will be the set of natural numbers.

Option C and D will apply.

A geometric sequence is a sequence of numbers obtained by either  multiplying or dividing by the same value.

The geometric sequence given is

640, 160, 40, 10, ...

Each number is divided by 4

So the nth term will be

[tex]\rm T_n = a_1 r^{n-1}[/tex]

where [tex]\rm a_1 \; is \; the \; first \; term[/tex]

and r is the common ratio

r =(1/4) for this sequence

The function is

[tex]\rm T_n = 640(\dfrac {1}{4})^{n-1}[/tex]

As from the function it can be understood , That The graph will show exponential decay and The domain will be the set of natural numbers.

Option C and D will apply.

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The sequence is a geometric sequence showing exponential decay with a factor of 0.25 (divisible by 4). The graph will show exponential decay and not appear linear. The domain is the set of natural numbers, while the range consists of specific values from the sequence, not all natural numbers.

The sequence given is 640, 160, 40, 10, ..., which is a geometric sequence. We can determine this because each term is obtained by multiplying the previous term by a constant factor.

In this case, each term is divided by 4 to get the next term (160 is 640 divided by 4, 40 is 160 divided by 4, and so on). Therefore, the common ratio r is ¼ or 0.25, which is less than 1.

Now, let’s evaluate the statements provided:

So, the correct statements are that the graph will show exponential decay and the domain will be the set of natural numbers.

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Finding the rate of change in something with respect to something is known as differentiation. For Example, Change in y with respect to x is known as the derivative of y with respect to x.

(a) [tex]9{x}^2-{y}^2 = 1[/tex]

Differentiating equation with respect to x :

[tex]9*2x - 2y\frac{dy}{dx} = 0\\ 18x = 2y\frac{dy}{dx}\\9\frac{x}{y} =\frac{dy}{dx}[/tex]

(b)

[tex]9{x}^2-{y}^2 = 1\\9{x}^2-1 = {y}^2 \\\sqrt[2]{9{x}^2-1} = y\\[/tex]

differentiating with respect to x gives:

[tex]\frac{1}{2\sqrt{9{x}^2-1} } *(18x) = \frac{dy}{dx}\\\frac{1}{\sqrt{9{x}^2-1} } *(9x) = \frac{dy}{dx}[/tex]

(c) [tex]9\frac{x}{y} =\frac{dy}{dx}[/tex]

substituting value of y

[tex]\sqrt[2]{9{x}^2-1} = y\\\\\frac{9x}{\sqrt[2]{9{x}^2-1}} = \frac{dy}{dx}[/tex]

Hence the solution is consistent.

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Answer:

Its false

Step-by-step explanation:

well first i pt the answer in and it came out correct.

The distance traveled by the ball until it stops bouncing is:

                                   18 meters

It is given that:

a ball bounces from a height of 2 meters and returns to 80% of its previous height on each bounce.

This means that the distance traveled by the ball is the distance it travels by going down as well as coming up on bouncing.

and is given as follows:

[tex]\text{Total Distance}=2+0.8\times 2\ up+0.8\times 2\ down+(0.8)^2\times 2\ up+(0.8)^2\times 2\ down+.....\\\\\text{Total distance}=2+4\times (0.8)+4\times (0.8)^2+4\times (0.8)^3+....\\\\\text{Total distance}=2+4\times [0.8+(0.8)^2+(0.8)^3+......]\\\\\text{Total distance}=2+4\times (\dfrac{0.8}{1-0.8})[/tex]

Since, the formula of infinite geometric progression is:

[tex]\sum_{n=1}^{\infty} ar^{n-1}=\dfrac{a}{1-r}[/tex]

i.e.

[tex]\text{Total distance}=2+4\times (\dfrac{0.8}{0.2})\\\\\text{Total distance}=2+4\times 4\\\\\text{Total distance}=2+16\\\\\text{Total distance}=18\ \text{meters}[/tex]

Answer:

50

Step-by-step explanation:

10=20/100*50/1=1000/100=10

Using the normal distribution, it is found that:

a) [tex]Z_0 = -1.75[/tex].

b) [tex]Z_0 = 1.96[/tex].

c) [tex]Z_0 = 1.645[/tex].

d) [tex]Z_0 = -0.83[/tex].

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

This is Z with a p-value of 0.0401, thus [tex]Z_0 = -1.75[/tex].

Item b:

Item c:

Same logic as b, just middle 90%, thus [tex]Z_0 = 1.645[/tex].

Item d:

This is Z with a p-value of 1 - 0.2967 = 0.2033, thus [tex]Z_0 = -0.83[/tex].

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Final answer:

The value of the standard normal random variable Z that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.

Explanation:

The z-score that corresponds to the area 0.90 under the standard normal distribution can be found using a z-table or a calculator.

Therefore, the value of the standard normal random variable Z, denoted as Z0, that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.

Answer:

false

Step-by-step explanation:

There are 840 seats in total in Cinema Hall.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

Given:

First term, [tex]a_1[/tex] = 22

second row = 22 + 3 = 25

Third row = 25 + 3 = 28

So, the Recursive Formula is

[tex]a_n[/tex] = a + (n-1)d

[tex]a_n[/tex] = 10 + (n-1)3

[tex]a_n[/tex] = 10 + 3n - 3

[tex]a_n[/tex] = 7 + 3n

In 21th rows the seats are

= 7 +3 (21)

= 7 + 63 = 70

Now, to find the number of seats in hall we have to find the sum of seats from row 1 to row 21 using Formula

= n×([tex]a_1[/tex]+ [tex]a_n[/tex])/2

= 21 x (10 + 70) /2

= 21 x 80 /2

= 21 x 40

= 840

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To solve the equation 15-28i=3l+(4m)i, separate the real and imaginary parts of the equation and solve for l and m separately.

To solve the equation 15-28i=3l+(4m)i, we can separate the real and imaginary parts of the equation. The real part is 15, and the imaginary part is -28. Similarly, the real part of the right side is 3l and the imaginary part is 4m. Equating the real parts and imaginary parts separately, we get two equations: 15 = 3l and -28 = 4m. Solving these equations will give us the values of l and m.

In the first equation, dividing both sides by 3 gives us l = 5. In the second equation, dividing both sides by 4 gives us m = -7.

Therefore, the solution to the equation 15-28i=3l+(4m)i is l = 5 and m = -7.

Answer:

the root of 13

Step-by-step explanation:

To calculate the height of a sail that is four times as high as it is wide and made from 32 square meters of material, we use the area formula for a triangle and find that the height is 16 meters.

The student's question concerns the height of a sail in the shape of a right triangle, where the sail's height is four times its width and the total area of the sail is 32 square meters. To find the height, we can let the width be x meters, which makes the height 4x meters due to the given ratio.

Using the formula for the area of a triangle, A = bh/2, where b is the base and h is the height, we can write an equation for the area in terms of x: 32 m² = x × (4x) / 2.

Simplifying this, we get 32 = 2x2, which can be further simplified to x² = 16. Taking the square root of both sides gives us x = 4. Therefore, the height of the sail, being four times the width, is 16 meters.