evaluate the expression when x=7 and y= -2 -x+8y​

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Value of the expression in which each variable was swapped out with a number from its corresponding domain sinh⁡ (l5)

sinh (5)

=sinh(1.6094) =2.39990 rad

=sinh⁡(1.6094) =2.3

By doing the following, you may determine the numerical value of an algebraic expression: Replace each variable with the specified number. Then, enter your score in your team's table.

Value of the expression in which each variable was swapped out with a number from its corresponding domain. In the case of a number with only one digit, referring to the numerical value associated with a digit by its "value" is a convenient shorthand.

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Answer:

Step-by-step explanation:

[tex]f(x) = \frac{4}{x}\\\\f(a) = \frac{4}{a}\\\\f(a+h) = \frac{4}{a+h}\\\\\frac{f(a+h) - f(a)}{h} = \frac{\frac{4}{a+h} - \frac{4}{a}}{h}[/tex]

                [tex]=\frac{\frac{4(a)}{(a+h)a} - \frac{4(a+h)}{a(a+h)}}{h}\\\\=\frac{\frac{4a - 4a - 4h}{a(a+h)}}{h}\\\\=\frac{\frac{ - 4h}{a(a+h)}}{h}\\\\= \frac{-4h}{a(a+h) \times h}\\\\= -\frac{4}{a(a+h)}\\\\[/tex]

Actual data table :

X __ y

2 15

6 13

7 9

8 8

12 5

Answer:

0.953

Step-by-step explanation:

The question isnt well formatted :

The actual data:

X __ y

2 15

6 13

7 9

8 8

12 5

Using a correlation Coefficient calculator, the correlation Coefficient obtained by fitting the data is 0.953 which depicts a strong linear correlation between the x and y variable. This shows that the value of y increases with a corresponding increase in x values and vice versa.

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8

Answer:

[tex]CI=189.5,194.5[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=40[/tex]

Mean [tex]\=x =192[/tex]

Standard deviation[tex]\sigma=8[/tex]

Significance Level [tex]\alpha=0.05[/tex]

From table

Critical Value of [tex]Z=1.96[/tex]

Generally the equation for momentum is mathematically given by

 [tex]CI =\=x \pm z_(a/2) \frac{\sigma}{\sqrt{n}}[/tex]

 [tex]CI =192 \pm 1.96 \frac{8}{\sqrt{40}}[/tex]

 [tex]CI=192 \pm 2.479[/tex]

 [tex]CI=189.5,194.5[/tex]

Answer:

The answer is 40 chocolates in the box in total

Answer:

12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.

Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1

4x = y + 1

[tex]x = \dfrac{y+1}{4}[/tex]

[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

By integration, the required surface area in the revolve is:

[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]

where;

g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

∴

[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]

[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]

[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]

[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]

Answer:

You can go ahead with option D

Step-by-step explanation:

Answer:

2.25 miles per hr

Answer:

2.25 miles per hour

Step-by-step explanation:

speed = distance / time

speed = [tex]\frac{3}{4} / \frac{1}{3}[/tex] (take the reciprocal of [tex]\frac{1}{3}[/tex])

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

= [tex]\frac{9}{4}[/tex] = 2.25 miles per hour

Answer:

x=[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Hi there!

We are given the following equation:

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

and we need to find the value of x

To do this, we need to isolate the value of x with a coefficient of 1 (1x) on one side. The value of x, or everything else is on the other side

So let's get rid of [tex]\frac{1}{10}[/tex] from the left side by adding [tex]\frac{1}{10}[/tex] to both sides (-[tex]\frac{1}{10}[/tex]+[tex]\frac{1}{10}[/tex]=0).

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

  +[tex]\frac{1}{10}[/tex]  +[tex]\frac{1}{10}[/tex]

___________

[tex]\frac{4x}{5}[/tex]=[tex]\frac{3}{10}[/tex]+[tex]\frac{1}{10}[/tex]

as the fractions on the right side both have the same denominator, we can add them together

[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]

Now we need to have the value of 1x. Currently we have [tex]\frac{4x}{5}[/tex].

In order to get x with a coefficient of 1, multiply both sides by the reciprocal of [tex]\frac{4}{5}[/tex], which is [tex]\frac{5}{4}[/tex]

[tex]\frac{5}{4}[/tex]×[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]*[tex]\frac{5}{4}[/tex]

which simplifies down to

x=[tex]\frac{20}{40}[/tex]

Now reduce the fraction by dividing the numerator and denominator both by 20

x=[tex]\frac{1}{2}[/tex]

Hope this helps!  

Answer:

C

Step-by-step explanation:

x + 2 < -5

x < - 5 - 2

x < - 7

Answer:

{x| x R, x<-7}

Step-by-step explanation:

=> x+2<-5

=> x<-5-2

=> x<-7

Answer:

1. 3

2. D

3. KE

4. B

5. A

Step-by-step explanation:

those should be your answers

Answer:

1. 3

2. D

3. E and K

4. B

5. A

negative integers lie on the negative side of the number line(usually having a minus sign in front of them)

positive ones lie on the positive side( usually have no signs in front of them)

Answer:

The interval is [98,132]

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set 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]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal with mean 115 and standard deviation 25.

This means that [tex]\mu = 115, \sigma = 25[/tex]

Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.

Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

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

[tex]-0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = -0.675*25[/tex]

[tex]X = 98[/tex]

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

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

[tex]0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = 0.675*25[/tex]

[tex]X = 132[/tex]

The interval is [98,132]

Answer:

15.9

Step-by-step explanation:

The distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

It is given that:

Two numbers on a number line:

-10.2 and 5.7

As we know, a number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

Indicating the above numbers on a number line:

= 5.7 -(-10.5)

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

= 5.7 + 10.5

= 15.9

Thus, the distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.

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Answer:

The measure of the smallest angle is 30º

Step-by-step explanation:

Let the angles be:

[tex]x \to[/tex] the first angle (the smallest)

[tex]y \to[/tex] the second angle

[tex]z \to[/tex] the third angle

So, we have:

[tex]y = 2x[/tex]

[tex]z=x + 60[/tex]

Required

Find x

The angles in a triangle is:

[tex]x + y +z = 180[/tex]

Substitute values for y and z

[tex]x + 2x +x + 60 = 180[/tex]

[tex]4x + 60 = 180[/tex]

Collect like terms

[tex]4x = 180-60[/tex]

[tex]4x = 120[/tex]

Divide by 4

[tex]x = 30[/tex]

Answer:

[tex]x=\frac{5}{2} \\y=5[/tex]

( 5/2, 2 )

Step-by-step explanation:

Solve by substitution method:

[tex]2x+5=10\\\2x+3y=20[/tex]

Solve [tex]2x+5=10[/tex] for [tex]x[/tex]:

[tex]2x+5=10[/tex]

[tex]2x=10-5[/tex]

[tex]2x=5[/tex]

[tex]x=5/2[/tex]

Substitute [tex]5/2[/tex] for [tex]x[/tex] in [tex]2x+3y=20[/tex]:

[tex]2x+3y=20[/tex]

[tex]2(\frac{5}{2} )+3y=20[/tex]

[tex]3y+5=20[/tex]

[tex]3y=20-5[/tex]

[tex]3y=15[/tex]

[tex]y=15/3[/tex]

[tex]y=5[/tex]

∴ [tex]x=\frac{5}{2}[/tex] and [tex]y=5[/tex]

hope this helps....

Answer:

1) Isosceles

2) Acute

3) Right angled

4( Obtuse

5) Equilateral

Step-by-step explanation:

Recall that

[tex]1 + \tan^2 x = \sec^2 x[/tex]

and

[tex]\dfrac{d}{dx}(\tan x) = \sec^2 x[/tex]

so that

[tex]\displaystyle \int \tan^2 x = \int (\sec^2 x - 1)dx[/tex]

[tex]\:\:\:\:\:\:\:\:\:=\int \sec^2 xdx - \int dx[/tex]

[tex]\:\:\:\:\:\:\:\:\:=\tan x - x + C[/tex]

where C is the constant of integration.

Answer:

0.7994 = 79.94% probability that the proportion of persons with myopia will differ from the population proportion by less than 3%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set 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]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 42% of the population has myopia.

This means that [tex]p = 0.42[/tex]

Random sample of size 442 is selected

This means that [tex]n = 442[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.42[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.42*0.58}{442}} = 0.0235[/tex]

What is the probability that the proportion of persons with myopia will differ from the population proportion by less than 3%?

Proportion between 0.42 + 0.03 = 0.45 and 0.42 - 0.03 = 0.39, which is the p-value of Z when X = 0.45 subtracted by the p-value of Z when X = 0.39.

X = 0.45

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.45 - 0.42}{0.0235}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

X = 0.39

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

[tex]Z = \frac{0.39 - 0.42}{0.0235}[/tex]

[tex]Z = -1.28[/tex]

[tex]Z = -1.28[/tex] has a p-value of 0.1003

0.8997 - 0.1003 = 0.7994

0.7994 = 79.94% probability that the proportion of persons with myopia will differ from the population proportion by less than 3%.

The first sum is a geometric series:

[tex]1+\dfrac15+\dfrac1{5^2}+\dfrac1{5^3}+\cdots+\dfrac1{5^n}+\cdots=\displaystyle\sum_{n=0}^\infty\frac1{5^n}[/tex]

Recall that for |x| < 1, we have

[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]

Here we have |x| = |1/5| = 1/5 < 1, so the first sum converges to 1/(1 - 1/5) = 5/4.

The second sum is exponential:

[tex]1+5+\dfrac{5^2}{2!}+\dfrac{5^3}{3!}+\cdots+\dfrac{5^n}{n!}+\cdots=\displaystyle\sum_{n=0}^\infty \frac{5^n}{n!}[/tex]

Recall that

[tex]\exp(x)=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}[/tex]

which converges everywhere, so the second sum converges to exp(5) or e⁵.

Answer:

remember the chain rule:

h(x) = f(g(x))

h'(x) = f'(g(x))*g'(x)

or:

dh/dx = (df/dg)*(dg/dx)

we know that:

z = 4*e^x*ln(y)

where:

y = u*sin(v)

x = ln(u*cos(v))

We want to find:

dz/du

because y and x are functions of u, we can write this as:

dz/du = (dz/dx)*(dx/du) + (dz/dy)*(dy/du)

where:

(dz/dx)  = 4*e^x*ln(y)

(dz/dy) = 4*e^x*(1/y)

(dx/du) = 1/(u*cos(v))*cos(v) = 1/u

(dy/du) = sin(v)

Replacing all of these we get:

dz/du = (4*e^x*ln(y))*( 1/u) + 4*e^x*(1/y)*sin(v)

          = 4*e^x*( ln(y)/u + sin(v)/y)

replacing x and y we get:

dz/du = 4*e^(ln (u cos v))*( ln(u sin v)/u + sin(v)/(u*sin(v))

dz/du = 4*(u*cos(v))*(ln(u*sin(v))/u + 1/u)

Now let's do the same for dz/dv

dz/dv = (dz/dx)*(dx/dv) + (dz/dy)*(dy/dv)

where:

(dz/dx)  = 4*e^x*ln(y)

(dz/dy) = 4*e^x*(1/y)

(dx/dv) = 1/(cos(v))*-sin(v) = -tan(v)

(dy/dv) = u*cos(v)

then:

dz/dv = 4*e^x*[ -ln(y)*tan(v) + u*cos(v)/y]

replacing the values of x and y we get:

dz/dv = 4*e^(ln(u*cos(v)))*[ -ln(u*sin(v))*tan(v) + u*cos(v)/(u*sin(v))]

dz/dv = 4*(u*cos(v))*[ -ln(u*sin(v))*tan(v) + 1/tan(v)]

Answer:

[tex]\frac{-2x+11}{(x-4)(x+1)}[/tex]

Step-by-step explanation:

I don't think we can factor this so we'll have to multiply to make the denominators the same

[tex]\frac{3(x+1)}{(x^2-3x-4)(x+1)}-\frac{2(x^2-3x-4)}{(x+1)(x^2-3x-4)}\\\\\frac{3x+3-(2x^2-6x-8)}{(x^2-3x-4)(x+1)}=\frac{-2x^2+9x+11}{(x^2-3x-4)(x+1)}\\-2x^2+9x+11=(x+1)(-2x+11)\\\\x^2-3x-4=(x+1)(x-4)\\\frac{(x+1)(-2x+11)}{(x+1)(x-4)(x+1)}=\frac{-2x+11}{(x-4)(x+1)}[/tex]

Given :-

To Find :-

Answer :-

Taking the given expression,

→ 4x² - 8x + 4

→ 4x² - 4x -4x + 4

→ 4x ( x - 1 ) -4( x -1)

→ (4x - 4)(x-1)

Hence the required answer is (4x - 4)( x - 1) .

Answer:

the total square footage = 194

1.88 x 194 = 364.72

Step-by-step explanation:

Area for triangle ends.

A = [tex]\frac{2.5 (8)}{2}[/tex]   (Times two, because there are two ends.)

Base of prism = 8 x 10 = 80

Sides of prism = 2(10 x 4.7 ) = 94  (What's the 2?  There's two of them)

Add all together : 10 + 10 + 80 + 94 = 194

1.88 x 194 = 364.72

Answer:

A) [ 7/3,  (-7/9)(x/2),  7/27(x-2)^2,  (-7/81)(x-2)^3 ]

B) attached below

Step-by-step explanation:

A)  Using the definition of a Taylor series

The first four nonzero terms of the series for f(x) = 7/ (1 +x), a = 2

= [ 7/3,  (-7/9)(x/2),  7/27(x-2)^2,  (-7/81)(x-2)^3 ]

attached below is the detailed solution

B) Finding Maclaurin series for f(x)

f(x) = e^-5x

attached below

Associated radius of convergence = ∞  ( infinity )

Step-by-step explanation:

Answer:

[tex]x<41[/tex]

Step-by-step explanation:

[tex](x)+(x+1)<83[/tex]

simplify both sides

[tex]2x+1<83[/tex]

subtract one from the both sides to isolate the variable

[tex]2x<82[/tex]

divide both sides by 2 to isolate the variable

[tex]x<41[/tex]

SOLUTION:

10•10= 100