Use the function below to find f(-2)

f(x)=5^x

Answer:

Step-by-step explanation:

This problem could keep you going for quite a while. My suggestion is that you go get a cup of coffee and sip it slowly as you read this.

Equation One

Sqrt(x - 1)^3 = 8

(x - 1)^(3/2) = 8

Square both sides to get rid of the 2.

(x - 1)^3 = 8^2  

(x - 1)^3 = 64

Now take the cube root of both sides to get rid of the 3 on the left

x - 1 = cuberoot(64)

x - 1 = 4                     Add 1 to both sides

x - 1+1 = 4 + 1

x  =  5

==============================

Second Equation

4th root (x - 3)^5 = 32

Take the 5th root of both sides.

4th root(x - 3) = 2

This can be written as (x - 3)^(1/4) = 2

Now take the 4th power of both sides.

(x - 3) = 2^4

x - 3 =  16

add 3 to both sides.

x = 16 + 3

x = 19

============================

Equation 3

(x - 4)^(3/2) = 125

Take the cube root of both sides

(x - 4)^(1/2) = 125^(1/3)     1/3 is the cube root of something

(x - 4)^(1/2) = 5    

square both sides to get rid of the 2    

(x - 4) = 5^2

x - 4 = 25

Add 4 to both sides.

x = 25 + 4

x = 29

============================

Fourth Equation

(x + 2)^(4/3) = 16        

take the 4th root of both sides

(x + 2) ^(1/3) = 16^(1/4)

(x + 2)^(1/3) = 2

Cube both sides

(x + 2) = 2^3

x + 2 = 8  

Subtract 2 from both sides

x + 2 - 2 = 8-2

x = 6

##########################

The first step is the most critical. You must look at what you are going to take the root of. When you do, for this question, it must come out even.

Answer:

The tangent vector for [tex]t = 0[/tex] is:

[tex]\vec T (t) = \left \langle \frac{8}{10}, 0, \frac{6}{10} \right\rangle[/tex]

Step-by-step explanation:

The function to be used is [tex]\vec r(t) = \langle 8\cdot t, 10, 3\cdot \sin (2\cdot t)\rangle[/tex]

The unit tangent vector is the gradient of [tex]\vec r (t)[/tex] divided by its norm, that is:

[tex]\vec T (t) = \frac{\vec \nabla r (t)}{\|\vec \nabla r (t)\|}[/tex]

Where [tex]\vec \nabla[/tex] is the gradient operator, whose definition is:

[tex]\vec \nabla f (x_{1}, x_{2},...,x_{n}) = \left\langle \frac{\partial f}{\partial x_{1}}, \frac{\partial f}{\partial x_{2}},...,\frac{\partial f}{\partial x_{n}} \right\rangle[/tex]

The components of the gradient function of [tex]\vec r(t)[/tex] are, respectively:

[tex]\frac{\partial r}{\partial x_{1}} = 8[/tex], [tex]\frac{\partial r}{\partial x_{2}} = 0[/tex] and [tex]\frac{\partial r}{\partial x_{3}} = 6 \cdot \cos (2\cdot t)[/tex]

For [tex]t = 0[/tex]:

[tex]\frac{\partial r}{\partial x_{1}} = 8[/tex], [tex]\frac{\partial r}{\partial x_{2}} = 0[/tex] and [tex]\frac{\partial r}{\partial x_{3}} = 6[/tex]

The norm of the gradient function of [tex]\vec r (t)[/tex] is:

[tex]\| \vec \nabla r(t) \| = \sqrt{8^{2}+0^{2}+ [6\cdot \cos (2\cdot t)]^{2}}[/tex]

[tex]\| \vec \nabla r(t) \| = \sqrt{64 + 36\cdot \cos^{2} (2\cdot t)}[/tex]

For [tex]t = 0[/tex]:

[tex]\| \vec r(t) \| = 10[/tex]

The tangent vector for [tex]t = 0[/tex] is:

[tex]\vec T (t) = \left \langle \frac{8}{10}, 0, \frac{6}{10} \right\rangle[/tex]

Answer:

Number = 34

Step-by-step explanation:

We are looking for our mystery "number". I will call this number N.

We can find out what our equation looks like based on what the question tells us.

"three times a number" is 3N

"added to 2" is + 2

Which so far is 3N + 2

"divided by the number plus 5" is ÷ [tex]{N+5}[/tex]

Combined with the first two parts to give us (3N + 2) ÷ (N + 5)

"the result is eight third" So the above equation is equal to 8/3

Combining all these comments together to get the following equation

(3N + 2) ÷ (N + 5) = 8/3

Rearrange by multiplying both sides of the = by (N+5)

3N + 2 ÷ (N + 5) × (N + 5) = 8/3 × (N + 5)

Simplify

3N + 2 = 8/3 × (N + 5)

3N + 2 = 8N/3 + 40/3

Bring the N numbers to one side and the non N numbers to the other side, by subtracting 2 from both sides of the =

3N + 2 - 2 = 8N/3 + 40/3 - 2

Simplify

3N = 8N/3 + 34/3

and then subtracting 8N/3 from both sides

3N - 8N/3 = 8N/3 - 8N/3 + 34/3

Simplify

1N/3 = 34/3

Simplify for our final answer by multiplying both sides of the = by 3

1N/3 x 3 = 34/3 x 3

N = 34

Many of these steps can be skipped when solving for yourself but I wanted to be thorough

Answer:

The probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.

Step-by-step explanation:

The complete question is:

Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm Anew book will be printed on 500 sheets of this paper. Approximate the probability that the thicknesses at the entire book (excluding the cover pages) will be between 49.9 mm and 50.1 mm. Note: total thickness of the book is the sum of the individual thicknesses of the pages Do not round your numbers until rounding up to two. Round your final answer to the nearest hundredth, or two digits after decimal point.

Solution:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e S, will be approximately normally distributed.  

Then, the mean of the distribution of the sum of values of X is given by,  

 [tex]\mu_{S}=n\mu[/tex]

And the standard deviation of the distribution of the sum of values of X is given by,  

[tex]\sigma_{S}=\sqrt{n}\sigma[/tex]

The information provided is:

[tex]n=500\\\mu=0.1\\\sigma=0.002[/tex]

As n = 500 > 30, the central limit theorem can be used to approximate the total thickness of the book.

So, the total thickness of the book (S) will follow N (50, 0.045²).

Compute the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm as follows:

[tex]P(49.9<S<50.1)=P(\frac{49.9-50}{0.045}<\frac{S-E(S)}{SD(S)}<\frac{50.1-50}{0.045})[/tex]

                               [tex]=P(-2.22<Z<2.22)\\\\=P (Z<2.22)-P(Z<-2.22)\\\\=0.98679-0.01321\\\\=0.97358\\\\\approx 0.97[/tex]

Thus, the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.

Answer:

3*(root3)

Step-by-step explanation:

square root of 75 = sq. root of ( 5 × 5 × 3 )= 5root3

now 5root3 - 2root3 = (5-2)root3 = 3root3

Answer:

Step-by-step explanation:

The interval from 0 to 4 is divided into 8 equal parts, so each has a width of 0.5 units. For the trapezoidal and Simpson's rules, the function is evaluated at each end of each interval, and those results are combined in the manner specified by the rule.

__

For the trapezoidal rule, the function values are taken as the "bases" of trapezoids, whose "height" is the interval width. The estimate of the integral is the sum of the areas of these trapezoids.

__

For the midpoint rule, the function is evaluated at the midpoint of each interval, and that value is multiplied by the interval width to form an estimate of the integral over the interval. In the spreadsheet, midpoints and their function values are listed separately from those used for the other rules. The midpoint area is the rectangle area described here.

__

For Simpson's rule, the function values at the ends of each interval are combined with weights of 1, 2, or 4 in a particular pattern. The sum of products is multiplied by 1/3 the interval width. In the spreadsheet, the weights are listed so the SUMPRODUCT function could be used to create the desired total.

We note the Simpson's rule estimate of the integral (-5.61) is very close, as the actual value rounds to -5.64.

___

A graph of the function and a computation of the integral is shown in the second attachment.

Answer:

the answer is 7.2

Step-by-step explanation:

Answer:

A)

The number of weights of an organ in adult males = 374.85

B)

The percentage of organs weighs between 275 grams and 375

P(275≤x≤375) = 0.6826 = 68%

C)

The percentage of organs weighs between 275 grams and 425

P(275≤x≤375) = 0.8185 = 82%

Step-by-step explanation:

A)

Step(i):-

Given mean of the normal distribution = 325 grams

Given standard deviation of the normal distribution = 50 grams

Given Z- score = 99.7% = 0.997

[tex]Z = \frac{x-mean}{S.D} = \frac{x-325}{50}[/tex]

[tex]0.997 = \frac{x-325}{50}[/tex]

Cross multiplication , we get

[tex]0.997 X 50= x-325[/tex]

x - 325 = 49.85

x = 325 + 49.85

x = 374.85

The number of weights of an organ in adult males = 374.85

Step(ii):-

B)

Let X₁ = 275 grams

[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{275-325}{50} = -1[/tex]

Let X₂ = 375 grams

[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{375-325}{50} = 1[/tex]

The probability of organs weighs between 275 grams and 375

P(275≤x≤375) = P(-1≤Z≤1)

                       = P(Z≤1)- P(Z≤-1)

                      =  0.5 + A(1) - ( 0.5 - A(-1))

                     = A(1) + A(-1)

                    = 2 A(1)

                    = 2 × 0.3413

                    = 0.6826

The percentage of organs weighs between 275 grams and 375

P(275≤x≤375) = 0.6826 = 68%

C)

Let X₁ = 275 grams

[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{275-325}{50} = -1[/tex]

Let X₂ = 425 grams

[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{425-325}{50} = 2[/tex]

The probability of organs weighs between 275 grams and 425

P(275≤x≤425) = P(-1≤Z≤2)

                       = P(Z≤2)- P(Z≤-1)

                      =  0.5 + A(2) - ( 0.5 - A(-1))

                     = A(2) + A(-1)

                    = A(2) + A(1)       (∵A(-1) =A(1)

                    = 0.4772 + 0.3413

                    = 0.8185

The percentage of organs weighs between 275 grams and 425

P(275≤x≤375) = 0.8185 = 82%

Answer:

In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.7 percent are within 3 standard deviations of the mean.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Also:

The normal distribution is symmetric, which means that 50% of the data is above the mean and 50% is below.

Then:

In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.7 percent are within 3 standard deviations of the mean.

In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.9 percent are within 3 standard deviations of the mean.

The normal distribution is a probability distribution that is important in many areas. It is, in fact, a family of distributions of the same form, each with different location and scale parameters: the mean and standard deviation respectively. The standard normal distribution is the normal distribution with mean equal to zero, and standard deviation equal to one. The shape of its probability density function is similar to that of a bell.

Learn more in https://brainly.com/question/12421652

Answer:

20-29: Make it 1 unit tall

30-39: Make it 5 units tall

Step-by-step explanation:

20-29: 22 (1 number)

30-39:  31, 32, 32, 32, 32 (5 numbers)

Answer:

The correct answers are (1) Option d (2) option a (3) option a

Step-by-step explanation:

Solution

(1) Option (d) The statement is false. A diagonalizable matrix must have n linearly independent eigenvectors: what it implies is that a matrix is diagnostic if it has linearity independent vectors.

(2) Option (a) The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors: what this implies is that a diagonalizable matrix  can have repeated eigenvalues.

(3) option (a) The statement is true. AP = PD implies that the columns of the product PD are eigenvalues that correspond to the eigenvectors of A : this implies that P is an invertible matrix whose column vectors are the linearity independent vectors of A.

Answer:

a) [tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]

And replacing we got:

[tex]\bar X \sim N(\mu=25, \frac{4}{\sqrt{30}}= 0.730) [/tex]

b) [tex] z =\frac{27-25}{\frac{4}{\sqrt{30}}}= 2.739[/tex]

And using the normal standard distribution table and the complement rule we got:

[tex] P(z>2.739) =1- P(z<2.739) = 1-0.997= 0.003[/tex]

Step-by-step explanation:

From the info given if we define the random variable X as "amount of saturated fat in a daily serving of a particular brand of breakfast cereal " we know that the distribution of X is given by:

[tex] X \sim N(\mu =25, \sigma =4)[/tex]

Part a

For this case the sample size would be n =30 and then the distribution for the sample mean would be given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]

And replacing we got:

[tex]\bar X \sim N(\mu=25, \frac{4}{\sqrt{30}}= 0.730) [/tex]

Part b

We want to find this probability:

[tex] P(\bar X >27)[/tex]

And we can use the z score formula given by:

[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And replacing we got:

[tex] z =\frac{27-25}{\frac{4}{\sqrt{30}}}= 2.739[/tex]

And using the normal standard distribution table and the complement rule we got:

[tex] P(z>2.739) =1- P(z<2.739) = 1-0.997= 0.003[/tex]

Answer:

The equation can be used to find m, the midpoint of the

two numbers is:

[tex]m^2-100 = -99[/tex]

Step-by-step explanation:

Two numbers are 10 units away in different directions from their midpoint, m, on a number line.

Then, we can define the two numbers as:

[tex]x_1=m+10\\\\x_2=m-10[/tex]

The product of the  numbers is -99. This can be written as:

[tex]x_1\cdot x_2=-99\\\\(m-10)(m+10)=-99\\\\m^2-10m+10m-100=-99\\\\m^2-100=-99\\\\m^2=-99+100=1\\\\m=\pm1[/tex]

Answer: Option  D

(D) m2 – 100 = –99

Step-by-step explanation:

Answer:

[tex]50\%, \: 40\%, \: 10\%[/tex]

Step-by-step explanation:

[tex]150:120:30[/tex]

[tex]5:4:1[/tex]

[tex]\frac{100}{5+4+1}[/tex]

[tex]=\frac{100}{10}[/tex]

[tex]=10[/tex]

[tex]5 \times 10:4\times 10:1\times 10[/tex]

[tex]50:40:10[/tex]

Answer:

Cupcakes: 50%

Cookies: 40%

Cakes: 10%

Step-by-step explanation:

150 + 120 + 30 = 300 (there are 300 baked goods)

150 out of 300 = 50%

120 out of 300 = 40%

30 out of 300 = 10%

Okay, I really want to eat this.

Hope it helps!

Answer:

The policy has an effect because the null hypothesis rejected since P-value < significance level.

Step-by-step explanation:

Since (P-value = 0.0108) < 0.1 significance level, we have sufficient evidence to show that the mean is not equal to 39.8. This means that the policy has an effect on the average number of the emails received per day.

The workings are clearly written in the file attached below. Please check.

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: number of emails a profession employee receives per day

This variable has an average of μ= 39.8 emails/day and the standard deviation is known to be δ= 16.2 emails/day

A company considers that the large amount of emails creates distraction, reducing the employees concentration and thus their efficiency, so they established a new priority list that all employees were to use before sending an e-mail. After one month they took a random sample of employees obtaining:

n= 38

X[bar]= 33.1 emails/day

If the company's new policy worked, then the company would expect the mean number of emails an employee receives per day to decrease, symbolically: μ < 39.8

The hypotheses are:

H₀: μ ≥ 39.8

H₁: μ < 39.8

α: 0.10

To analyze the population mean you need as condition that the variable of interest is at least normal.

There is no information about the population distribution, but the sample size is big enough for it to be valid to apply the Central Limit Theorem. This states that for variables of unknown distribution, if a sample large enough is taken (normally n≥30 is considered ok) you can approximate the distribution of the sample mean to normal:

X[bar]≈N(μ;σ²/n)

This allows you to use the standard normal as statistic for the test:

Z= (X[bar] - μ)/(σ/n) ≈ N(0;1)

[tex]Z_{H_0}= \frac{33.1-39.8}{\frac{16.2}{\sqrt{38} } }= -2.549= -2.55[/tex]

Using the critical value approach, this test is one tailed to the left, meaning that you will reject the null hypothesis to low values of Z.

The critical value is:

[tex]Z_{\alpha }= Z_{0.10}= -1.283[/tex]

The decision rule is:

If [tex]Z_{H_0}[/tex] ≤ -1.283, reject the null hypothesis.

If [tex]Z_{H_0}[/tex] > -1.283, do not reject the null hypothesis.

The calculated value is less than the critical value so the decision is to reject the null hypothesis.

At a 10% significance level, the null hypothesis was rejected. You can conclude that the new policy reduced the average number of emails a professional employee receives per day.

I hope this helps!

Answer:

125

Step-by-step explanation:

[tex]25=5^2[/tex]

[tex]36=6^2[/tex]

[tex]125=5^3[/tex]

[tex]300=...[/tex]

Answer:

a)x−2=10

b) 2x=24

Two equations have have the solution

x = 12

Question:

How many of these equations have the solution x=12 ?

x−2=10

2x=24

10−x=2

2x−1=25

Step-by-step explanation:

To determine which of the above equations have x= 12, we would solve for x in each of the equations.

a) x−2=10

Collecting like terms

x = 10+2

x = 12

This equation has x= 12 as a solution

b) 2x =24

Divide through by coefficient of x which is 2

2x/2 = 24/2

x = 12

This equation has x= 12 as a solution

c) 10−x=2

Collecting like terms

10-2 - x = 0

8 - x = 0

x = 8

d) 2x−1=25

Collecting like terms

2x = 25+1

2x = 26

Divide through by coefficient of x which is 2

2x/2 = 26/2

x = 13

Note: that (b) x2 = 24 from the question isn't clear enough. I used 2x = 24.

If x2 = 24 means x² = 24

Then x = √24 = √(4×6)

x = 2√6

Then the number of equations that have the solution x = 12 would be 1. That is (a) x−2=10 only

Answer:

1/2x + 12 >10

Step-by-step explanation:

Answer: 15 dogs

Step-by-step explanation:

75 / 5 = 15

Answer:

15 dogs

Step-by-step explanation:

Let the number of dogs be x

number of cats be y

5 times the number of cats = number of dogs

y = x*5

Since y = 75

75 = 5x

Bring 5 to the other side n divide

x= 75/5

= 15

Answer:

  B.  Left limits are the same; right limits are different.

Step-by-step explanation:

When we talk about "end behavior," we are generally concerned with the limiting behavior of the function for x-values of large magnitude. Decreasing exponential functions all have the same end behavior: they approach infinity on the left (for large negative values of x), and they approach a horizontal asymptote on the right (for large positive values of x).

If we are to write the end behavior in terms of specific limiting values, we would have to say that ...

  as x → -∞, f(x) → ∞

  as x → -∞, g(x) → ∞ . . . . . . the same end behavior as  f(x)

__

and ...

  as x → ∞, f(x) → -4

  as x → ∞, g(x) → (some constant between 0 and 5) . . . . . different from f(x)

__

So, in terms of these limiting values, the left-end behavior is the same; the right-end behavior is different for the two functions, matching choice B.

Answer:

c. all accounts fewer than 31 or more than 60 days past due.

Step-by-step explanation:

The Universal Set is the set of all past due accounts.

Event A = the event that the account is between 31 and 60 days past due.

Event B = the event that the account is that of a new customer.

Therefore, the complement of A will be the event of all the accounts fewer than 31 or more than 60 days past due.

The correct option is C.

Answer:

17.5

Step-by-step explanation:

Remember PEMDAS

step 1 : divide 7 by 2

7 ÷ 2 = 3.5

step 2 : rewrite the equation

19 + 3.5 - 5

step 3  : add 19 + 3.5

19 + 3.5 = 22.5

step 4 : subtract 22.5 - 5

22.5 - 5 = 17.5

Answer:

(C)90 – 10y = 5x

Step-by-step explanation:

Given:

x = number of times she hiked the 5-mile trail

y = number of times she hiked the 10-mile trail

Maria hikes a total of 90 miles

Therefore, total distance hiked can be represented by the equation:

5x+10y=90

Subtract 10y from both sides, we have:

5x=90-10y

This is option C.

Answer:

C

Step-by-step explanation:

Answer:

The range will decrease by 1

Step-by-step explanation:

Range: Largest no. - Smallest no.

The range with the original numbers is 7 -1 =6

The range when 1 is replaced by 6,the smallest no. becomes 2 which makes the range 7-2= 5

So 1st range - 2nd range =6 - 5 = 1

Answer:

[tex](a)-\dfrac{11\sqrt{5}}{25} \\(b) -\dfrac{2\sqrt{5}}{25} \\(c)\dfrac{11}{2}[/tex]

Step-by-step explanation:

[tex]\tan \alpha =\dfrac12, \pi < \alpha< \dfrac{3 \pi}{2}[/tex]

Therefore:

[tex]\alpha$ is in Quadrant III[/tex]

Opposite = -1

Adjacent =-2

Using Pythagoras Theorem

[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\=(-1)^2+(-2)^2=5\\Hypotenuse=\sqrt{5}[/tex]

Therefore:

[tex]\sin \alpha =-\dfrac{1}{\sqrt{5}}\\\cos \alpha =-\dfrac{2}{\sqrt{5}}[/tex]

Similarly

[tex]\cos \beta =\dfrac35, \dfrac{3 \pi}{2}<\beta<2\pi\\\beta $ is in Quadrant IV (x is negative, y is positive), therefore:\\Adjacent=$-3\\$Hypotenuse=5\\Opposite=4 (Using Pythagoras Theorem)[/tex]

[tex]\sin \beta =\dfrac{4}{5}\\\tan \beta =-\dfrac{4}{3}[/tex]

(a)

[tex]\cos(\alpha + \beta)=\cos\alpha\cos\beta-\sin \alpha\sin \beta\\[/tex]

[tex]=-\dfrac{2}{\sqrt{5}}\cdot \dfrac{3}{5}-(-\dfrac{1}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{2\sqrt{5}}{5}\cdot \dfrac{3}{5}+\dfrac{\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{2\sqrt{5}}{25}[/tex]

(b)

[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta[/tex]

[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta\\=-\dfrac{1}{\sqrt{5}}\cdot\dfrac35+(-\dfrac{2}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{\sqrt{5}}{5}\cdot\dfrac35-\dfrac{2\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{11\sqrt{5}}{25}[/tex]

(c)

[tex]\tan(\alpha + \beta)=\dfrac{\sin(\alpha + \beta)}{\sin(\alpha + \beta)}=-\dfrac{11\sqrt{5}}{25} \div -\dfrac{2\sqrt{5}}{25} =\dfrac{11}{2}[/tex]

Answer:

A = 1.02 P

Step-by-step explanation:

A = P + 0.02P

Formula in Factorized form

(Taking P common)

A = P(1+0.02) [The required factorized from]

Then,

A = 1.02 P

Answer:

  square; perimeter 20 units; area 25 square units.

Step-by-step explanation:

As the attachment shows, each side of the polygon is the hypotenuse of a 3-4-5 right triangle, so has length 5 units. The perimeter is the sum of those lengths, 4×5 = 20; the area is the product of the lengths of adjacent sides, 5×5 = 25.

The figure is a square of side length 5 units.

The perimeter is 20 units; the area is 25 square units.

Answer:

2.88

Step-by-step explanation:

Data provided in the question

[tex]\sigma[/tex] = Population standard deviation = 7 miles per hour

Random sample = n = 32 vehicles

Sample mean = [tex]\bar X[/tex] = 64 miles per hour

98% confidence level

Now based on the above information, the alpha is

= 1 - confidence level

= 1 - 0.98

= 0.02

For [tex]\alpha_1_2[/tex] = 0.01

[tex]Z \alpha_1_2[/tex] = 2.326

Now the margin of error is

[tex]= Z \alpha_1_2 \times \frac{\sigma}{\sqrt{n}}[/tex]

[tex]= 2.326 \times \frac{7}{\sqrt{32}}[/tex]

= 2.88

hence, the margin of error is 2.88

Answer:

2.879 (rounded 3 decimal places)

Step-by-step explanation:

Answer:

(A)[tex]\angle A =\angle A.[/tex]

Step-by-step explanation:

[tex]\triangle AED \sim \triangle ACB$ by SAS and:\\\dfrac{AE}{AD} =\dfrac{AC}{AB}[/tex]

By the SAS Similarity Theorem, if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Therefore, for the two triangle to be similar by SAS, [tex]\angle A \cong \angle A.[/tex]

Answer:

A

Step-by-step explanation:

edg

Answer:

its 4x

Step-by-step explanation:

Answer:

4x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello,

by definition the absolute value is always positive

so |4x-9| >= 0

so the equation |4x-9| > -12 is always true

so all real numbers are solution of this equation

hope this helps