inverse of f(x)=e^(3x-1)

Answer:

55.41 feet

Step-by-step explanation:

Let the width be x.

ATQ, (x+50)*x=300, x=5*srt(37)-25=5.41. Length is 55.41 feet

Answer:

[tex]v = at + 16 {t}^{2} \\ v - 16 {t}^{2} = at \\ \frac{v - 16 {t}^{2} }{t} = a \\ (27 - 16 \times {4}^{2}) \div 4 = a\\ \frac{27 - 256}{4} = a\\ \frac{ - 229}{4} = - 57.25 \\ thank \: you[/tex]

Answer:

m=3*sqrt(2) and n=3

Step-by-step explanation:

tan(45)=3/n

1=3/n, n=3. As it's a right angled triangle, 3^2+3^2=m^2, m=3*sqrt(2)

Answer:

Outliers have great effect on the mean and standard deviation of the data set

Step-by-step explanation:

Mean =(43+37+50+51+58+52+45+45+58+130)/10

Mean= 579/10

Mean = 57.9

Arranging in ascending order

= 37,43,45,45,50,51,52,58,58,130

Median= (50+51)/2

Median= 101/2

Median= 50.5

IQR= (130-37)/2

IQR= 93/2

IQR= 46.5

Standard deviation

=√(((37-57.9)²+(43-57.9)²+(45-57.9)²+(45-57.9)²+(50-57.9)²+(51-57.9)²+(52-57.9)²+(58-57.9)²+(58-57.9)²+(130-57.9)²)/10)

Standard deviation= 25.1

1.5*(46.5)= 69.75

The number more than 69.75 is 130 and it's the outlier

Without outlier

Mean= (43+37+50+51+58+52+45+45+58)/9

Mean = 449/9

Mean = 49.88

Arranging in ascending order

= 37,43,45,45,50,51,52,58,58

Median= 50

IQR= (58-37)/2

IQR=21/2

IQR=10.5

Standard deviation

Answer:

Mean: 169.4

Median: 171

Mode: 181

Step-by-step explanation:

I first sorted the numbers by value, least to greatest.

145 147 153 153 167 170 170 172 181 181 181 182 185 185

We can see that 181 occurs the most, 3 times, so it's the mode.

The median of this set will be the middle number(s).

When we take away 6 numbers from both sides we are left with 170 and 172, and the mean of these two numbers is 171. So the median is 171.

We can add all the numbers and divide by 14 to get the mean.

[tex]147+153+170+172+185+181+182+185+181+170+181+167+153+145=2372\\\\2372\div14\approx169.4[/tex]

Hope this helped!

The final amount is $7,615.27

A = P(1 + r/n)^t

Where,

A = Final amount

P = principal = $7, 200

r = interest rate = 2.5% = 0.025

n = number of periods = 4

t = time = 9 years

A = P(1 + r/n)^t

= 7,200(1 + 0.025/4)^9

= 7,200(1 + 0.00625)^9

= 7,200(1.00625)^9

= 7,200(1.0576769512798)

= 7,615.2740492152

Approximately,

A = $7,615.27

https://brainly.com/question/14003110

Answer:

[tex]f(t)=6(1.12^t)[/tex]

Step-by-step explanation:

every week the plant grows by 12%, so the ratio is 1.12. the original height of the plant is 6. f(x)=a(b^x) such that a=6, b=1.12, and x=t

Answer:

6 hours

Step-by-step explanation:

A: y=125+7x

B: y=110+10x

for A to be a better deal than B, 125+7x<110+10x has to be true

Answer:

B 5

Step-by-step explanation:

Company A

total cost = 125+7h  where h is the number of hours

Company B

total cost = 110 + 10h  where h is the number of hours

125 + 7h < 110 + 10h

Subtract 7 h from each side

125 + 7h-7h<110+10h-7h

125 < 110+3h

Subtract 110 from each side

125-110< 110+3h

15 <3h

Divide by 3

15/3 <3h/3

5 <h

More than 5 hours

Answer: S₁₉ = 855

Step-by-step explanation:

T₄ = a + ( n - 1 )d  = 5 , from the statement above , but n = 4

       a + 3d  = 5 -------------------------1

S₆ = ⁿ/₂[(2a + ( n - 1 )d]  =  10, where n = 6

    = ⁶/₂( 2a + 5d )         = 10

    = 3( 2a + 5d ) = 10

    = 6a + 15d      = 10 -----------------2

Now solve the two equation together simultaneously to get the values of a and d

   a + 3d     = 5

   6a + 15d = 10

from 1,

a = 5 - 3d -------------------------------3

Now put (3) in equation 2 and open the brackets

6( 5 - 3d )  + 15d = 10

30 - 18d + 15d      = 10

30 - 3d                 = 10

            3d            = 30 - 10

             3d           = 20

                         d = ²⁰/₃.

Now substitute for d to get a in equation 3

           a = 5 - 3( ²⁰/₃)

           a = 5 - 3 ₓ ²⁰/₃

              = 5 - 20

          a  = -15.

Now to find the sum of the first 19 terms,

we use the formula

S₁₉ = ⁿ/₂( 2a + ( n - 1 )d )

     = ¹⁹/₂( 2 x -15 + 18 x ²⁰/₃ )

     = ¹⁹/₂( -30 + 6 x 20 )

     = ¹⁹/₂( -30 + 120 )

     = ¹⁹/₂( 90 )

     = ¹⁹/₂ x 90

     = 19 x 45

     = 855

Therefore,

S₁₉ = 855

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{0.001}[/tex]

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{\dfrac{1}{1000}}[/tex]

[tex]\\ \sf\longmapsto 10x=1000[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{1000}{10}[/tex]

[tex]\\ \sf\longmapsto x=100[/tex]

Answer:

1) The dependent variable is : time to complete the maze

2) The analysis used should be : One -way within-subjects ANOVA ( B )

3) Null hypothesis is ; There will be no difference between any group means

4) Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3

5) degree of freedom for the denominator = 11

6) critical F value = 3.49

Step-by-step explanation:

The dependent variable is the time to complete the maze this is because the time depends on the effects of the stimulant drugs on the rats in the maze .

The analysis used should be : One -way within-subjects ANOVA ( B )

Null hypothesis is ; There will be no difference between any group means

Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3

degree of freedom for the denominator = N - k = 16 - 4 = 12. the closest answer from the options is 11

The critical value is 3.49 ,because at degree of freedom = 12 , ∝ = 0.05, and Dfn = 3, from the F -  table the critical value would be 3.49

Answer:

Kindly check explanation

Step-by-step explanation: Jullian's claim that the distance she drives to work is exactly 11.7miles is incorrect because, in other to record or get the exact result of a certain calculation such as Jullian's Distance, the value of the distance obtained will not be approximated or rounded. In this scenario, Distance was to the nearest tenth of a mile, thereby altering the true outcome of the calculation.

The word exact means that what is stated is very precise and does not fall below or above in any respect. However, a number whose accuracy is to the nearest tenth of a mile, violates this assertion.

Answer:

The center of the circle:

(2, -1)

The radius of the circle:

r = 4

Step-by-step explanation:

The first step is to complete the square on both x and y:

x^2 + y^2 -4x + 2y - 11 = 0

x^2 -4x +y^2 +2y = 11

We determine c1 to complete the square on x:

c1 = (b/2)^2

c1 = (-4/2)^2 = 4

We then determine c2 to complete the square on y:

c2 = (2/2)^2 = 1

The equation of the circle is then re-written as:

x^2 -4x + 4 +y^2 +2y + 1 = 11 +4 +1

We then factorize the expressions in x and y separately:

(x-2)^2 + (y +1)^2 = 16

The center of the circle is thus:

(2, -1)

The radius is the square root of 16:

r = 4

Answer:

center :  (2, -1)

radius :  r = 4

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

hope this helps :)))))

Answer:

[tex]Mean = 5[/tex]

[tex]S_x = 4.123[/tex]

Step-by-step explanation:

Given

Number of Lions, n: 6

Ages: 13, 2, 1, 5, 2, 7

Required

Determine the:

1. Mean

2. Standard Deviation

Mean is calculated as;

[tex]Mean = \frac{\sum x}{n}[/tex]

[tex]Mean = \frac{13+2+1+5+2+7}{6}[/tex]

[tex]Mean = \frac{30}{6}[/tex]

[tex]Mean = 5[/tex]

Standard Deviation is calculated as follows

[tex]S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{N}}[/tex]

Where Mx represent mean

Substitute values for x, Mean and Land

[tex]S_x = \sqrt{\frac{(13 - 5)^2+(2 - 5)^2+(1 - 5)^2+(5 - 5)^2+(2 - 5)^2+(7 - 5)^2}{6}}[/tex]

[tex]S_x = \sqrt{\frac{(8)^2+(- 3)^2+(-4)^2+(0)^2+(-3)^2+(2)^2}{6}}[/tex]

[tex]S_x = \sqrt\frac{64+9+16+0+9+4}{6}}[/tex]

[tex]S_x = \sqrt\frac{102}{6}}[/tex]

[tex]S_x = \sqrt{17}[/tex]

[tex]S_x = 4.123[/tex]

The mean and standard deviation is 5 and 4.123 respectively

We want to find the mean or average and the standard deviation of the given set.

The average age is 5 years old and the standard deviation is 4.52 years old.

We know that for a general set of N elements {x₁, x₂, ..., xₙ} the average or mean is given by:

[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]

And the standard deviation is given by:

[tex]S = \sqrt{\frac{(x_1 - M)^2 + ... + (x_n - M)^2}{N - 1}[/tex]

The given set is:

{13, 2, 1, 5, 2, 7}

Now we just need to use the two given formulas for our set.

The mean is:

[tex]M = \frac{13 + 2 + 1+ 5 + 2 +7}{6} = 5[/tex]

And the standard deviation is:

[tex]S = \sqrt{\frac{(13 - 5)^2 + (2 - 5)^2 + (1 - 5)^2 + (5 - 5)^2 + (2 - 5)^2 + (7 - 5)^2}{6 - 1} } = 4.52[/tex]

So the average age is 5 years old and the standard deviation is 4.52 years old.

If you want to learn more you can read:

https://brainly.com/question/12402189

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent Atsu's current age. Then Agyappng is 3x. Three years ago the relationship was ...

  (3x -3) = 4(x -3)

  9 = x . . . . . . . . . . . . add 12-3x

Atsu is 9; Agyappng is 27.

Step-by-step explanation:

sin∠M = cos∠N

sin∠M = cos(30°)

sin∠M = √3 / 2

m∠M = 60° or 120°

If ∠M is acute, m∠M = 60°.

Answer: The measure of ∠M is 60°

Step-by-step explanation:

The complement of 30° is 60°

sin∠M =cos∠N

sin∠60°=cos∠30°

the measure of ∠M is 60°

Answer:

i thank its 4000

Step-by-step explanation:

please mark this answer as brainlist

Answer:

18

Step-by-step explanation:

Okay first we know that for every one baboon there is 2 orang-utans (6 / 3 = 2)

So, I like to play the guess and check:

Lets just use the numbers 12 orang-utans and 6 baboons. We know that those two don't equal 27, so thats not it.

Now we can have 18 orang-utans and 9 baboons. 18 + 9 = 27, which means there are 18 orang-utans.

Hope this helps, and have a good day.

Answer: There are no real number roots (the two roots are complex or imaginary)

The discriminant D = b^2 - 4ac tells us the nature of the roots for any quadratic in the form ax^2+bx+c = 0

There are three cases

Answer:

Step-by-step explanation:

When naming lines, you can use the label of the line, in this case, m, and can also name the points in either direction, since the line goes on forever in both directions (it's different with rays). The leaves only line B as an answer.

The vertex of XYZ would be Y, since the vertex is always the middle number.

Answer:

Let the chord- part of VC inside smaller circle be a, and same of CU be b.

According to intersecting secants theorem we have:

and

From the second equation we get:

From the first equation we get:

substitute this into the second equation:

Proved

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  95% interval for [tex]p_1 - p_2[/tex] is  [tex]-0.0171 ,0.0411[/tex]

Option A is correct

Step-by-step explanation:

From the question we are told that

   The sample size of male  is [tex]n_1 = 1211[/tex]

    The number of males that  said they have at least one tattoo is [tex]r = 182[/tex]

   The sample size of female is [tex]n_2 = 1041[/tex]

     The number of females that  said they have at least one tattoo is [tex]k = 144[/tex]

Generally the sample proportion of male is  

            [tex]\r p_1 = \frac{r}{ n_1}[/tex]

substituting values

            [tex]\r p_1 = \frac{ 182}{1211}[/tex]

             [tex]\r p_1 = 0.1503[/tex]

Generally the sample proportion of female is  

            [tex]\r p_2 = \frac{k}{ n_2}[/tex]

substituting values

           [tex]\r p_2 = \frac{ 144}{1041}[/tex]

           [tex]\r p_2 = 0.1383[/tex]

Given that the confidence level is  95% then the level of  significance is mathematically represented as

          [tex]\alpha =100-95[/tex]

          [tex]\alpha =5\%[/tex]

          [tex]\alpha =0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is

          [tex]Z_\frac{\alpha }{2} = 1.96[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }[/tex]

substituting values

       [tex]E = 1.96 * \sqrt{\frac{ 0.1503 (1- 0.1503)}{1211} + \frac{0.1383 (1- 0.1383)}{1041} }[/tex]

       [tex]E = 0.0291[/tex]

The 95% confidence interval is mathematically represented as

        [tex](\r p_1 - \r p_2 ) - E < p_1-p_2 < (\r p_1 - \r p_2 ) + E[/tex]

substituting values

         [tex](0.1503- 0.1383 ) - 0.0291 < p_1-p_2 < (0.1503- 0.1383 ) + 0.0291[/tex]

          [tex]-0.0171 < p_1-p_2 < 0.0411[/tex]

So the interpretation is that there is 95% confidence that the difference of the proportion is in the interval .So conclude that there is insufficient evidence of a significant difference in the proportion of male and female that have at least one tattoo

This because the difference in proportion is less than [tex]\alpha[/tex]

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

Explanation:

Angle UOT is vertical to the angle x. This angle combines with 4x and 40 to get a straight angle of 180 degrees

(angle POU) + (angle UOT) + (angle TOS) = 180

4x + x + 40 = 180

5x + 40 = 180

5x = 180-40

5x = 140

x = 140/5

x = 28

Side note: if x = 28, then 4x = 4*28 = 112.

We see that 112+28+40 = 180, which is the sum of the three angles mentioned earlier. Since we got 180, this confirms the answer.

Answer:

2(w+3)

Step-by-step explanation:

2(w+3) or 2w+6

Answer:

Alpha (α) is used to measure the error for decisions concerning true null hypotheses, while beta (ß) is used to measure error for decisions concerning false null hypotheses.

Step-by-step explanation:

Suppose we have events X and Y.

1. If it is said that X equals Y, when X is actually not equal to Y, α is used in this case, the null hypotheses.

2. If X is said to not be equal to Y, when X is actually equal to Y, β is used in this case, the false null hypotheses.

Answer:

10x +35

Step-by-step explanation:

5(2x+7) = 5*2x + 5*7 = 10x+35

Answer:

10, 35.

Step-by-step explanation:

5(2x + 7)

= 5^2x + 5*7

= 10x + 35

Answer:

27

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

-9 × -3

= 27

Note: When you multiply two integers with same sign, then their product is positive.

9514 1404 393

Answer:

  multiply (×)

Step-by-step explanation:

5 ×4 - 3 +2 ÷1 = 19

Emma would place the multiply (×) operation first.