Write the equation in equivalent logarithmic form.
1
3=81​

Answer: B. 1.414

Step-by-step explanation:

let x be the random variable denotes the number of die.

Numbers on 5-faced die = 1,2,3,4,5

Probability of getting any number = [tex]\dfrac{1}{5}[/tex]

Mean = [tex]\bar {x}=\sum p_ix_i[/tex]

[tex]\\\\\Rightarrow\bar{x}=\dfrac{1}{5}(1)+\dfrac{1}{5}(2)+\dfrac{1}{5}(3)+\dfrac{1}{5}(4)+\dfrac{1}{5}(5)\\\\=\dfrac{1}{5}(1+2+3+4+5)\\\\=\dfrac{1}{5}(15)=3[/tex]

Standard deviation: [tex]\sigma=\sum \sqrt{\dfrac{(x_i-\bar{x})^2}{N}}[/tex]

[tex]=\sqrt{\dfrac{(1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2}{5}}\\\\=\sqrt{\dfrac{4+1+0+1+4}{5}}\\\\=\sqrt{\dfrac{10}{5}}\\\\=\sqrt{2}\approx1.414[/tex]

Hence, the standard deviation of the random variable x is 1.414.

Thus, the correct option is B.

Answer:

-111 and -110

Step-by-step explanation:

If x is the lesser integer, and x+1 is the next integer, then:

x + x+1 = -221

2x = -222

x = -111

x+1 = -110

The two integers are -111 and -110.

Answer:

-111,-110

Step-by-step explanation:

Let n represent the first integer. Then n+1 will represent the next consecutive integer.

Translate into an equation.

We can restate the given information in one sentence as "The sum of the integers is −221."

As an equation this sentence is represented as:

n+n+1=−221

Solve the equation.

n+n+1=-221

2n+1=−221

2n=−222

n=−111

So, n=−111 is the first integer and n+1=−110 is the second integer.

Answer:

a

    [tex]0.5043 < p <0.9075[/tex]

b

   [tex]n = 24[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  34

    The  number of damaged helmets is  x  =  24

Now the proportion of damaged helmets is mathematically represented as

      [tex]\r p = \frac{k}{n }[/tex]

substituting values

     [tex]\r p = \frac{24}{34 }[/tex]

    [tex]\r p = 0.7059[/tex]

Given that the confidence level is 99% the level of significance can be evaluated as

     [tex]\alpha = 100 - 99[/tex]

     [tex]\alpha = 1[/tex]%

    [tex]\alpha = 0.01[/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} } = 2.58[/tex]

The reason we are obtaining critical values of   [tex]\frac{\alpha }{2}[/tex] instead of   [tex]\alpha[/tex] is because  

[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval (  [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex]is just the area of one tail which what we required to calculate the margin of error

   The margin of error is mathematically represented as

     [tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p ( 1 - \r p)}{n} }[/tex]

substituting values

      [tex]MOE = 2.58 * \sqrt{\frac{ 0.7059 ( 1 - 0.7059)}{34} }[/tex]

     [tex]MOE =0.2016[/tex]

The 99% confidence interval for p is mathematically represented as

      [tex]p-MOE < p < p + MOE[/tex]

substituting values

       [tex]0.7059 - 0.2016 < p <0.7059 + 0.2016[/tex]

      [tex]0.5043 < p <0.9075[/tex]

The  sample size required for the width of a 99% Cl to beat most 0.10, irrespective of p ? is mathematically represented as  

     [tex]n \ge \frac{ Z_{\frac{\alpha }{2} } * \sqrt{\r p (1- \r p )} }{\frac{\sigma }{2} }[/tex]

Here  [tex]\sigma = 0.10[/tex]  telling  us that the deviation from the sample proportion is  set to 0.10 irrespective of the value of  [tex]\r p[/tex]

so the  sample size for this condition is

    [tex]n \ge \frac{ 2.58 * \sqrt{ 0.7059 (1- 0.7059)} }{\frac{0.10 }{2} }[/tex]

    [tex]n \ge 23.51[/tex]

=>   [tex]n = 24[/tex]

Answer:

Step-by-step explanation:

1). Equation of a line which has slope 'm' and y-intercept as 'b' is,

y = mx + b

If slope 'm' = 1 and y-intercept 'b' = -3

Equation of the line will be,

y = x - 3

x - y = 3

2). Equation of a line having slope 'm' and passing through a point (x', y') is,

y - y' = m(x - x')

If the slope 'm' = 1 and point is (-1, 2),

The the equation of the line will be,

y - 2 = 1(x + 1)

y = x + 1 + 2

y = x + 3

x - y = -3

3). Equation of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,

[tex]y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)[/tex]

If this line passes through (-2, 3) and (-3, 4),

[tex]y-3=\frac{(4-3)}{(-3+2)}(x+2)[/tex]

y - 3 = -1(x + 2)

y = -x - 2 + 3

y = -x + 1

x + y = 1

Answer:

The researcher cannot conclude that salary and gender are dependent.

Step-by-step explanation:

A dependent variable is a variable, for example "Salary" that depends on an independent variable, e.g. "Gender."  Salary is the dependent variable while gender is the independent variable.  This means that the value of salary changes in relation to the gender and not vice versa.  Two variables become dependent if they change based on another independent variable that is operating on them.  In this research, the researcher is not trying to measure gender but the relationship between salary and gender.  To achieve her purpose, she shows that salary depends on gender and not that gender depends on salary.

Answer:

x = -8 and x= 7

Step-by-step explanation:

recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.

Hence the asymptototes will occur in x-locations where the denominator , i.e

(x+8)(x-7) = 0

solving this, we get

(x+8) = 0 ----> x = -8

or

(x-7) = 0 ------> x = 7

hence the asymptotes occur x = -8 and x= 7

Answer:

x = -8 and x = 7.

Step-by-step explanation:

The vertical asymptotes are lines that the function will never touch.

Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.

[tex]\frac{x - 6}{(x + 8)(x - 7)}[/tex], so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.

x + 8 = 0

x = -8

x - 7 = 0

x = 7

The vertical asymptotes are at x = -8 and x = 7.

Hope this helps!

Answer:

1/5 are towboats

Step-by-step explanation:

In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together

30k + 10k + 10k= 50k

In total there are 50,000 flag vessels

Of those 50,000, 10,000 of them are tow boats

10,000/50,000 can be simplified to 1/5

1/5 are towboats

Answer:

1/5

Step-by-step explanation:

Well to find the fraction we first need to know the total amount of Flag Vessels.

30,000 + 10,000 + 10,000 = 50,000

If there are 10,000 towboats we can make the following fraction.

10,000/50,000

Simplified

1/5

Thus,

the answer is 1/5.

Hope this helps :)

To clear the fractions we multiply both sides by the least common multiple of all the denominators.

1/2  x + 2/3 = 4

Denominators 2 and 3, so multiply both sides by [Answer]: 6

3/4 x + 1 = 5/6

Denoms 4 and 6, LCM=12  Answer: 12

6/7 x - 2/3 = 5/21

LCM(7,3,21)=21 Answer: 21

3/5 + x/2 = 9

LCM(5,2)  Answer: 10

25/4 = 6 + 1/2 x

LCM(4,2)  Answer: 4

Answer:

p=2m

p+m=51

take the 2m and plug that in for p -> 2m+m=51

3m=51

m=51/3

m=17 then plu the value of m into Paula's points

p=2(17)

p=34

Answer:

10 miles

Step-by-step explanation:

1 inch = 4 miles

3 - 0.5  = 2.5

2.5 * 4 = 10 miles

Answer:

14v - 5

Step-by-step explanation:

The product of 14 and v is 14v. 5 less than that is 14v - 5.

Answer:

7v = 119

Step-by-step explanation:

Answer:

A 23 of people who prefer plan 1 are from the 35-45 age group and 42% of people from the 46-55 age group prefer plan 2.

Step-by-step explanation:

add everyone who prefers plan 1 = 60

age 36-45 / total of plan 1 = 14/60 = .23 or 23%

add everyone in age group 46-55 = 50

in age group 46-55 and prefers plan 2 = 21 / 50 = 0.42 or 42%

Answer:

[tex]\boxed{\mathrm{Option \ B}}[/tex]

Step-by-step explanation:

Total people in 36 - 45 age group = 50

Who prefer plan I = 14

%age of people preferring plan 1 among 36-45 age group:

=> [tex]\frac{14}{50} * 100[/tex]

=> 0.28 * 100%

=> 28%

Now,

Total People in 46-55 age group = 50

Those who prefer plan II = 21

%age of people preferring plan II among 46-55 age group:

=> [tex]\frac{21}{50} * 100[/tex]

=> 0.42 * 100%

=> 42%

Answer:

The calculated value Z = 2 > 1.96 at 0.05 level of significance

Alternative Hypothesis is accepted

The proportion of defective tablets manufactured in this factory is less than 6%."

Step-by-step explanation:

Step(i):-

Given Population proportion P = 0.06

Sample size 'n' = 500

A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective.

Sample proportion

                                  [tex]p^{-} = \frac{x}{n} = \frac{20}{500} =0.04[/tex]

Null hypothesis :H₀: P = 0.06

Alternative Hypothesis :H₁:P<0.06

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step(ii):-

       Test statistic

                          [tex]Z = \frac{p^{-} -P}{\sqrt{\frac{P Q}{n} } }[/tex]

                         [tex]Z = \frac{0.04 -0.06}{\sqrt{\frac{0.06 X 0.94}{500} } }[/tex]

                        Z =  - 2

                    |Z|= |-2| = 2

Step(iii):-

The calculated value Z = 2 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

Alternative Hypothesis is accepted

The proportion of defective tablets manufactured in this factory is less than 6%."

Answer:

[tex]\large \boxed{\sf \ \ x \geq -9 \ \ }[/tex]

Step-by-step explanation:

Hello, please find below.

[tex]6\leq x+15\\\\\text{*** subtract 15 from both sides ***}\\\\6-15=-9\leq x \\\\x \geq -9[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A

Step-by-step explanation:

Answer:

[tex]\approx[/tex] 17.5% per annum

Step-by-step explanation:

Given:

Money invested = $20,000 at the age of 20 years.

Money expected to be $500,000 at the age of 40.

Time = 40 - 20 = 20 years

Interest is compounded annually.

To find:

Rate of growth = ?

Solution:

First of all, let us have a look at the formula for compound interest.

[tex]A = P \times (1+\frac{R}{100})^T[/tex]

Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.

Here, We are given:

P = $20,000

A = $500,000

T = 20 years

R = ?

Putting all the values in the formula:

[tex]500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%[/tex]

So, the correct answer is [tex]\approx[/tex] 17.5% per annum and compounding annually.

Answer:

16.1%

Step-by-step explanation:

(the other person is wrong, trust me)

Answer:

The correct answer will be "56".

Step-by-step explanation:

Use a combination of 8 things taken 3 at a time :

⇒  [tex]8_{C_{3}}[/tex]

⇒  [tex]\frac{8!}{(3!(8 - 3)!)}[/tex]

⇒  [tex]\frac{8!}{(3!5!)}[/tex]

⇒  [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}[/tex]

⇒  [tex]8\times 7[/tex]

⇒  [tex]56[/tex]

Using the principle of combination, the number of different random samples of size 3 that can be selected is 56.

Using the principle of combination :

Hence, we have ;

8C3 = [8! ÷ (8 - 3)! 3!]

8C3 = [8! ÷ 5!3!]

8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1)

8C3 = 8 × 7

8C3 = 56

Hence, there are 56 different possible samples.

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Answer:

Number of shares = 32 shares

Accountant total expenses= $254000

Step by step explanation:

The accountant salary is $262000

He spends $99000 on mortage

Spends $54000 on foods

Spends $32000 on clothing

Spends $41000 on household

Spends $28000 on others

Total expenses= 99000+54000+32000+41000+28000

Total expenses =$254000

Remaining money = 262000-254000

Remaining money= $8000

If shares = $250 for one

To know the amount he buys with the remaining money

We divide remaining money by shares cost

= $8000/$250

= 32 shares

<-------------------------------------------------->

   8      9     10     11     12     13     14  (number of hours spent)

                dot plot

Answer:

(A) Draw a number line from 8 to 14. Show the frequency of each number. Title the dot plot.

Step-by-step explanation:

false, an independent event is an event that isn't affected

The statement given is false

Two events are dependent, when the outcome of the first event influences the outcome of the second event.

Given that, Picking the first second and third place winners at a track meet is an independent even,

This statement is not correct.

The event is a dependant variable, the 1st person is picked based on the 1st mark on the track, so is the second and the 3rd. their position influence the outcome of the other.

the position of the 1st, 2nd or 3rd is influenced by time and speed, so the positions will be picked based on the participant scores /effect of time or speed of the 1st person to reach the track meet.

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Answer:

0.6921 (69.21%)

Step-by-step explanation:

The area of the shaded region between the two z-scores refer to the probability between the two z-scores value( The total area under a standard normal distribution curve is 1)

So the area we want to determine in this case is as follows;

P(-1.24<z<0.84) = P(z<0.84) - P(z<-1.24)

What we use to calculate this finally is the standard normal distribution table

We use this to get these values so we can calculate the probability.

Using the standard normal distribution table;

P(-1.24<z<0.84) = 0.69206 which is approximately 0.6921

Answer:

[tex]\boxed{D = 6.4 units}[/tex]

Step-by-step explanation:

She stops by (0,0)

She further needs to travel to (5,-4)

Let's calculate the distance using the Distance Formula:

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

D = [tex]\sqrt{(5-0)^2+(-4-0)^2}[/tex]

D = [tex]\sqrt{(5)^2+(-4)^2}[/tex]

D = [tex]\sqrt{25+16}[/tex]

D = [tex]\sqrt{41}[/tex]

D = 6.4 units

She needs to travel 6.4 units more.

Answer:

2sqrt41

Step-by-step explanation:

Origin=(0,0)

Brenda wants to go from (-4,5) to (0,0) and then to (5,-4). So we need to calculate the distance from (-4,5) to (0,0), and the distance of (0,0) to (5,-4).

The distance formula is sqrt (x2-xs1)^2+(y2-y1`)^2.

So: sqrt (5-0)^2+(-4-0)^2

sqrt (5^2+-4^2)

sqrt 25+16

sqrt 41

Now we need to figure out the distance from (0,0) to (5,-4)

sqrt(0-5)^2+(0-(-4))^2

sqrt(-5^2+4^2)

sqrt 25+16

sqrt 41

sqrt 41+sqrt 41

2sqrt41

Answer:

The standard deviation of the sample mean is  [tex]\sigma _ {\= x } = 2.711[/tex]

Step-by-step explanation:

From the question we are told that

   The mean is  [tex]\= x = 60[/tex]

    The standard deviation is  [tex]\sigma = 21[/tex]

     The sample size is [tex]n = 60[/tex]

Generally the standard deviation of the sample mean is mathematically represented as  

               [tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]

               [tex]\sigma _ {\= x } = 2.711[/tex]

Answer:

son is 12

dad is 36

Step-by-step explanation:

Say the son is x years old.

Then the father is 3x. Also 3x+x must be 48.

So 4x = 48 => x= 48/4 = 12

Let x be how old the son is. We know that the dad is 3 times older and their sum is 48. Creating an equation to represent this situation gives us:

[tex]x+3x=48[/tex]

[tex]4x=48[/tex]

Divide both sides by 4

[tex]x=12[/tex]

The son is 12 years old, but we want to find the age of the dad. Since we know the dad is 3 times older, multiply 12 with 3

[tex]12 \times 3 = 36[/tex]

The dad is 36 years old. Let me know if you need any clarifications, thanks!

Answer: it should be b, 1. :)

Step-by-step explanation:

Answer:

B or 24 mm2

Step-by-step explanation:

Just did the test :)

The area of the shaded region is 24mm^2

Step 1: Find area of the larger triangle

Here base b = 5 mm

Height h = 12 mm

Area of the larger triangle = (5*12)/2 = 60/2 = 30mm^2

Step 2: Find area of the smaller triangle

Here base b = 3 mm

Height h = 4 mm

Area of the smaller triangle = (3*4)/2 = 12/2 = 6 mm^2

Step 3: Find area of the required shaded region

Area of the required shaded region = Area of larger triangle - Area of smaller triangle

= 30 mm^2 - 6 mm^2

=24 mm^2

Hence, the area of the shaded region is 24mm^2

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Answer:

[tex]Probability = \frac{1}{8}[/tex]

Step-by-step explanation:

Given

Box of Cards -- 1 -- 2 -- 3 -- 4 -- 5 -- Total

Black --------------1 ---1 ----1 ----1 ---1 ----5

Red ---------------- 1 ---1 ----1 ----0--- 0--- 3

Total --------------- 2 ---2 --2-----1 -----1 ---8

Required

Determine the probability of a card being black and being card 1

To solve this, we the the number of card 1 that is black

This is shown below

Box of Cards -- 1

Black --------------1

This implies that, 1 card is black and also card 1

Represent this with [tex]n(Black\ and\ 1)[/tex]

[tex]n(Black\ and\ 1) = 1[/tex]

Next, is to get the total number of cards

From the given parameters;

[tex]Total = 8[/tex]

The probability is calculated as follows

[tex]Probability = \frac{n(Black\ and\ 1)}{Total}[/tex]

[tex]Probability = \frac{1}{8}[/tex]

Answer: The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.

Step-by-step explanation:

Given, Farmer has 240 apples and 150 pears.

The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out = GCF(240,150)

Prime factorization of 240 and 150 :

[tex]240=2\times2\times2\times2\times3\times5\\150=2\times3\times5\times5[/tex]

Greatest common factor of 240 and 150 = [tex]2\times3\times5=30[/tex]

Hence, the largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.

Step-by-step explanation:

Vertex for your equation is (-1, -8)