Solve by using logarithms, not the same base. I have absolutely no clue how to solve so any help would be amazing, thanks

Answer: Franklin could end at 4 different points.

Step-by-step explanation:

Given: Franklin the fly starts at the point (0,0) in the coordinate plane.

At each point, Franklin takes a step to the right, left, up, or down.

i.e. there are 4 choices of directions [A coordinate plan has 4 quadrants]

If he moves 10 steps, then the number of different points Franklin could end up at =  choices of directions

= 4

Hence, Franklin could end at 4 different points.

Answer:

1/6

Step-by-step explanation:

The probability of even number is 1/2. The probability of number greater than 4 is 1/3, because only 5 and 6 are greater than 4.

Multiply these two values

1/2*1/3= 1/6

Answer:

y > -x/6 + 1

Step-by-step explanation:

Hope this can help

The graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex]  is option "A" .

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

According to the question

The inequality : [tex]y > -(\frac{1}{6} )x+1.[/tex]  

now first we take out points to plot graph for that we will assume inequality to equation

i.e  

[tex]y = -(\frac{1}{6} )x+1[/tex]

x          y  

0          1

6          0

Now , as inequality have > sign

i.e according to the graph of inequality rules:

The boundary line is dashed for > and < and If the symbol ≥ or > is used, shade above the line.

Therefore,

Graph will be option "A" only .

Hence, the graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex]  is option "A" .

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Answer:

13

Step-by-step explanation:

f(x) = 3x + 7

f(2) = 3(2) + 7

f(2) = 6 + 7

f(2) = 13

Answer:

(-1,-2)

Step-by-step explanation:

[tex]6x-y=-4\\y=6x+4\\y=6(-2)+4=-8\\y=6(-1)+4=-2\\y=6(0)+4=4[/tex]

so the only one is (-1,-2)

Answer:

The answer is option C.

3a - b = 10

Hope this helps you

Answer:

Step-by-step explanation:

1. Preferred Share dividends.

There are 300,000 preference shares and each of them got $2.85. Total dividends are;

= 300,000 * 2.85

= $855,000‬

2. Total dividends = $3,500,000

Dividends left for Common Shareholders (preference gets paid first)

= 3,500,000 - 855,000

= $2,645,000

Common shares number 2,500,000

Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]

= $1.06

Answer:

The confidence interval is  [tex]25.16 < \mu < 26.85[/tex]

Step-by-step explanation:

From  the question we are given a data set

     25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

The mean of the this sample data is  

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

where is the sample size with values  n =  10

         [tex]\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}[/tex]

          [tex]\= x = 26[/tex]

The standard deviation is evaluated as

             [tex]\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }[/tex]

substituting values

     [tex]= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }[/tex]

                  [tex]\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }[/tex]

     [tex]\sigma = 1.625[/tex]

The  confidence level is given as 90% hence the level of significance is calculated as

    [tex]\alpha = 100 -90[/tex]

    [tex]\alpha =10[/tex]%

   [tex]\alpha = 0.10[/tex]

Now the critical values of [tex]\frac{\alpha }{2}[/tex] is obtained from the normal distribution table as

      [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

The reason  we are obtaining  the critical values of [tex]\frac{\alpha }{2}[/tex] instead of  [tex]\alpha[/tex] is because  we are considering two tails of the area under the normal curve

  The margin of error is evaluated as

            [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

           [tex]MOE = 1.645 * \frac{1.625 }{\sqrt{10} }[/tex]

           [tex]MOE = 0.845[/tex]

The  90%, two sided confidence interval is mathematically evaluated as

           [tex]\= x - MOE < \mu < \= x + MOE[/tex]

           [tex]26 - 0.845 < \mu < 26 + 0.845[/tex]

           [tex]25.16 < \mu < 26.85[/tex]

Given that the lower and the upper limit is greater than  25 then we can assure the manufactures  that the battery life exceeds 25 hours

Answer:

3.87

Step-by-step explanation:

The computation is shown below:

Data provided in the question

mean distance = [tex]\bar x[/tex] = 188 meters

Standard deviaton = [tex]\sigma = 14[/tex]

Hits drivers = 15

The distance = 174 meters

H_0: μ≤174;

H_a: μ>174

Based  on the above information, the test statistic z-score is

[tex]z = \frac{\bar x - \mu }{\sigma / \sqrt{n} } \\\\ = \frac{188 - 174}{\ 14 / \sqrt{15} }[/tex]

= 3.87

Hence, the test statistic is 3.87

Note:

We take the μ≤174 instead of μ=174;

Answer: It is a scalene triangle.

Step-by-step explanation:

It is scalene because the length between T and V are not equal,the length between T and S is not equal and the length between V and S is also not equal. All the side lengths of the triangle have different measures.

Answer:

54 units^2

Step-by-step explanation:

The formula to find the area of a right triangle is bh/2.

Plug the values in.

9*12/2

Multiply.

108/2

Divide.

52

The area is 54 units squared.

Answer: 54u²

Step-by-step explanation:

The area of a triangle is 1/2bh

1/2bh

1/2(12)(9)

(6)(9)

54

Hope it helps <3

Answer:

3x

Step-by-step explanation:

39*x / 13

39/13 * x

3*x

3x

Answer:

3x

Step-by-step explanation:

We are given the expression:

39*x /13

We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.

(39*x /13) / (13/13)

(39x/13) / 1

3x / 1

When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.

3x

The expression 39*x/13 can be simplified to 3x

Answer:

f(x) = -(x + 1)² - 2

Step-by-step explanation:

f(x) = a(x - h)² + k

-6 = a(1 - -1)² + -2

-6 = a(4) -2

-4 = 4a

a = -1

f(x) = -(x + 1)² - 2

Answer:  114°

Step-by-step explanation:

[tex]\overrightarrow{u}=\bigg<3, 2, -1\bigg>\\\\\overrightarrow{v}=\bigg<1,-4,2\bigg>\\\\\\u\cdot v=3(1)+2(-4)+\ -1(2)\quad =-7\\\\|u|=\sqrt{3^2+2^2+(-1)^2}\quad =\sqrt{14}\\\\|v|=\sqrt{1^2+(-4)^2+2^2}\quad =\sqrt{21}\\\\\\\cos\theta=\dfrac{u\cdot v}{|u|\ |v|}\\\\\\\cos\theta=\dfrac{-7}{\sqrt{14}\cdot \sqrt{21}}\\\\\\\cos\theta=\dfrac{-1}{\sqrt6}\\\\\\\large\boxed{\theta=114^o}[/tex]

Answer:

Thickness of rectangle prism is 20 inches.

Step-by-step explanation:

Given:

Surface area of rectangular prism, A =  992 sq inches.

Height, h = 12 inches

Width, w = 8 inches

To find:

Thickness / length of prism, [tex]l[/tex] = ?

Solution:

First of all, let us learn the formula for surface area of a rectangular prism.

Formula for surface area of a prism is given as:

[tex]A=2(wl+hl+hw)[/tex]

As there are 6 faces, each face is a rectangle and area of all the faces is considered in the formula. It is just like a cuboid like structure.

Putting all the given values in the formula to find the value of [tex]l[/tex]:

[tex]992=2(8l+12l+8 \times 12)\\\Rightarrow 496 = 20l + 96\\\Rightarrow 20 l =496-96\\\Rightarrow 20 l =400\\\Rightarrow l = \dfrac{400}{20}\\\Rightarrow l = 20\ inches[/tex]

So, the answer is Thickness of rectangle prism is 20 inches.

The value of x in terms of b is x = [tex]\frac{-3}{b}[/tex]. Therefore the value of x when b = 3 is x = [tex]\frac{-3}{3}[/tex] = -1.

We can find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:

-2(bx - 5) = 16

-2bx + 10 = 16

- 10

-2bx = 6

÷ -2

bx = -3

÷ b

x = -3/b, which is the answer to the first part.

To get the second answer, we just substitute b = 3 into this equation and we get:

x = -3/b = -3/3 = -1

I hope this helps!

The value of x in terms of b is x = -3/b. Therefore, the value of x when b = 3 is x = -1.

An equation is an expression that shows the relationship between two or more numbers and variables.

We need to find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:

-2(bx - 5) = 16

-2bx + 10 = 16

-2bx = 6

bx = -3

x = -3/b,

Now we just substitute b = 3 into this equation and we get:

x = -3/b = -3/3 = -1

The value of x in terms of b is x = -3/b.

Therefore, the value of x when b = 3 is x = -1.

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Answer:

(a) n(t) = P(0)*e^(0.010939940t)

(b) 12,674,681 (nearest unit)

(c) 14 years (nearest year)

Step-by-step explanation:

rate = 1.1% / year = 1.011

(a)

P(0) = 12,000,000  = population in 2010

In compound interest format, after t years

P(t) = P(0)* (1.011)^t

Given format = P(0)* e^(rt)

therefore

e^(rt) = 1.011^t       use law of exponents

(e^r)^t = 1.011^t

e^r = 1.011

r = log_e(1.011) = 0.010939940   (to 9 decimal places)

required formula is

n(t) = P(0)*e^(0.010939940t)

(b)

in 2015,

P(0)=12000000, n = 5 (years after 2010)

n(5) = 12000000*e^( 0.010939940 * 5 ) = 12,674,680.6 = 12,674,681 (nearest unit)

(c)

to reach 14 million, we equate

n(t) = 14,000,000

12,000,000 *e^(0.010939940*t) = 14,000,000

e^(0.010939940*t) = 14000000/12000000 = 7/6

take log on both sides

0.010939940*t = log(7/6)

t = log(7/6) / 0.010939940 = 14.091 years = 14 years to the nearest year.

See graph attached.  Y-axis is in millions, x-axis is in years.

a) [tex]n(t) = 12e^{0.011t}[/tex]

b) The estimate for the population in 2015 is of 12.7 million.

c) The fish population will reach 14 million after 14 years.

d) The sketch is given at the end of this answer.

------------------------------------

Item a:

The exponential model is:

[tex]n(t) = n(0)e^{rt}[/tex]

In which:

Thus, the model is:

[tex]n(t) = 12e^{0.011t}[/tex]

Item b:

2015 is 2015 - 2010 = 5 years after 2010, thus this is n(5).

[tex]n(5) = 12e^{0.011(5)} = 12.7[/tex]

The estimate for the population in 2015 is of 12.7 million.

Item c:

This is t for which n(t) = 14, thus:

[tex]n(t) = 12e^{0.011t}[/tex]

[tex]14 = 12e^{0.011t}[/tex]

[tex]e^{0.011t} = \frac{14}{12}[/tex]

[tex]\ln{e^{0.011t}} = \ln{\frac{14}{12}}[/tex]

[tex]0.011t = \ln{\frac{14}{12}}[/tex]

[tex]t = \frac{\ln{\frac{14}{12}}}{0.011}[/tex]

[tex]t = 14[/tex]

The fish population will reach 14 million after 14 years.

Item d:

At the end of this answer, the sketch is given.

A similar problem is given at https://brainly.com/question/23416643

Answer:

z-value of rachel = 1.875

z-value of rob = -2

z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.

Step-by-step explanation:

Let's denote the salary of Rob and Rachel per year by X. So, X = $50,000

We are told that;

For Rachel's industry;

Mean salary;μ1 = $35,000

Standard deviation;σ1 = $8,000

For Rob's industry;

Mean salary;μ2 = $60,000

Standard deviation;σ2 = $5,000

Formula for z - value is;

z = (X - μ)/σ

Thus;

z-value for rob is;

z2 = (X - μ2)/σ2

z2 = (50000 - 60000)/5000

z2 = -2

z-value for rachel is;

z1 = (X - μ1)/σ1

z1 = (50000 - 35000)/8000

z1 = 1.875

z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.

Step-by-step explanation:

Hey, there !!!

According to your question,

total c.p = 532.50

tax rate =6%

let original price be x.

now,

total c.p = x + tax rate of x.

or, 532.50= x+ (6/100) × x

or, 532.50 = 106x/100

or, 53200 = 106x

or, x= 53200/106

Therefore, the original price was 501.88.

Hope it helps...

Answer:

a. k = 3

b. N = 27

c. n = 9

Step-by-step explanation:

Given that,

Source :          sS                 dF            mS                F

Between:                            k -1        sSB/k-1             mSB

within                                  N-K        sSw/N-K           mSw

total                                     N-1

Therefore F ( 2, 24 ) = F ( K - 1, N - K )

so K - 1 = 2

K = 2 + 1

K = 3

N - K = 24

N - 3 = 24

N = 24 + 3

N = 27

married, single and divorced are equal sizes

so n = N/3

n = 27 / 3

n = 9

a. k = 3

b. N = 27

c. n = 9

Answer:

$125,800

Step-by-step explanation:

Amount (A) = ?

Principal (P) = $85,000

Rate (r) = 6%

Time (t) = 8 years

Simple interest formula;

A = P(1 + rt)

A = $85,000(1 + 0.48)

A = $125,800

Answer:

61 and -87

Step-by-step explanation:

If the numbers are x and x - 148, we can write the following equation:

x + x - 148 = -26

2x - 148 = -26

2x = 122

x = 61 so x - 148 = 61 - 148 = -87

Answer:

x=−3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  7*x-8-(8*x-5)=0

Pull out like factors :  -x - 3  =   -1 • (x + 3)

Solve  :    -x-3 = 0  

Add  3  to both sides of the equation :    -x = 3

Multiply both sides of the equation by (-1) :  x = -3

Answer:

56x^2−99x+40

Step-by-step explanation:

 Evaluate (8x−5)(7x−8)

Apply the distributive property by multiplying each term of 8x−5 by each term of 7x−8.

56x^2−64x−35x+40

Combine −64x and −35x to get −99x.

56x^2−99x+40

Answer:

867.44 ft²

Step-by-step explanation:

The area of the shaded region is A = 196π + 252.

We have the dimensions of the unshaded region are 14ft x 18ft.

We have to find the area of shaded region.

The area of a rectangle is -

A(R) = Length x Breadth = L x B

and the area of Circle is -

A(C) = [tex]\pi r^{2}[/tex]

According to the question -

Dimensions of the unshaded region -

L = 18ft

B = 14ft

Area of the shaded region (A) = Total Area - Area of Rectangle

Total Area = Area of 2 semicircles of radius (7 + 7) 14ft + Area of rectangle of length 18ft and breadth 28ft.

Total Area = ( [tex]2\times \frac{1}{2}\times \pi \times14 \times 14[/tex] ) + ( 18 x 28)

Total Area = 196π + 504

Area of the shaded region (A) = 196π + 504 - 252 = 196π + 252

Hence, the area of the shaded region is A = 196π + 252.

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Answer:

[tex]w=\frac{t+8}{3}[/tex]

Step-by-step explanation:

[tex]3w - 8 = t[/tex]

Add 8 on both sides.

[tex]3w - 8 + 8 = t + 8[/tex]

[tex]3w = t + 8[/tex]

Divide both sides by 3.

[tex]\frac{3w}{3} =\frac{t+8}{3}[/tex]

[tex]w=\frac{t+8}{3}[/tex]

The value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.

It is defined as the combination of constants and variables with mathematical operators.

We have an equation:

3w - 8 = t

To solve for w in terms of t

Make the subject as w

In the equation:

3w - 8 = t

Add 8 on both sides:

3w - 8 + 8 = t + 8

3w = t + 8

Divide by 3 on both sides:

3w/3 = (t + 8)/3

w = (t + 8)/3

The equation represents a function of w in terms of t

As we know, the function can be defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Thus, the value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.

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Answer:

Probability of orange hat = 0.0833

Step-by-step explanation:

We have to find the probability of getting an orange hat while we randomly choose from 444 pieces of clothing and 333 colors.

So we have to get hat from the clothing and we have to get orange color from the colors. All shirts , pants , socks and hats are in equal numbers and are 111 each. Also purple, blue and orange are 111 each in number.

The probability of getting hats =

                                                   = 0.25

The probability of getting orange =  = 0.333

Final probability = 0.25 0.333

                          = 0.0833

Answer: 1/12

Step-by-step explanation:

I just had khan academy

Answer:

aₙ = 0.2(-0.3)⁽ⁿ⁻¹⁾

Step-by-step explanation:

The geometric sequence with the first term a, a common ratio r has the nth term given as

Tₙ = arⁿ⁻¹

where Tₙ is the nth term

From the given sequence

a = 0.2

r = -0.06/0.2

= -0.3

Hence the nth term

= 0.2 * -0.3ⁿ⁻¹

The right option is E

Answer:

aₙ = 0.2(-0.3)⁽ⁿ⁻¹⁾

Step-by-step explanation:

Answer: Option D, composition.

Step-by-step explanation:

In a function f(x) = y

x is the input, and the set of the possible values of x is called the domain.

y is the output, and the possible values of y is called the range.

Now, if we have two functions:

f(x) = y

g(x) = y.

we can define the composition of functions as: using the output of one function as the input of the other function, we can write this as:

f( g(x)) or fog(x)

In words, first we evaluate the function g in the point x, and the output of that is used as the input for the function f.

Then, the correct option here is D, composition.

Answer:

(a) C = 80 a = 5.938cm c = 9.097cm

(b) unsure

(c) b= 22.147cm

A = 48.16 degrees

C = 22.82 degrees

Note angle sum higher than 180 due to rounding inaccuracies

Step-by-step explanation:

(a) <C == 180 - (40 + 60) == 80 (Interior angles on triangle have sum of 180 degrees)

side a = (8*sin(40))/sin(60) == 5.938cm by law of sines

side c = (8*sin(80))/sin(

60) == 9.097cm by law of sines

(b) unsure

(c) b^2 = 17^2 + 11^2 - 2(17)(11)cos(104) --> Law of cosines

b^2 = 289 + 121 - 2(187)cos(104)

b^2 = 400 - -90.479

b^2 = 490.479

b = 22.147 cm

sin(A)/17cm = sin(104)/22.147cm

A = arcsin((17/22.147)*sin(104))

A = 48.16 degrees

sin(C)/11cm = sin(104)/22.147cm

C = arcsin((11/22.147)*sin(104))

C = 28.82 degrees