what decimal is equivalent to 0.85

Answer:

Step-by-step explanation:

30t - 5t² = 10

5t² - 30t + 10 = 0

t = [30 ± √(30² - 4 ⋅ 5 ⋅ 10)] / [2 ⋅ 5]

= [30 ± √700] / 10

= [30 ± 10√7] / 10

= 3 ± √7

≈ 0.35 seconds and 5.65 seconds

Answer:

0.033316

Step-by-step explanation:

We use the z score formula to solve for this question.

Since we are given the number of samples in the question, our z score formula is given as:

z = (x-μ)/ S.E

where x is the raw score

μ is the sample mean

S.E is the Standard error.

x is the raw score = 900

μ is the sample mean = Population mean = 947

Standard error =

This is calculated as Population standard deviation/ √No of samples

= 205/√64.

= 205/8

= 25.625

We proceed to calculate the z score

z = (x-μ)/ S.E

z = 900 - 947/25.625

= -1.83415

Using the z score table for normal distribution,

P(x≤ z) = P(z ≤ -1.83) = P(x ≤ 900)

P(x<900) = 0.033316

Therefore, the probability the mean of the sample is below 900 is 0.033316

Answer:

3.6miles

Step-by-step explanation:

9/2.5=3.6

Answer: The car is traveling at 73.63638 Mph

Step-by-step explanation:

1 yard per second is the same as 3 feet per second.

there are 5280ft per mile

So, at 36 yards per second, the car is traveling at 108/5280th (0.02045455) of a mile per second

0.02045455 * 60 (seconds) * 60 (minutes) = 73.63638 Mph

Answer:

C = 4

Step-by-step explanation:

solution:

f(x) can be differentiated on (0,16)

By mean value theorem

= f(16) = 4

= f(0) = 0

= f(b) - f(a)/b - a

= f(4) - f(0)/ f(16) - f(0)

= f'(c) = 1/2√C

= 1/2√C = 4/16

= 1/2√C = 1/4

= 4 = 2√C

= √C = 4/2

we make c the subject of the formula and also eliminate the square root

= √C = 2

= C = 2²

= C = 4

Answer:

the like terms are:

3x+8x+x+y+8

12x+y+8

Answer:

The like terms are

3x, 8x, x

Step-by-step explanation:

3x+8x+y+x+8

The like terms are

3x, 8x, x

They are the terms that are in terms of the first power of x

Answer:

18

Step-by-step explanation:

Given that:

y∞ xz

y=kxz. Where k is constant

When z=196 and x= 2 then y= 7

7=(196)(2)k

7=392k

k=1/56

There fore y=(1/56)xz

When x=3 and z =336

y=(1/56)xz

y=(1/56)(336)(3)

y=18

if value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2 then the value of y when x = 3 and z = 336 is 18.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Value of y varies jointly with x and z.

y ∞ xz

y=kxz.

Where k is constant

When z=196 and x= 2 then y= 7

Let us find the value of k

7=(196)(2)k

7=392k

Divide both sides by 7

k=1/56

y=(1/56)xz

When x=3 and z =336

y=(1/56)xz

y=(1/56)(336)(3)

y=18

Hence,  the value of y when x = 3 and z = 336 is 18.

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Answer:

i [tex]\to[/tex] a

    [tex]n = 96040000[/tex]

i [tex]\to[/tex] b

    [tex]n_1 =24010000[/tex]

i [tex]\to[/tex] c

    [tex]n_2 =41602500[/tex]

ii[tex]\to[/tex]a

     [tex]E = 58.16[/tex]

ii[tex]\to[/tex]b

    [tex]291.84 < \mu < 408.16[/tex]\

ii[tex]\to[/tex]c

    There is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval

Step-by-step explanation:

From the question we are told that

     The sample size is [tex]n = 8[/tex]

      The sample mean is  [tex]\= x = \$ 350[/tex]    

      The sample standard deviation is  [tex]\$ 100[/tex]

Considering question i

    i [tex]\to[/tex] a

         At   [tex]E = 0.02[/tex]  

given that the confidence level is 95%  =  0.95

         the level of significance would be  [tex]\alpha =1-0.95 = 0.05[/tex]

The critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

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

So  the sample size is mathematically evaluated as

            [tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]

=>        [tex]n =[ \frac{ 1.96 * 100}{ 0.02} ]^2[/tex]

=>         [tex]n = 96040000[/tex]

 i [tex]\to[/tex] b

  At  [tex]E_1 = 0.04[/tex]    and  confidence level  = 95%  =>  [tex]\alpha_1 = 0.05[/tex]   =>  [tex]Z_{\frac{\alpha_1 }{2} } = 1.96[/tex]

             [tex]n_1 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_1} ]^2[/tex]

=>           [tex]n_1 =[ \frac{ 1.96 * 100}{ 0.04} ]^2[/tex]

=>           [tex]n_1 =24010000[/tex]

 i [tex]\to[/tex] c

       At   [tex]E_2 = 0.04[/tex]     confidence level  = 99%  =>    [tex]\alpha_2 = 0.01[/tex]

The critical value of  [tex]\frac{\alpha_2 }{2}[/tex] from the normal distribution table is  

        [tex]Z_{\frac{ \alpha_2 }{2} } = 2.58[/tex]

=>    [tex]n_2 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_2} ]^2[/tex]

=>    [tex]n_2 =[ \frac{ 2.58 * 100}{ 0.04} ]^2[/tex]

=>    [tex]n_2 =41602500[/tex]

Considering ii

Given that the level of significance is  [tex]\alpha = 0.10[/tex]

Then the critical value  of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

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

Generally the margin of error is mathematically represented as

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

substituting values

         [tex]E = 1.645 * \frac{100 }{\sqrt{8} }[/tex]

         [tex]E = 58.16[/tex]

Generally the 90% confidence interval is mathematically evaluated as

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

=>      [tex]350 - 58.16 < \mu < 350 + 58.16[/tex]

=>     [tex]291.84 < \mu < 408.16[/tex]

So the interpretation is that there is 90% confidence that the mean  fee charged to H&R Block customers last year is in the interval .So there is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval.

Answer:

f(x) = (x - 3)² - 5

Step-by-step explanation:

equate equation to 0

(x - 3)² = 0

take the square root on both sides

x - 3 = 0

add 3

x = 3

If x = 3 then you are moving to 3 units to the right.

- 5 means you are going downward 5 units.

Answer:

angleABC=isosceles triangle

angleB=(180-50)÷2=65

angle B=angleX(alternative angle)

angleB=65degree

It sounds like R is the region (in polar coordinates)

R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}

Then the integral is

[tex]\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}[/tex]

Answer:

1/3

Step-by-step explanation:

there are twelve marbles total. there are 4 blue marbles.

4/12 = 1/3

Answer:

9-x^2

Step-by-step explanation:

The difference of means subtracting. the first number is 9 and the second is x^2, so you get 9-x^2

Answer:

Please see the Step-by-step explanation for the answers

Step-by-step explanation:

1)

∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] 2j

The sum of series from j=1 to j=5 is:

∑ = 2(1) + 2(2) + 2(3) + 2(4) + 2(5)

  =  2 + 4 + 6 + 8 + 10

∑ = 30

2)

This question is not given clearly so i assume the following series that will give you an idea how to solve this:

∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²

The sum of series from k=1 to j=4 is:

∑ = 2(1)² + 2(2)² + 2(3)² + 2(4)²

  = 2(1) + 2(4) + 2(9) + 2(16)

  =  2 + 8 + 18 + 32

∑ = 60

∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²

∑ = (2*1)² + (2*2)² + (2*3)² + (2*4)²

  = (2)² + (4)² + (6)² + (8)²

  = 4 + 16 + 36 + 64

∑ = 120

∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²- 4

∑ = (2*1)²-4 + (2*2)²-4 + (2*3)²-4 + (2*4)²-4

  = (2)²-4 + (4)²-4 + (6)²-4 + (8)²-4

  = (4-4) + (16-4) + (36-4) + (64-4)

  = 0 + 12 + 32 + 60

∑ = 104

∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²- 4

∑ = 2(1)²-4 + 2(2)²-4 + 2(3)²-4 + 2(4)²-4

  = 2(1)-4 + 2(4)-4 + 2(9)-4 + 2(16)-4

  = (2-4) + (8-4) + (18-4) + (32-4)

  = -2 + 4 + 14 + 28

∑ = 44

3)

∑[tex]\left \ {{6} \atop {k=3}} \right.[/tex] (2k-10)

∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)  

  = (6-10) + (8-10) + (10-10) + (12-10)

  = -4 + -2 + 0 + 2  

∑ = -4

4)

1+1/2+1/4+1/8+1/16+1/32+1/64

This is a geometric sequence where first term is 1 and the common ratio is 1/2 So

a = 1

This can be derived as

1/2/1 = 1/2 * 1 = 1/2

1/4/1/2 = 1/4 * 2/1 = 1/2

1/8/1/4 = 1/8 * 4/1  = 1/2

1/16/1/8 = 1/16 * 8/1  = 1/2

1/32/1/16 = 1/32 * 16/1  = 1/2

1/64/1/32 = 1/64 * 32/1  = 1/2

Hence the common ratio is r = 1/2

So n-th term is:

[tex]ar^{n-1}[/tex] = [tex]1(\frac{1}{2})^{n-1}[/tex]

So the answer that represents the series in sigma notation is:

∑[tex]\left \ {{7} \atop {j=1}} \right.[/tex] [tex](\frac{1}{2})^{j-1}[/tex]

5)

−3+(−1)+1+3+5

This is an arithmetic sequence where the first term is -3 and the common difference is 2. So  

a = 1

This can be derived as

-1 - (-3) = -1 + 3 = 2

1 - (-1) = 1 + 1 = 2

3 - 1 = 2

5 - 3 = 2

Hence the common difference d = 2

The nth term is:

a + (n - 1) d

= -3 + (n−1)2

= -3 + 2(n−1)

= -3 + 2n - 2

= 2n - 5

So the answer that represents the series in sigma notation is:

∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] (2j−5)

For (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is  [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex]  where j = 1 to j = 7, and for (5) the sigma notation is  [tex]\rm\sum j = (2j-5)[/tex]  where j = 1 to j = 5.

We have different series in the question.

It is required to find the sum of all series.

In mathematics, a series can be defined as a group of data that followed certain rules of arithmetic.

1) We have:

[tex]\rm \sum j=2j[/tex]   where j = 1 to j = 5

After expanding the series, we get:

= 2(1)+2(2)+2(3)+2(4)+2(5)

=2(1+2+3+4+5)

= 2(15)

=30

2) We have:

[tex]\rm \sum k=(2k^2-4)[/tex]  where k = 1 to k = 4

After expanding the series, we get:

[tex]\rm = (2(1)^2-4)+(2(2)^2-4)+(2(3)^2-4)+(2(4)^2-4)+(2(5)^2-4)\\[/tex]

[tex]\rm = 2[1^2+2^2+3^2+4^2+5^2]-4\times5\\\\\rm=2[55]-20\\\\\rm = 90[/tex]

3) We have:

[tex]\rm \sum k= (2k-10)[/tex]  where k = 3 to k = 6

After expanding the series, we get:

[tex]= (2(3)-10)+(2(4)-10)+(2(5)-10)+(2(6)-10)\\\\=2[3+4+5+6] - 10\times4\\\\=2[18] - 40\\\\= -4[/tex]

4) The series given below:

[tex]1, \frac{1}{2} ,\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},\frac{1}{64}[/tex]

It is a geometric progression:

[tex]\rm n^t^h[/tex] for the geometric progression is given by:

[tex]\rm a_n = ar^{n-1}[/tex]

[tex]\rm a_n = 1(\frac{1}{2})^{n-1}\\\\\rm a_n = (\frac{1}{2})^{n-1}\\[/tex]

In sigma notation we can write:

[tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex]  where j = 1 to j = 7

5) The given series:

−3+(−1)+1+3+5, it is arithmetic series.

[tex]\rm n^t^h[/tex] for the arithmetic progression is given by:

[tex]\rm a_n = a+(n-1)d[/tex]

[tex]\rm a_n = -3+(n-1)(2)\\\\\rm a_n = 2n-5[/tex]

In sigma notation we can write:

[tex]\rm\sum j = (2j-5)[/tex]  where j = 1 to j = 5

Thus, for (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is  [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex]  where j = 1 to j = 7, and for (5) the sigma notation is  [tex]\rm\sum j = (2j-5)[/tex]  where j = 1 to j = 5.

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perimeter of triangle: P = l+w+h

9+12+10= 31in.

area of triangle: A=b×h÷2

21 + 21 = 42in^2

Answer:

3

Step-by-step explanation:

[tex]f(-1)g(-1) \text{ is the same thing as } f(-1)\cdot g(-1). \\\text{Therefore, find f(-1) and g(-1)}[/tex]

[tex]f(-1)=(-1)^2-4\\f(-1)=1-4\\f(-1)=-3[/tex]

[tex]g(-1)=3(-1)+2\\g(-1)=-3+2\\g(-1)=-1[/tex]

Therefore:

[tex]f(-1)\cdot g(-1)\\=(-3)(-1)=3[/tex]

Answer:

x = 11

Step-by-step explanation:

3/x+1=2/x-3

Solve by using cross products

2 (x+1) = 3 (x-3)

Distribute

2x+2 = 3x-9

Subtract 2x

2x+2-2x = 3x-2x-9

2 = x-9

Add 9 to each side

2+9 =x-9+9

11 =c

Answer:

It is, indeed, a reduction. But, the scale factor of the dilation should be a fraction instead of a whole number, since the shape has shrunk.

Instead of [tex]\frac{KN}{K'N'}[/tex], it should be [tex]\frac{K'N'}{KN}[/tex]. That would make it (4 - 2) / (8 - 4) = 2 / 4 = 1/2.

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Divide by y

kl/y = f/(p + n) + r/u              Subtract r/u from both sides

kl/y - r/u = f/(p + n)               Multiply both sides by (p + n)

(kl/y - r/u ) (p + n) = f            Divide by (kl/y - r/u)

p + n = f / (kl/y - r/u)             Subtract n from both sides

p  =  f / (kl/y - r/u)  - n

I think I'd leave this as the answer. I don't think you are expected to make it a 2 tier fraction.

Answer: A. The sampling follows a normal distribution.

              B. Between 25.14 and 30.86

              C. About 95% will contain the true mean and about 5% won't

Step-by-step explanation: A. The sampling is normally distributed because:

B. For a 95% confidence interval: α/2 = 0.025

Since n = 210, use z-score = 1.96

To calculate the interval:

mean ± [tex]z.\frac{s}{\sqrt{n} }[/tex]

Replacing for the values given:

28 ± [tex]1.96.\frac{21}{\sqrt{210} }[/tex]

28 ± [tex]1.96*1.45[/tex]

28 ± 2.84

lower limit: 28 - 2.84 = 25.14

upper limit: 28 + 2.84 = 30.86

Confidence Interval is between 25.14 and 30.86.

C. Confidence Interval at a certain percentage is an interval of values that contains the true mean with a percentage of confidence. In the case of number of times per day students text, 95% of the interval will contain the true mean, while 5% will not contain it.

Answer:

√32

Step-by-step explanation:

Complete Question

The data represent the membership of a group of politicians. If we randomly select one politician, what is the probability of getting a Republican given that a male was selected?    

        Republican      Democrat           Independent

Male           11                  6                                   0

Female       70                  17                                  7

The probability is approximately_____?

Answer:

The  probability is  [tex]P(k) = 0.647[/tex]

Step-by-step explanation:  

From the question we are told that

   The  sample size of male is  [tex]n_m = 11 + 6 =17[/tex]

     The  number of male Republican is  [tex]k = 11[/tex]  

Generally the probability of getting a Republican given that a male was selected is

            [tex]P(k) = \frac{k}{n_m}[/tex]

substituting values

          [tex]P(k) = \frac{ 11}{17}[/tex]

          [tex]P(k) = 0.647[/tex]

Answer:

hi

Step-by-step explanation:

hji

Answer:

O (-4,1)

I hope I helped you^_^

Answer:

Hello,

Step-by-step explanation:

Roots are -2 and 4

y=k*(x+2)(x-4)

Vertex = (1,-9) is a point of the parabola

-9=k*(1+2)(1-4) ==> k=1

Equation of the parabola is y=(x+2)(x-4)

But you don' t have given the graphs !!!!

The graph show a parabola with a vertex that has Roots are -2 and 4.

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.

Given that,

The vertex of (1,-9) and solutions of (-2,0) and (4,0).

y = k*(x+2)(x-4)

Vertex = (1,-9) is a point of the parabola

-9 = k*(1+2)(1-4)

Substitute the value of k = 1 in the equation,

The equation of the parabola is y = (x+2)(x-4).

The graph show a parabola with a vertex that has Roots are -2 and 4.

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Answer:

7*2=14

Step-by-step explanation:

7*2=14 because is multiplication

Answer:

14 because it is multiplication