Use the equation and type the ordered-pairs. y = log 2 x {(1/2, a0), (1, a1), (2, a2), (4, a3), (8, a4), (16, a5)}

Answer:

y= 1/5x + 12/5

Step-by-step explanation:

Parallel line to this has same slope and passes through the point (-2, 2)

The required equation in slope- intercept form is:

Answer:

[tex]y-4p[/tex]

Step-by-step explanation:

Add/subtract like terms.

[tex]5y+2p-4y-6p\\5y-4y+2p-6p\\y-4p[/tex]

Answer:

B

Step-by-step explanation:

Answer:

  Exponential; $376.32

Step-by-step explanation:

Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.

The same would be true for the second month, so the overall multiplier for the two months is ...

  (1.12)(1.12) = 1.12^2 = 1.2544

This makes the food bill for the second month amount to ...

  1.2544 × $300 = $376.32

_____

As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.

If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.

Answer:

x =2

Step-by-step explanation:

becaue 2-1 is smaller than 3

Answer:

Hello!

I believe your answer is:

x=2

If this is not correct, please let me know and I will try again!

Step-by-step explanation:

Question:  

The physiological blind spot refers to a very small zone of functional blindness in the eye where the optic nerve passes through the retina. We do not notice it because our nervous system compensates for it. Can eye training reduce the size of a person's physiological blind spot? Researchers recruited a representative sample of 10 adults with normal vision. Each participant performed training exereises with one eye for three weeks. The size of the physiological blind spot was measured (in degrees of visual angle squared) with a motion detection task both prior to training and again after the training was completed. Which of the options is the response variable?

A) The size of the physiological blind spot

B) The number of adults.

C) The type of training exercises performed by each participant.

D) The size of the physiological blind spot.

E) The number of times an adult performed training exercises.

Answer:

The correct answer is A)

Explanation:

The response variable (when experimenting) is the variable or factor about which the researcher is concerned. It can also be (as the name entails) the variable which respond to changes in the experiment.  

The changes in the experiment is the training. The variable which the researcher is concerned about and which may or may not change with the introduction of training is the size of the physiological blind spot.

Cheers!

Answer:

a) H0: [tex]\sigma = 1.34[/tex]

H1: [tex]\sigma \neq 1.34[/tex]

b) [tex] df = n-1= 10-1=9[/tex]

And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:

[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]

c) [tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]

d) For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34

Step-by-step explanation:

Information provided

n = 10 sample size

s= 1.186 the sample deviation

[tex]\sigma_o =1.34[/tex] the value that we want to test

[tex]p_v [/tex] represent the p value for the test

t represent the statistic  (chi square test)

[tex]\alpha=0.01[/tex] significance level

Part a

On this case we want to test if the true deviation is 1,34 or no, so the system of hypothesis are:

H0: [tex]\sigma = 1.34[/tex]

H1: [tex]\sigma \neq 1.34[/tex]

The statistic is given by:

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

Part b

The degrees of freedom are given by:

[tex] df = n-1= 10-1=9[/tex]

And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:

[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]

Part c

Replacing the info we got:

[tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]

Part d

For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34

Answer:

  GH¢2082.12

Step-by-step explanation:

Let "a" represent the amount invested at 12%. Then (a+580) is the amount invested at 14%. The total amount invested (t) is ...

  t = (a) +(a +580) = 2a+580

Solving for a, we get

  a = (t -580)/2

__

The accumulated amount from the investment at 12% is 1.12a. And the accumulated amount from the investment at 14% is 1.14(a+580). Together, these accumulated amounts total GH¢2358.60.

  1.12(t -580)/2 +1.14((t -580/2 +580) = 2358.60

  0.56t -0.56(580) +0.57t -0.57(580) +1.14(580) = 2358.60 . . . remove parens

  1.13t + 5.8 = 2358.60 . . . . . . . . . simplify

  1.13t = 2352.80 . . . . . . . . . . . . . . subtract 5.8

  t = 2352.80/1.13 = 2082.12 . . . . divide by the coefficient of t

Mr. Azu's total investment was GH¢2082.12.

Answer:

a) CI = (113,637.5  ,  124,672.5)

b) CI = (112,581  ,  125,729)

c) CI = (110,501.4  ,  127,808.6)

Step-by-step explanation:

You have the following information:

[tex]\overline{x}[/tex]: mean annual household income = 119,155

σ: standard deviation = 30,000

n: sample = 80

The interval of confidence is given by the following expression:

[tex]\overline{x}\pm Z_{\alpha/s}(\frac{\sigma}{\sqrt{n}})[/tex]

Z_α/2: distribution density factor

where α and Z_α/2 are given by the range of the confidence interval.

a) For a 90% confidence interval you have:

α = 1 - 0.9 = 0.1

Z_0.1/2 = Z_0.05 = 1.645   (found in a table of normal distribution)

You replace in the equation (1) to obtain the confidence interval:

[tex]119,155\pm (1.645)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm5,517.5[/tex]

Then, the confidence interval is (119,155 + 5,517.5 , 119,155 - 5,517.5  )

= (113,637.5  ,  124,672.5)

b) For a 95% confidence interval you have:

α = 1 - 0.95 = 0.05

Z_0.05/2 = Z_0.025 = 1.96

[tex]119,155\pm (1.96)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 6,574.0[/tex]

The confidence interval is (112,581  ,  125,729)

c) For a 99% confidence interval:

α = 1 - 0.99 = 0.01

Z_0.01/2 = Z_0.005 = 2.58

[tex]119,155\pm (2.58)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 8,653.6[/tex]

The confidence interval is (110,501.4  ,  127,808.6)

d) When the confidence level increases the width of the confidence increases too. This can be noticed in the normal distribution, when the confidence level is higher, the area of the tails is reduced, and so, the confidence interval is higher.

Answer:

x = 22

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the interior angles

6x+1 = 79+ 2x+10

Combine like terms

6x+1 = 2x+89

Subtract 2x from each side

4x+1 = 89

Subtract 1 from each side

4x = 88

Divide by 4

4x/4 = 88/4

x = 22

Answer:

The answer is

Step-by-step explanation:

We can cross out A. So it has to be either B, C, or D.

Answer:

The maximum possible difference between the largest and the smallest of these 5 numbers is 65( if numbers aren't repeated )

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The point of diminishing returns (x , y ) is  (11, 21462)

Step-by-step explanation:

From the question we are told that

     The function is  [tex]R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20[/tex]

Here R(x)  represents revenue (in thousands of​ dollars) and  x  represents the amount spent on advertising​ (in thousands of​ dollars).

           Now  differentiating  R(x) we have  

               [tex]R'(x) = -3x^2 +66x + 800[/tex]

Finding the second derivative of R(x)

              [tex]R''(x) = -6x +66[/tex]

at  inflection point    [tex]R''(x) = 0[/tex]

    So      [tex]-6x +66 = 0[/tex]

=>           [tex]x= 11[/tex]

    substituting value of x into R(x)

     [tex]R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,[/tex]

      [tex]R(x) = 21462[/tex]

Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is

     (11, 21462)

Answer:

D

Step-by-step explanation:

An arithmetic sequence is a series of numbers that increases or decreases by a certain quantity every step. A is not an arithmetic sequence, since it alternates between 2 and -2. B is not an arithmetic sequence, since it does not grow constantly in one direction. C is not an arithmetic sequence, but rather a geometric one. D is an arithmetic sequence, decreasing by 3 with each step. Hope this helps!

Answer:

Step-by-step explanation:

This is  the method I am familiar with.

I Hope It helps :)

[tex]METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\[/tex]

[tex]Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6[/tex]

Answer:

Correct answers is

Step-by-step explanation:

1. 3

2. B

3. 6

4. (6,13)

Answer:

Look at the money bags below!!! (but I'll give you the answer)

Step-by-step explanation:

John F: 7 full bags - 1 half

Juan A: 9 full bags

Jason A: 3 full bags

Nick J: 3 full bags- 1 half

Alfonso S: 8 full bags

Hope this helped and wasn't confusing!!! xx - Asia

Answer:

C.

Step-by-step explanation:

First finding height using Pythagoras theorem

(H)²=(B)²+(P)²

8.2²=5.4²+P²

P² = 67.24 - 29.16

P² = 38.08

P = 6.2

Now

Volume of cone = (1/3)πr²h

= (1/3)(3.14)(5.4)²(6.2)

= (1/3)(567.9)

= 189.2 cm³

Answer:

f(1/2)=1.5

f(1/4)=0.75

Answer:

Step-by-step explanation:

Simple regression was employed to establish the effects of childhood exposure to lead. THe effective sample size was about 122 subjects. THe independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.

Calculate the t statistic for each slope, at significance level = 0.01.

Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?

Slope Error

Highest grade achieved .061 −0.027 0.009 .008 No / Yes

Reading grade equivalent .121 −0.070 0.018 .000 No / Yes

Class standing .039 −0.006 0.003 .048 No / Yes

Absence from school .071 4.8 1.7 .006 No / Yes

Grammatical reasoning .051 0.159 0.062 .012 Yes / No

Vocabulary .108 −0.124 0.032 .000 No / Yes

Hand-eye coordination .043 0.041 0.018 .020 No / Yes

Reaction time .025 11.8 6.66 .080 No / Yes

Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No

B) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.

1. No

2. Yes

[tex]t=\frac{\text {estimated slope}}{\text {std error}}[/tex]

a)

Estimated Slope           Std error              t - calculated

-0.027                            0.009                   -3

-0.070                            0.018                    -3.89

-0.006                            0.003                   -2

4.8                                  1.7                         2.82

0.159                              0.062                   2.56

-0.124                             0.032                   -3.87

0.041                              0.018                    2.28

11.8                                6.66                      1.77

-0.639                           0.36                       -1.78

b) Yes, It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.

Answer:

GH¢.37480.36

Step-by-step explanation:

Let the amount invested at 12% per annum =GH¢.x

He  invested 580.00 more than the first at 14%.

Therefore:

The amount invested at 14% =GH¢.(x+580)

For each investment option:

Amount Accrued =Principal + Simple Interest

Amount Accrued at 12%

[tex]=x+x*0.12\\=1.12x[/tex]

Amount Accrued at 14%

[tex]=(x+580)+0.14(x+580)\\=x+580+0.14x+81.2\\=1.14x+661.2[/tex]

Mr. Azu had total accumulated amount of  GH42,358.60

Therefore:

1.12x+1.14x+661.2=42,358.60

2.26x=42,358.60-661.2

2.26x=41697.4

x=GH¢.18450.18

Therefore:

The amount invested at 12% per annum= GH¢.18450.18

The amount invested at 14% per annum= GH¢.18450.18+580

=GH¢.19030.18

Mr Azu's Total Investment = 18450.18 +19030.18

=GH¢.37480.36

Answer:

C

Step-by-step explanation:

Plugged into calculator

Vertical asymptotes: x=-2

Horizontal asymptotes: y=0

No oblique asymptotes

Answer:

-1/2 =x

Step-by-step explanation:

4x - 6 = 10x -3

Subtract 4x from each side

4x-4x - 6 = 10x-4x -3

-6 = 6x-3

Add 3 to each side

-6+3 = 6x

-3 = 6x

Divide each side by 6

-3/6 = 6x/6

-1/2 =x

[tex]answer \\ - \frac{1}{2} \\ solution \\ 4x - 6 = 10x - 3 \\ or \: 4x - 10x = - 3 + 6 \\ or \: - 6x = 3 \\ or \: x = \frac{3}{ - 6} \\ x = - \frac{1}{2} \\ hope \: it \: helps[/tex]

The complete question is;

A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide. The biologist estimates she will need 2600 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit in to the air tank. Write you answer in atmospheres

Answer:

10.5 atm

Step-by-step explanation:

Formula for Volume of a sphere is;

V = (4/3)πr³

r = 78/2 = 39 cm

V = (4/3)π(39)³

V = (4/3)*π*59319

V = 248475 cm³

Now, from conversions, 1000 cm³ = 1L

So,

V = 248475/1000

V = 248.5 L

This is the volume of the storage tank

If we assume that the 2600 L of air is measured at 1 atmosphere pressure, then we will obtain the following relationship:

From Boyles law,

P1 × V1 = P2 × V2

Thus;

(1 atm) × (2600 L) = (P2) × (248.5 L)

P2 = 2600/248.5

P2 = 10.463 atmospheres

Approximating to 3 significant figures is; P2 = 10.5 atm

Answer:

9/16

Step-by-step explanation:

captain has a 3/4 probability of hitting the ship

pirate has a 1/4 probability of hitting the ship

This means he has a 3/4 probability of missing the ship

P (captain hitting and pirate missing) = 3/4*3/4 = 9/16

Answer:

73.24% probability that 6 or more people from this sample are unemployed

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 100, p = 0.071[/tex]

So

[tex]\mu = E(X) = np = 10*0.071 = 7.1[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.071*0.929} = 2.5682[/tex]

What is the probability that 6 or more people from this sample are unemployed

Using continuity correction, this is [tex]P(X \geq 6 - 0.5) = P(X \geq 5.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 5.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5.5 - 7.1}{2.5682}[/tex]

[tex]Z = -0.62[/tex]

[tex]Z = -0.62[/tex] has a pvalue of 0.2676

1 - 0.2676 = 0.7324

73.24% probability that 6 or more people from this sample are unemployed

Answer:

sale prices = $252

Step-by-step explanation: 280 - (280 x 10%) = 280 - 28 = $252

Answer:

$189

Step-by-step explanation:

10% of 210 = 21

210 - 21  = 189

Answer:

The age difference between oldest the youngest is of 48 years.

Step-by-step explanation:

We can solve this question using a system of equations.

I am going to say that:

Kissi's age is x.

Esinam's age is y.

Lariba's age is z.

The ratio of the ages of Kissi and Esinam is 3:5

This means that [tex]\frac{x}{y} = \frac{3}{5}[/tex], so [tex]5x = 3y[/tex]

That of Esinam and Lariba is 3:5

This means that [tex]\frac{y}{z} = \frac{3}{5}[/tex], so[tex]5y = 3z[/tex]

The sum of the ages of all 3 is 147 years

This means that [tex]x + y + z = 147[/tex]

What is the age difference between oldest the youngest

z is the oldest

x is the youngest.

First i will find y.

We have that, from the equations above: [tex]x = \frac{3y}{5}[/tex] and [tex]z = \frac{5y}{3}[/tex]

So

[tex]x + y + z = 147[/tex]

[tex]\frac{3y}{5} + y + \frac{5y}{3} = 147[/tex]

The lesser common multiple between 5 and 3 is 15. So

[tex]\frac{3*3y + 15*y + 5*5y}{15} = 147[/tex]

[tex]49y = 147*15[/tex]

[tex]y = \frac{147*15}{49}[/tex]

[tex]y = 45[/tex]

Youngest:

[tex]x = \frac{3y}{5} = \frac{3*45}{5} = 27[/tex]

Oldest:

[tex]z = \frac{5y}{3} = \frac{5*45}{3} = 75[/tex]

Difference:

75 - 27 = 48

The age difference between oldest the youngest is of 48 years.

Answer:

50 inches

Step-by-step explanation:

Since the formula for the area of a triangle is bh/2, where b is the base and h is the height, you can set up the following equation:

30b/2=750

30b=1500

b=1500/30=50

Hope this helps!

The right answer is 50 inches.

Please see the attached picture for full solution

Hope it helps...

good luck on your assignment..

Answer:

[tex]x=5/48[/tex]

Step-by-step explanation:

[tex]2/5 + 1/x =10[/tex]

[tex]1/x=10-2/5[/tex]

[tex]1/x=48/5[/tex]

[tex]48x=5[/tex]

[tex]x=5/48[/tex]

Answer:

[tex]x = \frac{5}{48} [/tex]

Step-by-step explanation:

[tex]\frac{2}{5} + \frac{1}{x} = 10 \\ \frac{1}{x} = 10 - \frac{2}{5} \\ \frac{1}{x} = \frac{50 - 2}{5} \\ \frac{1}{ x } = \frac{48}{5} \\

use \: \: \: \: cross \: \: \: multiply

\\ 5 = 48x \\ \frac{5}{48} = \frac{48x}{48} \\ x = \frac{5}{48} \\ [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

See the explanation

Step-by-step explanation:

If and event can occur in A number of way and fail in B number of ways, then probability of its occurrence is:

[tex]P(A)= \frac{A}{A+B}[/tex]

or probability of its failing is:

[tex]P(B)=\frac{B}{A+B}[/tex]

Rolling a number smaller than 3 in a dice.

A= 2 (1,2)

B = 4 (3,4,5,6)

[tex]P(A)= \frac{2}{2+4}=\frac{1}{3}[/tex]

Definition of Probability in terms of past performances (data). It can be taken as how often things happens divided by all outcomes.

A batter has 50 safe hits at 200 bats, which makes his batting average [tex]\frac{50}{200}= 0.25[/tex] which is the probability.

When you define a probability due to personel beleif in the likelihood of an outcome. It involve no formal calculations and varies from person to person, depending on their past experience.

A person beleives that probability that the batter will hit safely in the next bat is 0.75

Answer:

1) The normal distribution should be used for the sample mean because the population distribution is known to be normal (answer b).

2) C. H0: mu = 519, H_1: mu not equal to 519, reject if z> 1.96 or z< -1.96.

3) Yes. There is enough evidence to support the claim that the true mean is not 519 ml.

Step-by-step explanation:

1) When the population follows a normal distribution, it is correct to assume a normal distribution for the sample mean.

2) As it is a two-tailed decision rule, we are interested in detecting a significant difference below and above the mean. This is why we use the unequal sign in the alternative hypothesis.

The null hypothesis state that there is not significant difference from 519.

The critical value for a significance level of 5% is z=1.96.

[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]

3) The claim is that the true mean is not 519 ml.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]

The significance level is 0.05.

The sample has a size n=16.

The sample mean is M=522.

The standard deviation of the population is known and has a value of σ=6.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{16}}=1.5[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{522-519}{1.5}=\dfrac{3}{1.5}=2[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=2\cdot P(z>2)=0.046[/tex]

As the P-value (0.046) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the true mean is not 519 ml.