on solving x/2 +5/3=_1/2 we get x=​

Answer:

Correct option is: Testing a claim about two population means.

Step-by-step explanation:

In this provided scenario, a researchers wants to determine if corporations require a longer work week for the employees "working full-time".

It is given that for many years "working full-time" was 40 hours per week.

The researchers researcher gathers data on the hours that corporate employees work each week.

It is quite clear that the researcher wants to determine whether the number of hours worked per week must be increased from 40 hours or not.

A test for the difference between two population means would help the researcher to reach the conclusion.

Thus, the correct option is: Testing a claim about two population means.

Answer:

the answer is E the number at the top tells you which position it falls under in the alphabet

Answer:

A) The probability that a randomly selected medical student who took the test had a total score that was less than 484 = 0.06178

B) The probability that a randomly selected study participant's response was between 504 and 516 = 0.29019

C) The probability that a randomly selected study participant's response was more than 528 = 0.00357

D) Option D is correct.

Only the event in (c) is unusual as its probability is less than 0.05.

Step-by-step explanation:

The b and c parts of the question are not complete.

B) Find the probability that a randomly selected study participant's response was between 504 and 516

C) Find the probability that a randomly selected study participant's response was more than 528.

D) Identify any unusual event amongst the three events in A, B and C. Explain the reasoning.

a) None.

b) Events A and B.

C) Event A

D) Event C

Solution

This is a normal distribution problem with

Mean = μ = 500

Standard deviation = σ = 10.4

A) Probability that a randomly selected medical student who took the test had a total score that was less than 484 = P(x < 484)

We first normalize or standardize 484

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (484 - 500)/10.4 = - 1.54

To determine the required probability

P(x < 484) = P(z < -1.54)

We'll use data from the normal distribution table for these probabilities

P(x < 484) = P(z < -1.54) = 0.06178

B) Probability that a randomly selected study participant's response was between 504 and 516 = P(504 ≤ x ≤ 516)

We normalize or standardize 504 and 516

For 504

z = (x - μ)/σ = (504 - 500)/10.4 = 0.38

For 516

z = (x - μ)/σ = (516 - 500)/10.4 = 1.54

To determine the required probability

P(504 ≤ x ≤ 516) = P(0.38 ≤ z ≤ 1.54)

We'll use data from the normal distribution table for these probabilities

P(504 ≤ x ≤ 516) = P(0.38 ≤ z ≤ 1.54)

= P(z ≤ 1.54) - P(z ≤ 0.38)

= 0.93822 - 0.64803

= 0.29019

C) Probability that a randomly selected study participant's response was more than 528 = P(x > 528)

We first normalize or standardize 528

z = (x - μ)/σ = (528 - 500)/10.4 = 2.69

To determine the required probability

P(x > 528) = P(z > 2.69)

We'll use data from the normal distribution table for these probabilities

PP(x > 528) = P(z > 2.69) = 1 - P(z ≤ 2.69)

= 1 - 0.99643

= 0.00357

D) Only the event in (c) is unusual as its probability is less than 0.05.

Hope this Helps!!!

Answer:

The expected value of the random variable with the given probability distribution = 12 .52

Step-by-step explanation:

Given data

 x    :   0         1            5       10     1000

p(x)  :  0.33  0.32   0.24     0.10    0.01

The expected value of the given random variable of given probability distribution

E(X)  =  ∑ x p ( X = x)

E(X)  =  0 × 0.33 + 1 × 0.32 + 5 × 0.24 + 10× 0.10 + 1000×0.01

E (X)  =  12.52

The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long  is 33.69 degrees

To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.

Given that:

The tree's height is 10 feet.

The length of the shadow is 15 feet.

Let's assume that the tree's height is "h"  feet.

Length of its shadow is represented by "s" feet

The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.

The angle can be determined using the tangent function.

[tex]tan\theta[/tex] = [tex]\dfrac{h}{s}[/tex]

Now, substitute the given values:

[tex]tan\theta[/tex]= [tex]\dfrac{10}{15}[/tex]

[tex]tan\theta[/tex] = [tex]\dfrac{2}{3}[/tex]

The angle of elevation can be obtained by  taking the inverse tangent of 2/3

angle of elevation =[tex]\tan^-1\dfrac{2}{3}[/tex]

angle of elevation ≈ 33.66 degrees

So, the angle of elevation of the sun is approximately 33.69 degrees.

Learn more about angle of elevation here:

https://brainly.com/question/31006775

#SPJ4

[tex]solution \\ x = 10 \\ now \\ (7x - 5) \\ = (7 \times 10 - 5) \\ = (70 - 5) \\ = 65[/tex]

Hope it helps....

Good luck on your assignment

Answer:

65

Step-by-step explanation:

= 7x-5

Putting x = 10

= 7(10)-5

= 70-5

= 65

Answer:

1/3 simplifed.

Step-by-step explanation:

To find the product of 3/7*7/9. We can multiply top and bottom. Top: 3*7=21 Bottom: 7*9=63. Our final answer is just the Top/Bottom= 21/63. We can also simplify this into 1/3 which is our final answer.

Answer:

A

Step-by-step explanation:

It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.

Answer:

A. G(x) = [tex]x^2+7[/tex]

Step-by-step explanation:

→For the function to shift upwards 7 units, 7 must be added to the function, like so:

G(x) = [tex]x^2+7[/tex]

→F(x) + c (in this case is 7), cases a vertical shift and the function is moved "c," units. The graph would shift downwards if 7 was being subtracted.

This means the correct answer is A.

Answer:

[tex] m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]

And replacing we got:

[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]

And we can use one of the points in order to find the intercept like this:

[tex] -3= \frac{2}{3} (-3) +b[/tex]

[tex] b =-3 +2=-1[/tex]

And the equation would be given by:

[tex] y= \frac{2}{3}x -1[/tex]

Step-by-step explanation:

We want an equation given by:

[tex] y=mx+b[/tex]

where m i the slope and b the intercept

We have the following two points given:

[tex] (x_1 = -3, y_1 =-3), (x_2=3, y_2 =1)[/tex]

We can find the slope with this formula:

[tex] m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]

And replacing we got:

[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]

And we can use one of the points in order to find the intercept like this:

[tex] -3= \frac{2}{3} (-3) +b[/tex]

[tex] b =-3 +2=-1[/tex]

And the equation would be given by:

[tex] y= \frac{2}{3}x -1[/tex]

Answer:

The slope of this curve where it meets the right pole is 1.130

The angle between the line and the right pole is 41.51 °

Step-by-step explanation:

Given that ;

[tex]y = 30 \ cos h (\dfrac{x}{15} - 4)[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{30}{15} sinh(\dfrac{x}{15})[/tex]

[tex]\dfrac{dy}{dx}=2 \ sinh(\dfrac{x}{15})[/tex]

x = 9 m;( i.e half of the distance of the two poles at 18 meters apart.

[tex]\dfrac{dy}{dx}=2 \ sinh(\dfrac{9}{15})[/tex]

= 1.130

The slope of this curve where it meets the right pole is 1.130

The angle between the line an the right rope can be determined by using the tangent of the slope .

tan ∝ = 1.130

∝ = tan⁻¹ (1.130)

∝ = 48.49°

The angle is θ; so

θ = 90 - ∝

θ = 90 - 48.49°

θ = 41.51 °

Thus; the angle between the line and the right pole is 41.51 °

Answer:

0.45

Step-by-step explanation:

9/20 is the same as 0.45

Answer:

0.45

Step-by-step explanation:

9/20= 9*5/20*5= 45/100= 0.45

Answer:

I think it is -2

Step-by-step explanation:

I think but I do not know

Answer:

35

Step-by-step explanation:

3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9

a+b=?

------

all numbers get cancelled apart from the first denominator and the last numerator:

1/2*a= 9

then

a+b= 18+17= 35

Answer:

The correct answer will be "0.400 gm".

Step-by-step explanation:

The give values are:

Needs of hospital, N = 0.100 gm

Time, t = 10 days

Minimum amount of Xenon, N₀ = ?

As we know,

⇒  [tex]N(t)=N_{0} \ e^{-\lambda t}[/tex]

∴  Decay constant, λ = [tex]\frac{ln2}{t_{1/2}}[/tex]

                                λ = [tex]\frac{ln2}{5}[/tex]

On putting values, we get

⇒  [tex]0.100=N_{0} \ e^{-\frac{ln2}{5}}\times 10[/tex]

⇒  [tex]0.1=N_{0} \ e^{-2ln2} = N_{0} \ e^{-ln4}[/tex]

⇒  [tex]0.1=N_{0} \ e^{ln\frac{1}{4}}[/tex]

⇒  [tex]0.1=\frac{N_{0}}{4}[/tex]

⇒  [tex]N_{0}=0.1\times 4[/tex]

⇒  [tex]MX_{e}=0.400 \ gm[/tex]

Answer:

The percentage of the employee will experience a lost-time accident in both years is 0.0%

Step-by-step explanation:

Let A denote events that employees suffered lost-time accidents during the last year

Let B denote events that employees suffered lost-time accidents during the current year

P(A) = 5% = 0.05

P(B) = 4% = 0.04

P(B | A) = 15% = 0.15

(a) P (A ∩ B) = P(B | A) × P(A)

= 0.15 × 0.05

= 0.0075

= 0.0 (1 decimal place)

The probability that an employee will experience a lost- time accident in both years is 0.0

Answer:

  24

Step-by-step explanation:

Let t represent the volume of the tank in gallons. Then we have ...

  (1/8)t + 15 = (3/4)t . . . . . . . . . . . adding 15 gallons fills the tank to 3/4

  15 = (6/8 -1/8)t = (5/8)t . . . . . . . subtract 1/8t

  15(8/5) = (8/5)(5/8)t . . . . . . . . . multiply by 8/5 (the inverse of 5/8)

  24 = t

The tank holds 24 gallons.

Answer:

8/9

Step-by-step explanation:

1 blue, 2 yellow, 7 red, 6 green, and 2 purple marbles = 18 marbles

The number that are not yellow = total - yellow

P( not yellow) = number that are not yellow / total

                       = (18-2) / 18

                       = 16/18

                       =8/9

Answer:

C. can have more than one factor, each with several treatment groups.

Step-by-step explanation:

A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.

Completely randomized design has found application in agricultural and environmental researches.

Answer:

Step-by-step explanation:

Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.

Thus , the parameter of the exponential distribution is calculated as,

μ = 6

[tex]\frac{1}{\lambda} =6[/tex]

[tex]\lambda = \frac{1}{6}[/tex]

a) The required probability is

[tex]P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}[/tex]

= 0.513

Hence, the probability that a randomly selected car battery will last more than four years is 0.513

b) The variance of the battery span is calculated as

[tex]\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36[/tex]

The 95% percentile [tex]x_{a=0.05}[/tex] (α = 5%) of the battery span is calculated

[tex]x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years[/tex]

c)  

Let [tex]X_r[/tex] denote the remaining life time of a car battery

i)the probability the battery will last an additional five years is calculated below

[tex]P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346[/tex]

ii) The average time that the battery is expected to last is calculated

[tex]E(X_r)=\frac{1}{\lambda} \\\\=6[/tex]

Answer:

  B = R/x -A

Step-by-step explanation:

  [tex]\text{Divide the equation by x:}\\\\\dfrac{R}{x}=A+B\\\\\text{Subtract A:}\\\\\dfrac{R}{x}-A = B\\\\\text{The solution is ...}\\\\\boxed{B=\dfrac{R}{x}-A}[/tex]

Answer:

[tex] b = \frac{r - ax}{x} \\ [/tex]

Step-by-step explanation:

[tex]r = x(a + b) \\ r = ax + bx \\ r - ax = bx \\ \frac{r - ax}{x} = b[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Step-by-step explanation:

We want to simplify the following expression:

[tex] \frac{a^3 b^2}{a^{-1} b^{-3}}[/tex]

And we can rewrite this expression using this property for any number a:

[tex] a^{-1}= \frac{1}{a}[/tex]

And using this property we have:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Answer:

x=-21

Step-by-step explanation:

x+12=-9

minus twelve on both sides

-9-12 equals -21

x=-21

Answer:

D: 13

I hope you understand, I am not that good at explaining. And I am not completely sure with my answer, but I think it's correct.

Answer:

Around 57.74 feet

Step-by-step explanation:

The tower and James form a right triangle, where the other two angles are 30 degrees and 60 degrees. The tangent of an angle is equivalent to the length of the opposite side divided by the length of the adjacent side, which means:

[tex]\tan 30=\dfrac{x}{100} \\\\x=\tan 30 \cdot 100 \approx 57.74[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

To find the average rate of change, find the change in function value, and divide that by the length of the interval.

1. ((g(1) -g(-1))/(1 -(-1)) = ((-4·1³ +4) -(-4(-1)³ +4)/(2) = (-8)/2 = -4

The average rate of change of g(x) on [-1, 1] is -4.

__

2. ((g(3) -g(-2))/(3 -(-2)) = ((6·3³ +3/3²) -(6·(-2)³ +3/(-2)²))/5

  = (6·27 +1/3 -6·(-8) -3/4)/5 = (2515/12)/5

  = 503/12 = 41 11/12

The average rate of change of g(x) on [-2, 3] is 41 11/12.

Answer:

Step-by-step explanation:

A graphing calculator shows there is one solution to ...

  [tex]\log_7{(3x^2+x)}-\log_7{(x)}=2[/tex]

However, the usual solution method would be to combine the logarithms and take the antilog to get ...

  [tex]\log_7{\left(\dfrac{3x^3+x}{x}\right)}=2\\\\\log_7{(3x^2 +1)}=2\\\\3x^2+1=7^2\\\\x^2=\dfrac{49-1}{3}=16\\\\x=\pm 4\qquad\text{take the square root}[/tex]

This gives two solutions. the "solution" x = -4 is extraneous, as it doesn't work in the original equation. "x" must be positive in the log expressions.

Answer:

x = - 4

Step-by-step explanation:

Got it right :)

Answer:

72°

Step-by-step explanation:

This is called an isosceles triangle. This means that the 2 angles related to the equal sides, are also equal. Hence, the answer is 72°

Answer:

A

Step-by-step explanation:

Since it is isosceles triangle (two equal sides) therefore, there are 2 equal angles too which at the base (72°)

The total angle of triange is 180°

So 180-72-72=36°

Answer:

10ft[tex]{3}[/tex]

Step-by-step explanation:

One face has 15 blocks of 1/3 ft. You can clearly see 2 sets of blocks.

15 x 2 = 30

30 ÷ 3 or 30 x 1/3

= 10 ft cubed

Answer:

A) 50 km : 45 km : 65 km

B) 18:45:3

Step-by-step explanation:

A) 160 km in the ratio 10:9:13

10:9:3 ⇔ 50 km : 45 km : 65 km

B) 66 in the ratio 6:15:1

6:15:1  ⇔ 18:45:3