LSAT test scores are normally distributed with a mean of 152 and a standard deviation of 10. Find the probability that a randomly chosen test-taker will score 142 or lower. (Round your answer to four decimal places.)

Answer:

3.5 buckets per cow

Step-by-step explanation:

Given

[tex]Buckets = 7\ equal\ sized[/tex]

Required

Determine the rate per bucket per each cow

From the question, we understand that both cows produced same quantity of milk;

And since, they're are two cows

Milk produced by each cow is calculated by dividing number of buckets by 2; as follows;

[tex]Each\ cow = \frac{7}{2}\ buckets[/tex]

[tex]Each\ cow = 3.5\ buckets[/tex]

Hence, the rate is 3.5 buckets per cow

Answer:

See Explanation

Step-by-step explanation:

The question required attachment; however, follow the following steps to answer your question.

See Attachment

Considering the horizontal plane of the gird.

Count the number of the squares in that plane;

This gives 4

Multiply 4 by length of each side of a square;

[tex]Perimeter = 8mm * 4[/tex]

[tex]Perimeter = 32mm[/tex]

Answer:

Distance= 1

Step-by-step explanation:

Distance be points using polar coordinates

Distance= √(8² +9² -2(8)(9)cos(0.2-1.7)

Distance=√(64 + 81-(144)cos(-1.5))

Distance= √(145-143.9506)

Distance=√ 1.0493

Distance= 1.0243

Distance= 1

Answer:

Step-by-step explanation:

No; it is rational.  25/9 is the ratio of two integers.

Explanation:

We have a fraction of two integers, so 25/9 is rational. A rational number is any fraction of two integers (as long as the denominator is not zero).

Something that is irrational would be pi = 3.14159... where we cannot write it as a fraction of two integers. We can get approximations such as 22/7, but we cannot land exactly on pi with a fraction like this. Another irrational value is sqrt(2).

Something like sqrt(25) is rational though because sqrt(25) = 5 = 5/1.

Answer:

5w+11n

:D

Hope this helped!

My regards

Complete Question

A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4 pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci.

a) In testing the scientist's belief, write the appropriate hypotheses:

           [tex]H_o:[/tex]                   Ha:

b) What decision should be made?

Answer:

a

The null hypothesis is  [tex]H_o : \mu \le 4 \ pci[/tex]

The  alternative  hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]

b

There is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 4 \ pci[/tex]

    The sample size [tex]n = 36 \ days[/tex]

     The  sample  mean is  [tex]\= x = 4.4 \ pci[/tex]

     The  standard deviation is  [tex]\sigma = 1 \ pci[/tex]

       The  level  of significance is  [tex]\alpha = 0.05[/tex]

The null hypothesis is  [tex]H_o : \mu = 4 \ pci[/tex]

The  alternative  hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]

  Generally the test statistics is mathematically represented as

          [tex]t = \frac{ \= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]

=>      [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]

=>      [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]

=>      [tex]t =2.4[/tex]

The  p-value  is mathematically represented as

      [tex]p-value = P(Z > 2.4 )[/tex]

From the  z-table  

          [tex]P(Z > 2.4 ) = 0.008[/tex]

    [tex]p-value =0.008[/tex]

So from this obtained value  we see that

     [tex]p-value < \alpha[/tex] so we reject the null hypothesis

Hence we can conclude that there is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less

Answer:

7 seconds

Step-by-step explanation:

The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second.

surface area of the completely inflated balloon is 784 cm²

SA=4r²

784= 4r²

784/4= r²

196 = r²

14cm = r

Yhe radius of the complete inflated balloon is 14cm

If the ball inflate at the rate of 2 cm per seconds

Then it took 14/2 = 7 seconds to inflate fully

Answer:

1012

Step-by-step explanation:

The ratio of student / applicant is 6 /11

So for 552 students, the applicants number is:

Number of applicants is 1012

Hello, let's  note a the positive real number.

A positive real number is 4 less than another.

So, the other number is a - 4

When 8 times the larger is added to the square of the smaller, the result is 96.

So, we need to solve the following equation.

[tex]8a+(a-4)^2=96[/tex]

Let's do it!

[tex]8a+(a-4)^2=96\\\\8a+a^2-8a+16=96\\\\a^2=96-16=80=4^2*5\\\\a=\pm4\sqrt{5}[/tex]

As a is positive, there is only one solution which is.

[tex]\Large \boxed{\sf \bf \ \ a=4\sqrt{5} \ \ }[/tex]

Thank you.

The amount given by the sum of numbers can be presented in an equation

form from which the value of each number can be obtained.

The large number is 4·√5, the smaller number is 4·(√5 - 1)

Reason:

Let x represent the large number, we have;

The smaller number = x - 4

8 × x + (x - 4)² = 96

8·x + (x - 4)² = 96

Required:

The values of the numbers

Solution:

8·x + (x - 4)² = 8·x + x² - 8·x + 16 = 96

8·x - 8·x + x² + 16 = 96

x² + 16 = 96

x² = 96 - 16 = 80

x = ±√(80) = ±4·√5

Given that the numbers are positive, we have;

The large number, x = 4·√5

The smaller number = x - 4 = 4·√5 - 4

The smaller number = 4·√5 - 4 = 4·(√5 - 1)

Learn more here:

https://brainly.com/question/24676383

Answer:

The first blank is 6.

The second blank is 7.

Step-by-step explanation:

The square root of 41 is between 6 and 7.

6 square is 36

7 square is 49.

So, the square root of 41 should be between 6 and 7.

The first blank is 6.

The second blank is 7.

Answer:

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

Step-by-step explanation:

Simplify the following:

-(2 x^2 - 3 x^3 + 1) - x^3 + 4 x + 3

Factor -1 out of -3 x^3 + 2 x^2 + 1:

--(3 x^3 - 2 x^2 - 1) - x^3 + 4 x + 3

(-1)^2 = 1:

3 x^3 - 2 x^2 - 1 - x^3 + 4 x + 3

Grouping like terms, 3 x^3 - x^3 - 2 x^2 + 4 x - 1 + 3 = (-x^3 + 3 x^3) - 2 x^2 + 4 x + (3 - 1):

(-x^3 + 3 x^3) - 2 x^2 + 4 x + (3 - 1)

3 x^3 - x^3 = 2 x^3:

2 x^3 - 2 x^2 + 4 x + (3 - 1)

3 - 1 = 2:

2 x^3 - 2 x^2 + 4 x + 2

Factor 2 out of 2 x^3 - 2 x^2 + 4 x + 2:

Answer: 2 (x^3 - x^2 + 2 x + 1)

Answer:

Step-by-step explanation:

4x - x^3 + 3 - 2x^2 + 3x^3 - 1

2x^3 - 2x^2 + 4x + 2 is the solution

Answer:

12+40= 52

180-52=128

Step-by-step explanation:

Angles in a triangle add up to 180

so if two sides are given , they must be added and subtracted from 180.

which gives us 180-52=128

Answer:

the angle is 128°

the right answer is C

Step-by-step explanation:

the angles of a triangle are always 180°

thus

the angle of the the triangle = 180° - (12°+40°)

= 180- 52° = 128°

Answer:

h=3

Step-by-step explanation:

-9h= - 27

Divide each side by -9

-9h/-9= - 27/-9

h = 3

Answer:

h = 3

Step-by-step explanation:

Step 1: Divide both sides by -9

[tex]\frac{-9h}{-9} =\frac{-27}{-9} \\h=3[/tex]

Therefore the h = 3

Answer:

y = x

Step-by-step explanation:

The inverse of f(x) = x is just y = x.

Answer:

27, it is divisible by 1, 3, 9, and 27

Step-by-step explanation:

the answer to your question is x= -2

Answer: 0

============================================

Explanation:

When we multiply 0 by any number, we get 0 as a result

x*0 = 0

0*x = 0

for any number x.

The number 0 is rational since we can write it as a fraction of two integers

0 = 0/1

If Daniel were to correct his statement to say "multiply by any nonzero rational number", then his statement would be correct that the result is irrational.

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

Extra info:

Here's a proof showing why Daniel's claim is correct if we consider nonzero rational numbers

Let p be a nonzero rational number, so p = a/b for integers a,b where neither a or b are zero

Let q be an irrational number. We cannot write q as a ratio of two integers

The claim is that p*q is irrational. For now let's assume the opposite. So assume p*q is rational. This means p*q = r/s for integers r,s

This would be the same as (a/b)*q = r/s which solves to q = (r/s)*(b/a) = (rb)/(sa) making q rational, but that contradicts the fact we made q irrational earlier.

Therefore, the assumption p*q is rational cannot be the case, and p*q must be irrational.

Answer:

the number of weeks the bird feeders are filled

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Just took the review

Answer:

[tex]\sin 2x = \frac{24}{25}[/tex] , [tex]\cos 2x = \frac{7}{25}[/tex], [tex]\tan 2x = \frac{24}{7}[/tex]

Step-by-step explanation:

The sine, cosine and tangent of a double angle are given by the following trigonometric identities:

[tex]\sin 2x = 2\cdot \sin x \cdot \cos x[/tex]

[tex]\cos 2x = \cos^{2}x -\sin^{2}x[/tex]

[tex]\tan 2x = \frac{2\cdot \tan x}{1-\tan^{2}x}[/tex]

According to the definition of sine function, the ratio is represented by:

[tex]\sin x = \frac{s}{r}[/tex]

Where:

[tex]s[/tex] - Opposite leg, dimensionless.

[tex]r[/tex] - Hypotenuse, dimensionless.

Since [tex]x[/tex], measured in sexagesimal degrees, is in third quadrant, the following relation is known:

[tex]s < 0[/tex] and [tex]y < 0[/tex].

Where [tex]r[/tex] is represented by the Pythagorean identity:

[tex]r = \sqrt{s^{2}+y^{2}}[/tex]

The magnitude of [tex]y[/tex] is found by means the Pythagorean expression:

[tex]r^{2} = s^{2}+y^{2}[/tex]

[tex]y^{2} = r^{2}-s^{2}[/tex]

[tex]y = \sqrt{r^{2}-s^{2}}[/tex]

Where [tex]y[/tex] is the adjacent leg, dimensionless.

If [tex]s = -3[/tex] and [tex]r = 5[/tex], the value of [tex]y[/tex] is:

[tex]y = \sqrt{(5^{2})-(-3)^{2}}[/tex]

[tex]y = -4[/tex]

Then, the definitions for cosine and tangent of x are, respectively:

[tex]\cos x = \frac{y}{r}[/tex]

[tex]\tan x = \frac{s}{y}[/tex]

If [tex]s = -3[/tex], [tex]y = -4[/tex] and [tex]r = 5[/tex], the values for each identity are, respectively:

[tex]\cos x = -\frac{4}{5}[/tex] and [tex]\tan x = \frac{3}{4}[/tex].

Now, the value for each double angle identity are obtained below:

[tex]\sin 2x = 2\cdot \left(-\frac{3}{5} \right)\cdot \left(-\frac{4}{5} \right)[/tex]

[tex]\sin 2x = \frac{24}{25}[/tex]

[tex]\cos 2x = \left(-\frac{4}{5} \right)^{2}-\left(-\frac{3}{5} \right)^{2}[/tex]

[tex]\cos 2x = \frac{7}{25}[/tex]

[tex]\tan 2x = \frac{2\cdot \left(\frac{3}{4} \right)}{1-\left(\frac{3}{4} \right)^{2}}[/tex]

[tex]\tan 2x = \frac{24}{7}[/tex]

Answer:

$48.76

Step-by-step explanation:

So, Sara bought the pair of shoes for $46 due to a discount.

Sales tax was 6% or 0.06. In other words, she had to pay 0.06(46)=2.76 for tax.

Thus, the total amount Sara paid for the shoes is $46+$2.76=$48.76

Answer:

p = -14

Step-by-step explanation:

5/7p - 2/7p + 12 = 6

Combine like terms

3/7 p +12 = 6

Subtract 12 from each side

3/7p + 12-12 = 6-12

3/7p = -6

Multiply each side by 7/3

7/3 * 3/7p = -6*7/3

p = -14

Answer:

p = - 14

Step-by-step explanation:

5/7p - 2/7p + 12 = 6

subtract 12 both sides

5p/ 7 - 2p/7  + 12  = 6 - 12

simplify

5p/7 - 2p/7 = -6

multiply both side by 7

5p/7 * 7    -    2p/7 * 7     =  -6 * 7

simplify

5p - 2p = -42

p = -42 / 3

p = - 14

Answer:

5/3 cup(s)

Step-by-step explanation:

Meghan needs 5/3 cups of strawberries to make 2 fruit salads and 2 fruit smoothies.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Need of cup of strawberries for making  one fruit salad recipe = 1/6,

And need of cup of strawberries for making one fruit smoothie recipe = 2/3.

To make 2 fruit salads,

Need of cup of strawberries = 2 x 1/6 = 1 / 3

To make 2 fruit smoothies,

Need of cup of strawberries = 2 x 2/3 = 4/3

Total number of cups of strawberries = 1/3 + 4/3 = 5/3

Meghan needs 5/3 cups of strawberries.

To learn more about Ratio on :

https://brainly.com/question/13419413

#SPJ2

Answer:

28th floor........

Step-by-step explanation:

...

Answer:

28

Step-by-step explanation:

current position: 9

down 4 floors: 9-4 = 5

up 7 floors: 5+7 = 12

up 8 floors: 12+8 = 20

up 8 floors: 20+8 = 28

Answer: D) 2

the value for the missing mean would result in no main effect for Factor A is 2

Step-by-step explanation:

Given that;

              B1             B2

A1            6               8          

B1            12               ?

To find the missing mean;

lets missing mean be x

Here mean of A1

( 6 + 8 ) / 2 = 14 / 2 = 7  

Now mean of A2

(12 + x ) / 2 = 7

x + 12 = 14\x = 14 -12 = 2

Therefore the value for the missing mean would result in no main effect for Factor A is 2

so option d) is the correct answer

Answer:

b

Step-by-step explanation:

Answer:

10,800 feet

Step-by-step explanation:

1000 * 10.8 because there are 1000 cars each 10.8 feet long

Answer:

C 1 to 11

Step-by-step explanation:

When rolling 2 dice, there are 36 possible outcomes.

The outcomes that have a sum of 10 are:

4, 6

5, 5

6, 4

There are 3 outcomes of 10 and 33 outcomes of not 10.

Odds of outcome of 10:

3:33 = 1:11

1 to 11 is the odds in favor of rolling the sum of 10 when rolling a pair of dice option (C) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

A standard dice is rolled:

The total number of outcomes(two dice are rollling) = 6x6 = 36

The outcomes that have a sum of 10 = ({4, 6}, (5, 5), (6, 4)}

The total number of outcomes = 3

Total outcomes(after removing 3 outcomes that have a sum of 10)

= 36 - 3 = 33

Odds of outcomes = 3

The odds in favor = 3/33 = 1/11 or 1 to 11

Thus, 1 to 11 is the odds in favor of rolling the sum of 10 when rolling a pair of dice option (C) is correct.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

Answer:

Step-by-step explanation:

The formula for calculating the margin of error is expressed as shown;

Margin of error = Z * S/√n

Z is the z-score at 95% confidence interval = 1.96

S is the standard deviation = 50

n is the sample size = 100

Substituting this values into the formula above;

Margin of error = 1.96 * 50/√100

Margin of error = 1.96 * 50/10

Margin of error = 1.96 * 5

Margin of error = 9.8

Hence the margin of error is 9.8

Answer:

b. 3/1    c. -1/3

Step-by-step explanation:

When a line is parallel to another they don't intersect and instead go in the same direction. Therefore they have the same slope

b. 3/1

When a line is perpendicular it has to be the negative reciprocal. This means that it you have to flip the numbers in the fraction and make it negative (unless it is already negative, then it becomes positive)

c. -1/3

Step-by-step explanation:

ultimately you need to end up with 30% solution

with 10%, 20%, and 50%, you are forced to tamper with the various percentages to reach the desired goal.

Since it is an even 12,000 (i.e. no 12500) and you have no hard container volumes to deal with, therefore find the easiest combination to reach 30%. In this case, (10%+50%)/2 = 30%

So therefore you need 12000 cubic centimeters of liquid, half of it being 50% and half being 10%.

12000/2 = 6000 cubic centimeters each

for 50%, each container is 1,000 cubic centimeters, so 6000/1000 =6 containers  for 10% each container is 500 cubic centimeters, so 6000/500 = 12 containers

Therefore, you need 6 containers of 50% solution and 12 containers of 10% solution.

Answer:

to much numbers

Step-by-step explanation: