In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.4 inches, and standard deviation of 4.1 inches.

A) What is the probability that a randomly chosen child has a height of less than 61.25 inches?

Answer= (Round your answer to 4 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 46.5 inches?

Answer= (Round your answer to 4 decimal places.)

Answers

Answer 1

(A)

P(X < 61.25) = P((X - 55.4)/4.1 < (61.25 - 55.4)/4.1)

… ≈ P(Z ≤ 0.1427)

… ≈ 0.5567

(B)

P(X > 46.5) = P((X - 55.4)/4.1 > (46.5 - 55.4)/4.1)

… ≈ P(Z > -2.1707)

… ≈ 1 - P(Z ≤ -2.1707)

… ≈ 0.9850


Related Questions

Which of the following is NOT equivalent to 22/7?
a) 2 + 8/7
b) 1 + 15/7
c) 3 (7/1) + 1/7
d) 3 (7/7) + 1/7

Answers

Answer:

the option c is the answer for this question

The stopping distance on wet pavement at 20mph is about 60feet. The stopping distance at 30mph is 120feet. What would you estimate the stopping distance is at 40mph? Construct a formula

Answers

Answer:

[tex]y = 6x - 60[/tex] --- formula

The stopping distance at 40mph is 180ft

Step-by-step explanation:

Given

[tex](x,y) = (20,60)[/tex]

[tex](x,y) = (30,120)[/tex]

Solving (a): Construct a formula

Calculate the slope (m)

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

[tex]m = \frac{120 - 60}{30-20}[/tex]

[tex]m = \frac{60}{10}[/tex]

[tex]m=6[/tex]

So, the equation is:

[tex]y = m(x - x_1) + y_1[/tex]

[tex]y = 6(x - 20) + 60[/tex]

Open bracket

[tex]y = 6x - 120 + 60[/tex]

[tex]y = 6x - 60[/tex]

Hence, the formula to use is: [tex]y = 6x - 60[/tex]

Solving (b): y, when x = 40

[tex]y = 6x - 60[/tex]

[tex]y = 6 * 40 - 60[/tex]

[tex]y = 180[/tex]

Use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. Then compare this with the actual change in cost.

Function x-Value
C=0.025x^2 + 3x + 4 x=10

dC= ___________
ΔC= __________

Answers

Answer:

dC=3.5

DC is between 3.475 and 3.525

Step-by-step explanation:

So let dx=1 since the change there is a change in 1 unit.

Find dC/dx by differentiating the expression named C.

dC/dx=0.05x+3

So dC=(0.05x+3) dx

Plug in x=10 and dx=1:

dC=(0.05×10+3)(1)

dC=(0.5+3)

dC=3.5

Let D be the change in cost-the triangle thing.

Since dx=1 we only want the change in unit to be within 1 in difference.

So this means we want it to be from x=9 to x=1] ot from x=10 to x=11.

Let's do from x=9 to x=10 first:

DC=C(10)-C(9)

DC=[0.025×10^2+3×10+4]-[0.025×9^2+3×9+4]

DC=[2.5+30+4]-[0.025×81+27+4]

DC=[36.5]-[2.025+31]

DC=[36.5]-[33.025]

DC=3.475

Now let's do from x=10 to x=11

DC=[0.025×11^2+3×11+4]-[0.025×10^2+3×10+4]

DC=[0.025×121+33+4]-[36.5]

DC=[3.025+37]-[36.5]

DC=[40.025]-[36.5]

DC=3.525

So DC, the change in cost where the change in unit is 1, is between 3.475 and 3.525.

What is the area of a triangle with a base of 9 units and a height of 7 units? O A. 15.75 sq. units O B. 126 sq. units O c. 63 sq. units O D. 31.5 sq. units SUBMIT வன் PREVIOUS​

Answers

Answer:

D. 31.5 sq. units

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

A = 1/2 ( 9)(7)

A = 63/2

A = 31.5 units^2

Step-by-step explanation:

For this, we'll use a formula for the area of a triangle.

Area (A) = ( Base (B) * Height (H) ) / 2

[tex]A = (B * H )/2[/tex]

Plug in given values.

[tex]A = (9*7)/2[/tex]

Multiply within parentheses.

[tex]A = (63)/2[/tex]

Divide by 2.

[tex]A = 31.5[/tex]

Answer:

D. 31.5 sq. units

A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events?

a. One out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.

Answers

Answer:

a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.

b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.

Step-by-step explanation:

For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

One out of four cars needs to have oil added.

This means that [tex]p = \frac{1}{4} = 0.25[/tex]

a. One out of the next four cars needs oil.

This is P(X = 1) when n = 4. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219[/tex]

0.4219 = 42.19% probability that one out of the next four cars needs oil.

b. Two out of the next eight cars needs oil.

This is P(X = 2) when n = 8. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115[/tex]

0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c.Three out of the next 12 cars need oil.

This is P(X = 3) when n = 12. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581[/tex]

0.2581 = 25.81% probability that three out of the next 12 cars need oil.

What is the squad root of 81

Answers

Answer:

[tex]9[/tex]

Step-by-step explanation:

Step 1:  Find the square root of 81

[tex]\sqrt{81}[/tex]

[tex]\sqrt{9*9}[/tex]

[tex]\sqrt{9^{2}}[/tex]

[tex]9[/tex]

Answer:  [tex]9[/tex]

Answer:

the square root of 81 is 9

A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence.

a. True
b. False

Answers

Answer:

a. True

Step-by-step explanation:

A series in the field of mathematics is defined as the operation of adding up or summation of infinitely many quantities of terms of a sequence.  In other words, it is the sum of the terms of the sequence provided.

Another way of defining a 'series' is it is list of numbers with the "addition" operations between the numbers.

Thus the answer is (a). True

What is the slope formula?

Answers

Answer:

D is your answer

Step-by-step explanation:

Answer:

Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx

Step-by-step explanation:

What is the domain of the relation described by the set of ordered pairs (-2,8), (-1,1) (0,0) (3,5), (4,-2)?

Answers

Step-by-step explanation:

(-2,-1,0,3,4) are the domain

(x,y)=(domain,range)

simply x components are the domain whereas y components are the range

find the exact value of tan -75​

Answers

the exact value of tan -75 can be found by finding the coterminal angle (285) and taking the tangent of that


(a). Find the value of log 216.

Answers

Answer:

2.334453751

Step-by-step explanation:

Press log on your Casio calculator (if you have one) and plug in 216, then close the parentheses!

PLEASE ANSWER I WILL GIVE BRAINLIEST FAST

Answers

Answer:

E &F

Step-by-step explanation:

The rules of a 30-60-90 Triangle is E, and F is just a different value of numbers (but the same ratio).

How do you know if a radical can be simplified? Explain.

Answers

Answer:

An expression is considered simplified only if there is no radical sign in the denominator. If we do have a radical sign, we have to rationalize the denominator . This is achieved by multiplying both the numerator and denominator by the radical in the denominator.

Answer quick please.

Answers

Answer

The Answer is A C D

Step-by-step explanation:

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=tcost, y=tsint, t=π

Answers

Step-by-step explanation:

the answer is in the image above

The angles in a triangle are 89, 1, and 90 degrees. Classify the triangle by its angles and sides.
A. Right isosceles
B. Right Scalene
C. Obtuse scalene
D. Acute isosceles
E. Acute scalene
F. Obtuse isosceles

Answers

Answer: B. Right Scalene

Step-by-step explanation: Right because one of the degrees is 90 and scalene because no of the sides of the triangle are the same length.

Answer:

b

Step-by-step explanation:

At the beginning of an experiment, a scientist has 120 grams of radioactive goo. After 135 minutes, her sample has decayed to 3.75 grams. Find an exponential formula for G ( t ) G(t) , the amount of goo remaining at time t t .

Answers

Answer:

[tex]G(t) = 120e^{-0.0257t}[/tex]

Step-by-step explanation:

Amount of substance:

The amount of the substance after t minutes is given by:

[tex]G(t) = G(0)e^{-kt}[/tex]

In which G(0) is the initial amount and k is the decay rate.

At the beginning of an experiment, a scientist has 120 grams of radioactive goo.

This means that [tex]G(0) = 120[/tex], so:

[tex]G(t) = G(0)e^{-kt}[/tex]

[tex]G(t) = 120e^{-kt}[/tex]

After 135 minutes, her sample has decayed to 3.75 grams.

This means that [tex]G(135) = 3.75[/tex].

We use this to find k. So

[tex]G(t) = 120e^{-kt}[/tex]

[tex]3.75 = 120e^{-135k}[/tex]

[tex]e^{-135k} = \frac{3.75}{120}[/tex]

[tex]\ln{e^{-135k}} = \ln{\frac{3.75}{120}}[/tex]

[tex]-135k = \ln{\frac{3.75}{120}}[/tex]

[tex]k = -\frac{\ln{\frac{3.75}{120}}}{135}[/tex]

[tex]k = 0.0257[/tex]

So

[tex]G(t) = 120e^{-0.0257t}[/tex]

Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 28. A pollster draws a sample of 92
people to interview.

Answers

Answer:

By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 41, standard deviation of 28:

This means that [tex]\mu = 41, \sigma = 28[/tex]

Sample of 92:

This means that [tex]n = 92, s = \frac{28}{\sqrt{92}} = 2.92[/tex]

Distribution of the sample means:

By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.

Which graph represents the function f (x) = StartFraction 5 minus 5 x squared Over x squared EndFraction? On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.

Answers

9514 1404 393

Answer:

2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3

Step-by-step explanation:

Technically, the curve is not a hyperbola. A hyperbola is of the form 1/x; this one is of the form 1/x².

The function can be simplified to ...

  f(x) = 5/x² -5

which is a "hyperbola" with a vertical asymptote at x=0 and a vertical translation of -5 units to bring parts of it into the 3rd and 4th quadrants.

You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x - 3y = 12
-x + 2y = 13
O A. Multiply the left side of equation 2 by 2. Then subtract the result from equation 1.
O B. Multiply equation 1 by 2 and equation 2 by 3. Then add the new equations.
C. Multiply equation 2 by-2. Then add the result to equation 1. ​

Answers

Answer:

A.

Step-by-step explanation:

The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.

If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.

If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.

When multiplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).

So, option B is not allowed (it is not allowed to multiply only one part of the equation)

ms.+sanchez+bought+3+pounds+of+turkey+to+make+sandwiches+for+her+family+.+She+uses+.25+of+a+pound+for+each+sandwich+.+How+many+sandwiches+can+she+make+?

Answers

Answer:

she can make 12 sandwiches

Step-by-step explanation:

3/.25 is the solution

Find the perimeter and area of a square with sides 6 inches in length.

Answers

Area is 36
And the perimeter is 24

Avi uses 11 toothpicks to form a row of 5 attached triangles, as shown. Suppose he continues this pattern, using 89 toothpicks in all. What is the total number of triangles formed? (sorry the picture wasn't uplodaing)

Answers

Answer:

44

Step-by-step explanation:

Given that Avi used 11 toothpicks to form a row of 5 attached triangles.

Total number of toothpicks used = 89

Let the total number of triangles formed be represented by x, so that:

11 toothpicks = 5 triangles

It would be observed that only the first triangle starting the pattern has 3 toothpicks. So that;

the average number of toothpicks for 1 triangle = [tex]\frac{11}{5}[/tex]

                                  = 2.2

The number of toothpicks per triangle = 2.0

Thus,

x = [tex]\frac{89}{2.0}[/tex]

  = 44.5

x = 44

The total number of triangles formed is 44.

Help? Thanks!!!!!!!!!!!

Answers

Answer:

A

Step-by-step explanation:

You can't really show work for this, but it's A because the angles are opposite each other.

Someone help me?????

Answers

Step-by-step explanation:

4. b 612 (72/100) x 850)

5. c. 275 (33/100) x 835

6. b. 39% (3.24 - 2.85) x100%)

A pyramid art installation has a surface area of 24 m2. An artist creates replicas with scale factors of 1/8, 1/10, and 1/12. What is the surface area of each replica?

Answers

Answer:

The replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.

Step-by-step explanation:

Given that a pyramid art installation has a surface area of 24 m2, and an artist creates replicas with scale factors of 1/8, 1/10, and 1/12, to determine what is the surface area of each replica, the following calculation has to be done:

24 x 1/8 = 3

24 x 1/10 = 2.4

24 x 1/12 = 2

Therefore, the replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.

Answer:

1/8 = 0.38 m^2

1/10= 0.24 m^2

1/12= 0.17 m^2

Step-by-step explanation:

The longest leg is Select one:

a. 5√3

b. 10√3

c. 5

d. 20

Answers

Answer:

D:20

sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20

Step-by-step explanation:

Didi invested a total of $16125 in two accounts paying 8.5% and 4% simple interest. If her total return at the end of 2 years was 1740 , how much did she invest in each account?

Answers

Answer:

5000 ;

11125

Step-by-step explanation:

Given :

Total principal = 16125

Rates = 8.5% and 4%

Period, t = 2 years

Total interest = 1740

Let :

Principal amount invested at 8.5% = x

Principal amount invested at 4% = 16125 - x

Interest formula :

Interest = principal * rate * time

Hence, mathematically ;

(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740

(0.17x + 1290 - 0.08x ) = 1740

0.09x + 1290 = 1740

0.09x = 1740 - 1290

0.09x = 450

x = 450 / 0.09

x = 5000

Amount invested at 4% :

16125 - 5000 = 11125

The diameter of a circle is inches what is the area?

Answers

Answer:

Pie( r ^2)

Step-by-step explanation:

Here value of r is in inches

For this exercise assume that the matrices are all nn. The statement in this exercise is an implication of the form​ "If "statement​ 1", then​ "statement 2"." Mark an implication as True if the truth of​ "statement 2" always follows whenever​ "statement 1" happens to be true. Mark the implication as False if​ "statement 2" is false but​ "statement 1" is true. Justify your answer.

If there is an n x n matrix D such that Ax =0​, then there is also an nxn matrix C such that CAI.

a. True
b. False

Answers

Answer:

A) True

Hope this helps!

Other Questions
La pizarra est ___ de la profesora Hernndez 3x+2y=4 4x+5y=10 solve the simultaneous equations (find x & y) this 2 pls i need help with explanation sum Question: Name the person who originally introduced the idea of patterns as a solution design concept. PLEASE HELP ME PLEASE AND BE CORRECT please help, its urgent ! :) . The Ksp of barium sulfate is 1.1 1010. What is the sulfate-ion concentration of a 1.0-L saturated solution of BaSO4 to which 0.025 mol of Ba(NO3)2 is added? 4.4 109M 1.0 105M 6.6 105M 2.8 1012M Which is f(5) for the function -2x^2+2x-3 Joe receives a cake for his birthday. He eats $\frac{1}{4}$ of the cake on the first day. On the second day, he eats $\frac{3}{4}$ of the amount of cake that is left after the first day. What fraction of a whole cake is left for Joe to eat on the third day I need a hang here anyone if anyone can help Dr. Miller is studying the effect of physiological stress on cognitive performance. To do this, he can either ask his subjects to endure mild temperature changes or painful electric shocks to evaluate how it affects their scores on brain teasers. If he is to be in compliance with the principle of protection from harm, Dr. Miller must: Where are spores located on a fern? 1. On the root systems 2. In the flowers of the ferns 3. On the underside of the fronds 4. In the capsule of the sporophyte How did Jane Addams try to improve the lives of poor immigrants? Each week CapeChem, a manufacturer of fine chemicals, uses up of Compound and of Compound in a reaction with only one product, Compound .What is the maximum theoretical mass of Compound that CapeChem could ship each week Which of the graphs below would result if you made the leading term of thefollowing function negative?F{x} = x + 3x2 A bed is 0.63 m wide, and a door frame is 0.70 m wide.By how much is the door frame wider than the bed? What is the slope of the line shown below? The equation of the line that goes through the point (10,8) and (3,-4) can be written in the form y=mx+bwhere m is:and where b is: Explain How a chloroplast helps a cell get the meterials it needs PLEASE HELP I WILL BE PICKING BRAINLIESTGiven the following equation where A = Area of a rectangle and w = width of the rectangle, what value of 'w' would maximize the area?A = LWP = 2L+2WP = 100w should be 625 unitsw should be 25 unitsw should be 0 unitsw should be 50 units