A lab found that 670 rats could run through a maze in a mean time of 4.7 seconds. What is the 99% confidence interval for the population mean? Use the formula for margin of error: z•σ/√n. Please explain each step, particularly how to find the population standard deviation.

Answers

Answer 1

Using the formula for margin of error as

MOE = z * σ / √n

would be very difficult since we are not given the value of the standard deviation. Standard deviation value must be given since it is obtained from the experiment.

However, we use another formula for MOE in the form of:

MOE = z sqrt [p (1 – p) / n]

where p is the proportion at 99% confidence interval at z crit value. From the standard distribution tables, this corresponds to a p value of:

z crit = 2.58

p = 0.9951

Therefore the margin of error is:

MOE = 2.58 sqrt [0.9951 (1 – 0.9951) / 670]

MOE = 6.96 x 10^-3 = 0.00696 s

We can see that at 99% Confidence interval, the Margin of Error is extremely small (almost 0). For the sake of calculation:

Confidence interval = 4.7 s ± 0.00696 s

Confidence interval = 4.69304, 4.70696

Related Questions

How to find the midpoint formula

Answers

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 6}}\quad ,&{{ -1}})\quad % (c,d) &({{ -3}}\quad ,&{{ -13}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{-3+6}{2}~,~\cfrac{-13-1}{2} \right)[/tex]

and fairly sure you know how much that is.

The perimeter of a rectangle is 120 feet. The ratio of the width to the length is 2:3. Find the length and width.

Answers

Since the ratio of width to length is 2:3, that is a total of 5 parts.
Multiply this by 2 (P = 2L + 2W) = 10 parts.
120/10 = 12
Each part = 12
W:L

12*2:12*3 = 24:36

CHECK

2(24) + 2(36) ??=?? 120

48 + 72 ??=?? 120

120 = 120 checks

Length = 36 ft
Width = 24 ft

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Line A passes through points (-1, 5) and (3, -1). Line B passes through points (7, 2) and (6, -1). At what point does line A intersect line B?

Answers

Line A
slope = (-1 - 5)/(3+1) = -6/4 = -3/2
y = mx + b
5 = -3/2(-1) + b
b = 5 - 3/2
b = 7/2
equation of line A: y = -3/2x + 7/2

Line B
slope = (-1 - 2)/(6-7) = -3/-1 = 3
y = mx + b
2 = 3(7) + b
b = 2- 21
b = - 19
equation of line B: y = 3x -19

line A intersect line B when -3/2x + 7/2 = 3x -19
so
-3/2x + 7/2 = 3x -19
3x + 3/2x = 19 + 7/2
9/2x = 45/2
x = (45/2) * (2/9)
x = 5

y = 3x - 19 = 3(5) -19 = 15 -19 = -4

(5 , -4)

answer
line A intersect line B at (5, -4)

A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24Â°. find the height of the tree to the nearest meter.

Answers

Final answer:

Using the trigonometric tangential function, the height of the tree casting a 26-meter shadow at an angle of elevation of 24° is approximately 11 meters.

Explanation:

The given problem can be solved by applying trigonometric principles, specifically the tangent function. In this case, we know the shadow length (26m) and the angle of elevation of the sun (24°). The height of the tree is the side opposite the angle, and the shadow is the adjacent side. Thus, we can use the tangent equation (Tan θ = Opposite/Adjacent). So, Tan 24° = Height of the tree / 26m. By cross multiplying and evaluating Tan 24°, we get the height of the tree to be approximately 11 meters.

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To which subset of real numbers does -18 not belong?

Answers

The subsets of the real numbers are the irrational numbers, rational numbers, integers, whole numbers, and the natural numbers. First, figure out where does -18 belong? Well, -18 is a rational number because it can be expressed as a fraction of two integers. It's also an integer.

So, it doesn't belong in the sets of irrational numbers, whole numbers, and the natural numbers.

We have that the -18 is a rational quantity due to the fact it can be expressed as a fraction of two integers. It's additionally an integer.

Rational number & Integer

Real numbers

Generally

The subsets of the actual numbers are as follows

Irrational numbersRational numbersWhole numbersNatural numbers etc

-18 is a rational quantity due to the fact it can be expressed as a fraction of two integers. It's additionally an integer.

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A ramp 24 ft long rises to a platform that is 20 ft off the ground. find x , the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.

Answers

[tex]sin(x)= \frac{BC}{AC}= \frac{20}{24} \approx 0.8333 \ \ \to \ \ x\approx56.4^o[/tex]

Final answer:

To determine the angle of elevation x, we use the sine function with the opposite side (20 ft) and the hypotenuse (24 ft) to get sin(x) = 20/24, and by taking the arcsin of the result, we find that x ≈ 56.4° when rounded to the nearest tenth of a degree.

Explanation:

To find x, the angle of elevation of the ramp, we can use trigonometric functions. Since we have the length of the ramp (hypotenuse) and the height of the platform (opposite side) in a right-angled triangle, we can use the sine function, which is defined as the ratio of the opposite side to the hypotenuse.

Using the sine function: sin(x) = opposite/hypotenuse = 20/24.

We first calculate the ratio: sin(x) = 20/24 = 0.8333.

To find the angle x, we take the inverse sine (also known as arcsine) of the ratio: x = arcsin(0.8333).

Using a calculator set to degree mode, we find that x ≈ 56.4° when we round to the nearest tenth of a degree.

In two supplemantary angles, the measure of one angles is 6 more than the twice the measure of the other.the measure of these two angles are

Answers

Answer:
________________________________________________________
The measurements of the 2 (TWO) supplementary angles are:
________________________________________________________
           58° and 122° .
________________________________________________________
Explanation:
_________________________________________________
Two supplementary angles:
_________________________________________________
Angle 1: "x:
_________________________________________________
Angle 2: "(6 + 2x)"
_________________________________________________
        All supplementary angles, by definition, add up to 180 degrees, so given that the 2 (two) angles are supplementary:

(x) + (6 + 2x) = 180 ; Find "x" and "(6 + 2x)" .
__________________________________________________
   x + 6 + 2x = 180 ;

      3x + 6 = 180 ;

   Subtract "6" from each side of the equation ;
___________________________________________________
      3x + 6 − 6 = 180 − 6 ;

          3x = 174 ;
___________________________________________________
Divide each side of the equation by "3" ;
to isolate "x" on one side of the equation ; and to solve for "x" ;

          3x / 3 = 172 / 3 ;

               x = 58 ;
________________________________________________
So:
________________________________________________
Angle 1: "x" : x = 58 .
________________________________________________
Angle 2: "(6 + 2x)" =  " 6 + 2(58) = 122 .
________________________________________________
122 + 58 =? 180 ? Yes!
________________________________________________
So, the measurements of the 2 (TWO) supplementary angles are:
           58° and 122° .
________________________________________________

Which value of m will create a system of parallel lines with no solution?

y = mx – 6

8x – 4y = 12

Answers

M=2. Hope this helps!

Answer:

answer is D ;)

Step-by-step explanation:

How did Greek mathematician Pythagoras come up with the Pythagorean Theorem. Explain

Answers

The theorem was known to the Babylonians and Indians long before Pythagoras's time. However it is thought That the Greek Pythagoras was the first to construct a proof of the theorem, that,s why it was named after him.

I'm having a bit of trouble, could you help?

Answers

Terms & Definitions:
-5-(3^2+2)=-16,
2^2-3*6=-14,
-2+4*3^2-6=28
5+4^2/2(3)=29

Evaluate: 12-6+(14-8)^2=42

not sure which youre having trosuble with so im gonna go with everything.

-5-(3^2 + 2)
= -5 - 9 -2
= -16
= D

2^2 - 3 × 6
= 4- (3 × 6) <==== principle of BODMAS
= -14
= C

-2 + (4×3^2) -6
= -2 + 36 - 6
= 28
= A

so the next answer is obviously B

Question 2.
12-6+(14-8)^2
= 6 + 6^2
= 6 + 36
= 42

The difference between the squares of two consecutive numbers is 23. what are the two numbers?

Answers

(x+1)^2-x^2=23

x^2+2x+1-x^2=23

2x+1=23

2x=22

x=11

11^2 = 121

x+1 =12

12^2=144

144-121 = 23

It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own

Answers

It would take Brian 20 hours to build the model car on his own.

To determine the time it would take Brian to build the model car on his own, we can follow these steps:

1. Let's denote the time it takes John to build the model car as J hours.

2. Since it takes Brian 15 hours longer than John, we can express the time it takes Brian as J +15 hours.

3. If they work together, they can build the model car in 4 hours. This means that in 1 hour, they complete [tex]$\frac{1}{4}$[/tex] of the job together.

4. In 1 hour, John completes [tex]$\frac{1}{J}$[/tex] of the job, and Brian completes [tex]$\frac{1}{J + 15}$[/tex] of the job.

5. So, the equation representing the rate at which they work together is:

[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]

6. Now, we solve this equation to find J, the time it takes John to build the model car on his own.

7. Once we find J, we can find J+15 which represents the time it takes Brian to build the model car on his own.

So, the equation representing the rate at which they work together is:

[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]

To solve this equation, we can multiply both sides by the least common denominator, which is [tex]$ 4J(J + 15) $[/tex], to clear the fractions:

[tex]\[ 4(J + 15) + 4J = J(J + 15) \][/tex]

Expanding and simplifying:

[tex]\[ 4J + 60 + 4J = J^2 + 15J \]\[ 8J + 60 = J^2 + 15J \]\[ J^2 + 15J - 8J - 60 = 0 \]\[ J^2 + 7J - 60 = 0 \][/tex]

Now, we have a quadratic equation. We can solve this equation using factoring, completing the square, or the quadratic formula. Let's use factoring:

[tex]\[ (J - 5)(J + 12) = 0 \][/tex]

Setting each factor equal to zero:

[tex]\[ J - 5 = 0 \] or $ J + 12 = 0 $[/tex]

Solving each equation:

[tex]For $ J - 5 = 0 $, we get $ J = 5 $.For $ J + 12 = 0 $, we get $ J = -12 $.[/tex]

Since time cannot be negative, we discard the negative solution.

Now that we have found J=5 hours, which represents the time it takes John to build the model car on his own, we can find [tex]$ J + 15 = 5 + 15 = 20 $[/tex] hours.

Jack's birthday is in 4 weeks. How many days is it until Jack's birthday? describe how you could use a number line to solve.

Answers

To determine how many days is it until Jack's birthday, we need a conversion factor to convert from weeks to days. We know, as a fact, that in one week there will be 7 days. So, we use this value. We do as follows:
4 weeks ( 7 days / 1 week ) = 28 days until Jack's day

what is the simplified form of (6^2+4)-15

Answers

First solve the parentheses and you get 36+4 which is 40 and then subtract 15 so you get 25

A student has some 1 and 5 bills in his wallet. he has a total of 14 bills that are worth 50 how many of each type of bill does he hae

Answers

x = ones

y = fives

x+y = 14 total bills

rewrite as x = 14-y

1x +5y = 50

1(14-y) +5y = 50

14-1y +5y = 50

14 +4y = 50

4y = 36

y = 36/4 = 9

x = 14-y = 14-9 = 5

9+5 = 14

9x5 = 45 +5x1 = 50

he had 9 fives and 5 ones

Answer:

There were 5 bills of '1' and 9 bills of '5'.

Step-by-step explanation:

let the number of '1' bill be x

let the number of '5' bill be y.

Total number of bills = 14

x + y = 14 ..[1]

Worth of 14 bills = 50

So,[tex]x\times 1+y\times 5=\$50[/tex]

[tex]x+5y=50[/tex]..[2]

x + y = 14

x = 14 - y

Putting value of x in [2]:

[tex]14- y +5y=50[/tex]

[tex]y=\frac{50-14}{4}=9[/tex]

y = 9

x = 14-y = 14 - 9 = 5

There were 5 bills of '1' and 9 bills of '5'.

What is the graph of the function?

f(x) = 2x 2

Answers

The function given is f(x)=2x²

Check the coordinate of y when x=0 ⇒ f(0)=0
Check the coordinate of x when y=0 ⇒ x=0

We have two pairs of coordinate, (0, 0) and (0, 0)

The first two graphs have these coordinates so we need to do further checking

take x=1 ⇒ f(1) = 2(1)² = 2
take x=2 ⇒ f(2) = 2(2)² = 8

we have two pairs of coordinates; (1, 2) and (2, 8)

The correct answer is OPTION A

Answer:

For f(x)=2x² graph, the answer is A.

Step-by-step explanation:

For x = -2; y = 8For x = -1; y = 2For x = 0; y = 0For x = 1; y = 2For x = 2; y = 8

Complete the statement f(3) is

Answers

f(3) is asking us "What output do I get with 3 as the input?". Looking at the Domain (all possible inputs) we see that 3 is indeed a possible input so that part is ok. Checking the Range (all possible outputs) we see that an input of 3 gives one and only one output (incidentally since this is true of all inputs, this is a function in 'x'). The only output that we get with an input of 3 is -1.

The corresponding output for an input value of 3 is -1. Hence f(3) is -1

from the mapping function given, the domain values are the input values of the function while the range is the output.

To get the value of f(3), we need to check the corresponding output when the input variable is 3.

From the given one-on-one mapping, we can see that the corresponding output for an input value of 3 is -1. Hence f(3) is -1

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All right triangles with the same acute angle θ are

Answers

All right triangles with the same acute angle θ are SIMILAR

How do you write 5/100 in decimal form?

Answers

.05

You just move the decimal place back, twice.

5/100...." / " means divide.....
so 5 divided by 100 = 0.05 <==

A set of n = 15 pairs of X and Y scores has SSX = ...A set of n = 15 pairs of X and Y scores has SSX = 10,SSY = 40, and SP = 30. What is the slope for the regression equation for predicting Y from X?

Answers

This question is asking only for the slope of the regression equation. This slope can be easily calculated using the following rule:
slope = SP / SSx

Examining the givens, we will find that both parameters are given where:
SP = 30 and SSx = 10

Substituting with the givens in the above mentioned equations, we can calculate the slope as follows:
slope = 30 / 10 = 3

A basketball is thrown with an initial upward velocity of 23 feet per second from a height of 7 feet above the ground. The equation h=−16t2+23t+7h=−16t2+23t+7 models the height in feet t seconds after the basketball is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop? Select one: a. 1.29 seconds b. 1.44 seconds c. 1.70 seconds

Answers

10=-16t^2+23t+7 subtracting the right side from both sides

16t^2-23t+3=0 using the quadratic formula

t=(23±√337)/32, since we are looking for the larger value of t, as the ball in returning downward...

t=(23+√337)/32

t≈1.29 seconds

Final answer:

Given the provided motion physics model and using the quadratic formula, it is determined that it would take approximately 3.79 seconds for the basketball to go into the hoop after it was thrown.

Explanation:

The subject in consideration here is a problem related to quadratic equations in motion physics. The equation given in the question signifies a model of the height of the basketball as a function of time in the format of a quadratic equation. The equation is h = -16t² + 23t + 7.

With this equation, we can apply the quadratic formula to find the amount of time it takes for the ball to reach the hoop.

Upon using the quadratic formula, two solutions come up, t = 3.79 s and t = 0.54 s. The ball is at a height of 10 m at two times during its trajectory—once on the way up (as it rises) and once on the way down (as it falls). Since the question is about the time the ball goes into the hoop after reaching its maximum height and coming down, the larger value of t (3.79s) is considered as the valid solution.

Therefore, the time it takes for the basketball to go into the hoop after it was thrown is approximately 3.79 seconds which is not an offered option.

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1) 8k-(6k-4)=10 show work please

2) -12x+8+5x=36 show work please

3) -2y+4=8y-6

Answers

1) 8k - (6k - 4) = 10

[tex]\mathsf{8k-6k+4=10}\\\\ \mathsf{2k=10-4}\\\\ \mathsf{2k=6}\\\\ \underline\mathsf{k=\dfrac{6}{2}=3}}[/tex]

2) -12x + 8 + 5x = 36

[tex]\mathsf{-12x+8+5x=36}\\\\ \mathsf{-12x+5x=36-8}\\\\ \mathsf{-7x=28}\\\\ \mathsf{x={28}{-7}}\\\\ \underline{\mathsf{x=-4}}[/tex]

3) -2y + 4 = 8y - 6

[tex]\mathsf{-2y+4=8y-6}\\\\ \mathsf{-2y-8y=-6-4}\\\\ \mathsf{-10y=-10}\\\\ \mathsf{y=\dfrac{-10}{-10}}\\\\ \underline{\mathsf{y=1}}[/tex]

A board is 27 inches long. How long is the board in centimeters? Use the following conversion: 1 inch is 2.54 centimeters.

Answers

1 inch = 2.54 cm

so multiply 27 by 2.54

27 x 2.54 = 68.58 cm long

To convert 27 inches to centimeters, multiply 27 by the conversion factor of 2.54 cm per inch, resulting in 68.58 centimeters.

The student has asked how long a board that is 27 inches long is in centimeters, given the conversion factor that 1 inch is equal to 2.54 centimeters. To convert inches to centimeters, you multiply the length in inches by the conversion factor. In this case, you would multiply 27 inches by 2.54 to find the length in centimeters.

Here is the calculation:
27 inches x 2.54 cm/inch = 68.58 centimeters.

Therefore, a board that is 27 inches long is 68.58 centimeters long.

which description matches the transformations y=cosx undergoes to produce y= -2cos3x

A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis
B. reflection through the y-axis, vertical shift of 2 units, horizontal shift right by 3 units
C.Horizontal shift 2 units, then vertical shift up by 3 units
D.Horizontal stretch by factor 2, reflection through the x-axis, then the vertical stretch by factor 3

Answers

the 3 before the x causes a horizontal compression , the -2 causes a vertical stretch followed by reflection in x axis. Its A

Answer: A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis

Step-by-step explanation:

Since, If there is a function, y= a cos bx

Then a shows vertical stretch while b shows horizontal compression.

Here, Given function, y= cos x

After transformation, It is giving y = -2 cos 3x

therefore here is a horizontal compression occurs with factor 1/3.

Also Negative sign shows there also did reflection through x-axis.

And, It also, stretched vertically by factor 2. ( also shown in the below graph)

Thus, Option A) is correct.

Create a set of numbers where the mode is equal to 10 the median is equal to 12 and the average is 12.

Please I really need help!

Answers

10,10,10,12,13,14,15

MEDIAN: 12
MODE: 10
MEAN: 12

mean 12 because it's the average so you have to add the data set all up and divided by the numbers that are in the data set like 84 divided 7 which is 12, your answer.

Solve −2x2 +3x − 9 = 0.

Answers

I assume you are asking to solve:

-2x^2 + 3x - 9 = 0

So first, this equation does not have real roots.

It only has 2 complex roots.

The roots are:

3/4 * (1-i√7) and 3/4 * (1+i√7)

g(a) = 3^3a-2 . Find g(1)

Answers

sub 1 for a

[tex]G(1)=3^{3(1)-2}[/tex]
[tex]G(1)=3^{3-2}[/tex]
[tex]G(1)=3^{1}[/tex]
[tex]G(1)=3[/tex]

A vehicle travels on a highway at a rate of 65 mi/h. How long does it take the vehicle to travel 25 mi?

Answers

[tex]\bf \begin{array}{ccll} miles&hour\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 65&1\\ 25&h \end{array}\implies \cfrac{65}{25}=\cfrac{1}{h}\implies h=\cfrac{25\cdot 1}{65}[/tex]

A ladder is leaning up against a 17 foot Wall at an angle of elevation of 37°. How far is the foot of the latter from the wall? Round your answer to the nearest 10th of a foot

Answers

This is the concept of trigonometry, the distance from the foot of the ladder will be given by:
tan theta=[opposite]/[adjacent]
opposite=17 ft
adjacent=x ft
theta=37°
thus
tan 37=17/x
x=17/tan 37
x=22.56 ft
=22.6 ft (to the nearest 10th of a foot)

William buys a basket of lemons on sale for $11 before tax. The sales tax is 15%. What is the total price William pays for the basket of lemons?

Answers

it would be 12.65 dollars because you multiply 11 times 0.15 and add that answer to 11

Compute the tax then add it to the original amount.

Convert the percent into a decimal by moving the % sign two places to the left and making the % sign into a decimal point.

15% = 0.15

0.15 * 11 = 1.65

Now add it back to the original amount.

11 + 1.65 = 12.65

So, $12.65 is the answer.

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