We want to conduct a hypothesis test of the claim that the population mean time it takes drivers to react following the application of brakes by the driver in front of them is more than 2. 5 seconds. So, we choose a random sample of reaction time measurements. The sample has a mean of 2. 4 seconds and a standard deviation of 0. 5 seconds. For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places. (a) The sample has size 110, and it is from a non-normally distributed population with a known standard deviation of. It is unclear which test statistic to use. (b) The sample has size 12,and it is from a normally distributed population with an unknown standard deviation. Z=

t=

It is unclear which test statistic to use.

Answer:

because 25/100 = 1/4

0.20 = 20/100

Step-by-step explanation:

because 25/100 = 1/4

0.20 = 20/100

because 0.20 means 20 tenths 0.23 > 1/2

because 0.23 = 23

0.4 = 1/4

because they are on the same place on a number lin

The sum of 18.420 and 28.49, rounded to the correct number of significant figures, is 46.91.

To add the numbers 18.420 and 28.49, we align the decimal points and perform the addition. After adding the numbers, we obtain a sum of 46.910. However, we need to round the answer to the correct number of significant figures.

The rule for determining the number of significant figures in addition is to retain the same number of decimal places as the number with the fewest decimal places being added. In this case, 18.420 has three decimal places, while 28.49 has two decimal places. Therefore, we round the sum to two decimal places: 46.910 rounded to two decimal places is 46.91.

Thus, the sum of 18.420 and 28.49, rounded to the correct number of significant figures, is 46.91.

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Answer:

False.

Step-by-step explanation:

It's ok to plan future activities for the group, but it's best to plan in the beginning of the group.

Answer:

No there not the same

Step-by-step explanation:

There are not equivalents to each other the answer would be 2:1

Answer:

1.  tan 35° = 0.700

2.  sin 60° = 0.866

3.  cos 25° = 0.906

4.  tan 75° = 3.732

5.  cos 45° = 0.707

6.  sin 20° = 0.342

7.  tan 80° = 5.671

8.  cos 40° = 0.766

9.  tan 55° = 1.428

10. sin 78° = 0.978

Step-by-step explanation:

Trigonometric ratios, also known as trigonometric functions, are mathematical ratios that describe the relationship between the angles of a right triangle and the ratios of the lengths of its sides. The primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).

Rounding to three decimal places is a process of approximating a number to the nearest value with three digits after the decimal point. In this rounding method, the digit at the fourth decimal place is used to determine whether the preceding digit should be increased or kept unchanged.

To round a number to three decimal places, identify the digit at the fourth decimal place (the digit immediately after the third decimal place).

Finally, remove all the digits after the third decimal place.

Entering tan 32° into a calculator returns the number 0.7002075382...

To round this to three decimal places, first identify the digit at the fourth decimal place:

\(\sf 0.700\;\boxed{2}\;075382...\\ \phantom{w}\;\;\;\;\;\;\:\uparrow\\ 4th\;decimal\;place\)

As this digit is less then 5, we do not change the digit at the third decimal place. Finally, remove all the digits after the third decimal place.

Therefore, tan 32° = 0.700 to three decimal places.

Apply this method to the rest of the given trigonometric functions:

Answer:

1/6

Step-by-step explanation:

3 and 6 are the only multiples of 3 on a dice

P(multiple of 3) = 2/6 or 1/3

P(tails) = 1/2

P(mult. 3 and tails) = 1/3 x 1/2 = 1/6

Answer:

A dice has 6 sides. or 6 events. A coin has two sides, or 2 events. So using law of counting, we have a total of 12 possibe. events.

Let create a proabliblity function to showcase.

Out of (1,2,3,4,5,6) and (H,T)

We have

1H

1T

2H

2T

3H

3T

4H

4T

5H

5T

6H

6T

A proabliblity function possibilities must add to 1 or 100% Since the dice and coin is fair, and we have 12 possibilities. We do

\( \frac{100}{12} = 8.33333\)

So each has 8.333% of occurring or 0.0833. or 100/12

We need to find the proabliblity of Getting a multiple of 3 and a tail.

3 and 6 are multiples of 3 and they get tail one time each so we get

P(3T) +P(6T)= P( proabliblity of getting a multiple of 3 and a tail).

Remeber each possibility has a 100/12 chance of occurring so we have

\( \frac{100}{12} + \frac{100}{12} = \frac{200}{12} \)

Which equals

\(16.6666\%\)

So the answer is 16.6666666% or 0.166666

The volume of the cuboid is 162 cubic centimeter.

Given that, a cuboid of side 3 cm.

We know that, the volume of a cube = a³.

So, volume of the cube is 3³=27 cubic centimeter

a) We know that, the volume of a cuboid = Length × Breadth × Height

Cuboid made with 6 of these cubes.

So, Length = 18 cm, Breadth = 3 cm and Height = 3 cm

Here, volume of cuboid = 18×3×3

= 162 cubic centimeter

b) Dimensions of cuboid of the base in the given figure are length = 12 cm, breadth = 3 cm and height = 3 cm

Surface area = 2(lb+bh+hl)

= 2(12×3+3×3+3×12)

= 2×81

= 192 square centimeter

Dimensions of cuboid of the top in the given figure are length = 9 cm, breadth = 3 cm and height = 3 cm

Surface area = 2(lb+bh+hl)

= 2(9×3+3×3+3×9)

= 2×63

= 126 square centimeter

Total surface area = 192+126

= 318 square centimeter

Therefore, the volume of the cuboid is 162 cubic centimeter.

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

the answer is fourteen (14)

The correct options are:

- The researcher randomly selects 10 classes and asks all the students in those classes to fill out an anonymous survey.

- The researcher takes a random sample from the enrollment list of the college and surveys the selected students.

The final sample is referred to be an unbiased sample if the sampling technique used was not biased. A representative sample is more likely to result from an impartial sample.

The unbiased methods that the researcher could use are:

- The researcher randomly selects 10 classes and asks all the students in those classes to fill out an anonymous survey. This method ensures that the sample is representative of the overall population of college students.

- The researcher takes a random sample from the enrollment list of the college and surveys the selected students. This method also allows for a random selection of participants, which helps in obtaining unbiased results.

Therefore, the correct options are:

- The researcher randomly selects 10 classes and asks all the students in those classes to fill out an anonymous survey.

- The researcher takes a random sample from the enrollment list of the college and surveys the selected students.

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The attached picture is a summary of all the six transformations you'd do.

Any change outside the f(x) notation impacts y-values of points on the graph.

Any changes inside the f(x) notation impacts x-values of points on the graph.

The trick is that the inside changes are usually the opposite of what you'd expect to have happen.

7. y=f(x)+8

This is an outside change.  You're adding 8 to all the y-values of points on the graph.  This will shift your entire graph up 8 units.

8. y=f(x+6)

This is an inside change.  Because it says "+6", you want to think, "Ah!  That means I'll actually subtract 6 from the x-value of every point on the graph." This graph is shifted 6 units to the left.

9. y=-f(x)

Inside change, impacts y-values.  Every y-value will be given the opposite signs.  Negatives become positive and positives become negative.  This will flip your graph over the x-axis.

10. y = f(-x) + 5

Give this one a shot on your own first in a comment and I'll let you know how you did.  

11. y = - 3 f(x-3)

There are three things happening.  A negative on the outside, multiplying by 3 on the outside, and subtracting 3 inside.  What will each of those do individually?  Take a shot on this one and let me know what you think.

12. y = 1/2 f( 1/2 x )

Again, three changes.  Try this one and let me know what you think.  Remember multiplying by 1/2 inside really means you'll do the opposite of multiplying by 1/2.

Based on the calculation below, the number of ounces of pate that should be ordered for 398 people is 796 ounces.

The number of ounces of pate that should be ordered for 398 people can be calculated as follows:

Number of ounces of pate previously ordered per person = Total number of ounces of pate previously ordered / Number of people at the engagement party = 54 / 27 = 2 ounces per person

Number of ounces of pate that should be ordered = Number of ounces of pate previously ordered per person * Number of people = 2 * 398 = 796 ounces

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The value of x when the tangents intersect is 24.

The theorem of tangent intersection states that the the measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's use the theorem to find the value of x in the circle as follows:

61 = 1 / 2 × ((10x + 1) - (5x - 1))

61 = 1 / 2 × (10x - 5x + 1 + 1)

61 = 1 / 2 × (5x + 2)

61 = 1 / 2 (5x + 2)

61 = 5 / 2 x + 1

61 - 1 = 5 / 2 x

60 = 5 / 2 x

cross multiply

5x = 120

divide both sides by 5

x = 120 / 5

x = 24

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\(360 - 140 - 62 - 85\)

\( = 73 \: degrees\)

the sum of the angles in a quadrilateral is 360° so just subtract the angles you have with the total to find the missing angle.

Answer:

73°

Step-by-step explanation:

The angles add to 360 hope this helps

To compute the Galois groups and determine if the field extensions are normal, we need to know the specific field extensions in question. However, I will provide a general method for computing Galois groups and determining normal field extensions.

Step 1: Identify the field extension
Let's say our field extension is given by K/Q, where K is the extension field and Q is the base field (the field of rational numbers).

Step 2: Determine the minimal polynomial
Find the minimal polynomial f(x) of the field extension K/Q. This is the smallest degree polynomial with rational coefficients for which the elements of K are roots.

Step 3: Compute the Galois group
The Galois group, G(K/Q), is the group of automorphisms of the field K that fix the base field Q. To compute G(K/Q), determine the set of automorphisms of K that keep the elements of Q fixed.

Step 4: Check for normality
A field extension K/Q is normal if and only if the minimal polynomial f(x) splits into distinct linear factors over K. If this is true, then K/Q is a normal field extension.

Step 5: Find a normal extension if necessary
If K/Q is not normal, we can find a normal extension L/Q containing K by considering the splitting field of the minimal polynomial f(x) over Q. The splitting field L is the smallest field containing Q and all the roots of f(x), and the extension L/Q will be normal.

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The decimal number that corresponds to the binary number 11111111 is 255.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. A decimal number is made up of two parts: a whole number and a fractional component separated by a decimal point. The decimal point is the dot between the whole number and the fractions. 25.5, for example, is a decimal number.

Here,

In binary, each digit represents a power of 2, starting with the rightmost digit. The rightmost digit in 11111111 represents 2^0, the second digit from the right represents 2^1, and so on. To convert a binary number to decimal, you add up the value of each digit times the corresponding power of 2.

For 11111111, the calculation would be:

=1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1

=255

The decimal equivalent of the binary number 11111111 is 255.

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Answer:

420m

Step-by-step explanation:

250÷5=50

1cm=5m

5×8.4=420m

Answer:

420 meters bestie

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

it is because in (a) the square root of 112. is 10.58 which is in between 10 and 11

(B) the square root of 180 is 13.42 which is between 13&14

(c) the square root of 12 is 3.46 which is not between 4&5

Answer:

C the square root  of 12 is between 4&5.

Step-by-step explanation:

Answer:

100000 = 8 (4) ^t

Step-by-step explanation:

We are multiplying by 4 each time

y = a (4)^t

The initial amount is 8

y = 8 (4)^t

We want to get to 100000

100000 = 8 (4) ^t

Answer:

B

8 ⋅ 4^t  = 100,000

Step-by-step explanation:

The value of "n" is 6.

"n" is related to a circle with intersecting chords labeled 5, n+4, 7, and n+8 [1]. To find the value of "n", we can use the property that states that if two chords intersect inside a circle, the products of their segments are equal. Using this property, we can set up the following equation:

7(n+4) = 5(n+8)

Expanding the brackets, we get:

7n + 28 = 5n + 40

Simplifying, we get:

2n = 12

n=6

A circle is a two-dimensional geometric shape that is defined as a set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). It is a closed shape, meaning that it has no beginning or end, and its boundary is a continuous curve.

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Answer:

its a luv

Step-by-step explanation:

Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15

x = arctan (8/15)

x = 28.1° (rounded)

Step-by-step explanation:

Answer:

i dont know do you learn dat in year 7?

The probability that a card drawn randomly from a standard deck of 52 cards is ed or a king = 7/13​

We know that the formula for the probability of an event is given by,

P = number of favourable outcomes / total number of possible outcomes of an event

Let us assume that event A : drawing a red card

and event B: drawing a king card

Here, sample space is a standard deck of 52 cards.

So, n(S) = 52

We know that there are 26 red cards in a standard deck of cards.

So, n(A) = 26

And there are 4 kings

So, n(B) = 4

Since there are two cards of king are red and two are black.

The favorable number of cards = 26+2

                                                 =28

So, the required probability is:

P = 28/52​

P = 7/13​

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Answer:

15% increase

Step-by-step explanation:

to find the percent increase from an initial value to a final value, first find the difference:

2070-1800=270

then divide the difference by the initial value:

270/1800= 0.15

and multiply by 100

0.15*100=15

so there is a 15% increase

Answer:

10 cm by 5cm

Step-by-step explanation:

We know that for every 5 meters, there will be 1 centimeter. The pool is 50 meters by 25 meters. So to find this in terms of centimters, divide by 5 to get 10 cm by 5 cm.