find the component form of the vecto obtained by rotating 80, 19 through an angle of 2p>3 radians

1.39 is the median of the distribution

Creating a table:

X :___0 __ 1 __ 2 ___ 3 ____ 4 ___ 5 ___ 6

P(x):0.02_0.03_0.07, 0.12, 0.30_ 0.28_0.18.

The standard deviation = √(Var(x))

Var(x) = Σx²*p(x) - E(x)²

E(x) = ΣX*p(x)

E(x) = (0*0.02) + (1*0.03) + (2*0.07) + (3*0.12) + (4*0.30) + (5*0.28) + (6*0.18) = 4.21

Var(X) :

\(((0^2*0.02) + (1^2*0.03) + (2^2*0.07) + (3^2*0.12) + (4^2*0.30) + (5^2*0.28) + (6^2*0.18)) - 4.21^2\)

19.67 - 17.7241

= 1.9459

Standard deviation = √(Var(X))

Standard deviation = √(1.9459)

Standard deviation = 1.3949551

= 1.39

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Full Question ;

Hannah has a chicken coop with 6 hens. Let X be the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.

A 2-column table with 7 rows. Column 1 is labeled number of eggs with entries 0, 1, 2, 3, 4, 5, 6. Column 2 is labeled probability with entries 0.02, 0.03, 0.07, 0.12, 0.30, 0.28, 0.18.

What is the standard deviation of the distribution?

1.39

1.95

2.16

4.67

Answer:

x

\( {x}^{2} - 3 \)

2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

The answer is 6

Step-by-step explanation:

I just took the test and got a 100% on it

Answer:

850x = y

Step-by-step explanation:

The particular equation of the outer ellipse is therefore: 1002x2 + 2402y2 - 2402 * 1002 = 0, the inner ellipse is therefore:502x2 + 2002y2 - 2002 * 502 = 0, Clearance= 343.29 yd and Approximate seats= 47124 seats

The plan for a new football stadium calls for the stands to be in a region defined by two concentric ellipses. The outer ellipse is to be 240 yd long and 200 yd wide. The inner ellipse is to be 200 yd long and 100 yd wide. A football field of standard dimensions, 120 yd by 160 ft, will be laid out in the center of the inner ellipse.

To find the particular equations of the two ellipses, we can make use of the following: standard form of equation of an ellipse:x2/a2 + y2/b2 = 1 The outer ellipse: Major axis = 240 yd = 480 yd/2a = 480/2 = 240 yd Minor axis = 200 yd/2b = 100 yd Now, substituting the values in the standard equation of an ellipse, we have:x2/2402 + y2/1002 = 1Multiplying both sides by 2402 * 1002, we have: 1002x2 + 2402y2 = 2402 * 1002

The particular equation of the outer ellipse is therefore: 1002x2 + 2402y2 - 2402 * 1002 = 0 The inner ellipse: Major axis = 200 yd = 400 yd/2a = 400/2 = 200 yd Minor axis = 100 yd/2b = 50 yd Now, substituting the values in the standard equation of an ellipse, we have: x2/2002 + y2/502 = 1 Multiplying both sides by 2002 * 502, we have:502x2 + 2002y2 = 2002 * 502The particular equation of the inner ellipse is therefore:502x2 + 2002y2 - 2002 * 502 = 0

The eccentricity of an ellipse is given by the formula: e = √(1 - b2/a2)For the outer ellipse: a = 240, b = 100∴ e = √(1 - 1002/2402) = √0.694 = 0.833 For the inner ellipse: a = 200, b = 50∴ e = √(1 - 502/2002) = √0.9375 = 0.968

To find the clearance between the corner of the field and the inner ellipse in the direction of the end line, we need to find the distance between the foci of the inner ellipse, which is given by: d = 2 * √(a2 - b2)where a = 200 yd and b = 50 yd. Substituting the values, we have: d = 2 * √(2002 - 502)≈ 387.29 yd The clearance between the corner of the field and the inner ellipse in the direction of the end line is approximately 387.29 - 120/2 = 343.29 yd.

The area of the stands is the area between the two ellipses. Using the formula given in the question, A = πab, where a = 240 yd/2 and b = 200 yd/2, the area is: A = π * 120 * 100 = 37,699.1 sq yd Approximate seating capacity of the stadium will be number of seats = 37,699.1 / 0.8 = 47123.88 ≈ 47124 seats.

A circle is a special case of an ellipse, where both radii are equal. In the case of a circle with radius r, the formula for the area of an ellipse is reduced to the formula for the area of a circle: A = πab = πr2 = area of a circle

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Answer:

Explanation:

Here, we want to get the values of f(x) at the given values of x

To get that, we have to substitute the values of x into f(x)

We take the x-values one after the other

when x = -4:

when x = -2:

when x = 0:

when x = 1:

when x = 3:

when x = 5:

For the given values of x:

Answer: nope

Step-by-step explanation:

Answer:

Ratio of sandwiches with white bread and brown bread is 10:3. Of the white sandwiches 2/3 are vegetarian, of the sandwiches that are brown half are vegetarian. What fraction of the sandwiches are vegetarian?

Step-by-step explanation:

Givens

The ratio between white bread and brown bread is 10:3, that is, for every 10 white bread, there are 3 brown bread.

2/3 of white sandwiches are vegetarian.

1/2 of brown sandwiches are vegetarian.

We know that white bread is represented by 10, and brown bread is represents by 3. So, 2/3 of 10 are vegetarians, and 1/2 of 3 are vegetarians. The sum of them is

2/3 of 10 are vegetarians = \(\frac{2}{3} \times 10 = \frac{20}{3}\)

1/2 of 3 are vegetarians = \(\frac{1}{2} \times 3 = \frac{3}{2}\)

\(=\frac{20}{3}+\frac{3}{2}\\\\=\frac{40+9}{6}\\\\=\frac{49}{6}\)

Therefore, 49/6 represents all the sandwiches which are vegetarian.

Answer:

1900 km

Step-by-step explanation:

train = 1050km

bus = 200 less than train or 1050-200 = 850

1050+850=1900

Answer:

625, just got it right

Step-by-step explanation:

The Given statement tells us that RT is a line segment that divides SU into two segments with equal lengths. This means that RS = TU.

Two-column proof that ΔRVS ≈ ΔUVT, given that RT bisects SU:

Given: RT bisects SU.

Prove: ΔRVS ≈ ΔUVT.

            Statement                                                Reason

     RT bisects SU.                                                Given

   RS = TU.                                                   Definition of bisect

∠RSV = ∠UVT.                                   Corresponding angles

∠RVS and ∠UVT are acute angles. Since RT and SU are segments, ∠RSV and ∠UVT are acute angles.

                ΔRVS ≈ ΔUVT.                      AA Similarity Theorem

The Given statement tells us that RT is a line segment that divides SU into two segments with equal lengths. This means that RS = TU.

The Corresponding angles statement tells us that the two angles that are on the same side of RT and are opposite RS and TU are congruent. This is because RT bisects SU, so it forms two congruent angles.

The Acute angles statement tells us that ∠RSV and ∠UVT are both acute angles. This is because RT and SU are segments, so ∠RSV and ∠UVT are both less than 90°.

The AA Similarity Theorem tells us that ΔRVS ≈ ΔUVT. This is because ∠RSV and ∠UVT are congruent, and RS = TU. Therefore, we have proven that ΔRVS ≈ ΔUVT, given that RT bisects SU.

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Answer:

 8

Step-by-step explanation:

Given point S outside a circle and tangents SR and ST, with SR = 8, you want to know the length of ST.

Tangents to a circle from an external point are the same length.

  ST = SR = 8

The length of ST is 8.

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The correct answer is D.

The variable of time that could cause a student’s GPA to increase is studying.

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The distance is 864 m.

Speed of the bee when it travels from hive to flowerbed = 9 ft/s

Speed of the bee when it travels from flowerbed to hive = 6 ft/s

The time taken for the bee to travel from hive to flowerbed = t1

The time taken for the bee to travel from flowerbed to hive = t2

Time the bee remained in the flower bed = 17 minutes

Time the bee was away from the hive = 19 minutes

Time to go the the flowerbed and return = 19 - 17 = 2 minutes or 120 seconds

t1 + t2 = 120

t1 = 120 - t2

distance = speed * time

9t1 = 6t2

9(120 - t2) = 6t2

t2 = 144 s

Distance = 6 * 144 = 864 m

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Answer:

y=49x

Step-by-step explanation:

As you can see from the graph, the distance from home increases by 49 miles per hour driven.

Therefore the distance driven for any given time in hours is 49x

Therefore y = 49x

50% of the data values are greater than 45, it is calculated using the concept of box-whisker plot.

An illustration of the variation in a set of data is called a box and whisker plot. A histogram analysis usually gives an adequate display, but a box and whisker plot can add more detail while enabling the display of different sets of data in the same graph.

Given the box-and-whisker plot below represents some data sets,

In light of the above, the box-whisker plot reflects a particular data set. There is a number 45 right next to it, and a vertical line next to it indicates that 45 is the median of the data and that 45 is the 50th percentile in this case.

It indicates that 50% of the values are higher than 45 and 50% of the values are less than 45.

Using this technique, we can easily determine the proportion of data for which the value is higher or lower. It aids in data analysis and result interpretation.

Hence 50% of values are greater than 45.

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The numeric value of the expression 16 + 4(3q + p) when q = 6 and p = 2 is given by: 96.

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value. This also works for multi-variable functions or expressions, as each instance of each variable will be replaced by their attributed values.

For this problem, the expression is given by:

16 + 4(3q + p)

The attributed values are given by:

q = 6, p = 2.

Hence the numeric value of the expression is found as follows:

16 + 4(3 x 6 + 2) = 16 + 4(18 + 2) = 16 + 4 x 20 = 16 + 80 = 96.

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The 95% confidence interval for the difference in the two means = (-2.56 , 0.16)

What is Confidence Interval?

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given,

Sample statistics                         size(n)               mean(x)                s.d(s)

Construction site                           16                  x₁ = 5.584               1.812

Undistributed Location                 16                  x₂ = 6.789               1.945

Standard error = 0.665

Degree of freedom = 30

Critical T-value for 95% confidence interval is 2.0423

The 95% confidence interval for the difference in the two means

(construction site - undistributed location)

= x₁ -x₂ ± (t-value) (standard error)

= 5.584 - 6.786 ± (2.0423) (0.665)

= -1.2020 ± 1.358130

= (-1.2020 - 1.358130 , -1.2020 + 1.358130)

= (-2.56 , 0.156)

= (-2.56 , 0.16)

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Given,

Sample statistics                         size(n)               mean(x)                s.d(s)

Construction site                           16                  x₁ = 5.584               1.812

Undistributed Location                 16                  x₂ = 6.789               1.945

Standard error = 0.665

Degree of freedom = 30

Critical T-value for 95% confidence interval is 2.0423

The 95% confidence interval for the difference in the two means

(construction site - undistributed location)

= x₁ -x₂ ± (t-value) (standard error)

= 5.584 - 6.786 ± (2.0423) (0.665)

= -1.2020 ± 1.358130

= (-1.2020 - 1.358130 , -1.2020 + 1.358130)

= (-2.56 , 0.156)

= (-2.56 , 0.16)

For a normal distribution, the probability of a value being between a positive z-value and its population mean is indeed the same as that of a value being between a negative z-value and its population mean.

This is due to the symmetric nature of the normal distribution curve, where probabilities are mirrored around the mean.

The normal distribution is characterized by its bell-shaped curve, which is symmetric around the mean. The mean is also the midpoint of the curve, and the curve approaches but never touches the horizontal axis. The standard deviation of the distribution controls the spread of the curve.

In a normal distribution, the probability of a value being between a positive z-value and its population mean is indeed the same as that of a value being between a negative z-value and its population mean.

This is due to the symmetric nature of the normal distribution curve, where probabilities are mirrored around the mean.

This means that if we have a normal distribution with a mean of μ and a standard deviation of σ, the probability of a value falling between μ+zσ and μ is the same as the probability of a value falling between μ-zσ and μ.

This property of the normal distribution makes it easy to compute probabilities for any range of values, by transforming them into standard units using the z-score formula.

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Answer:

6.3

Step-by-step explanation:

Substituting b=6.3, we have:

49 - (b² + 3) = 49 - (6.3² + 3)

= 49 - (39.69 + 3)

= 49 - 42.69

= 6.31

Therefore, 49 - (b² + 3) is approximately 6.31 if b is equal to 6.3.

Answer:

hsushsissnsuselsksbshaioanwjwowhahhshshhahha

Answer:

The answer is below

Step-by-step explanation:

a) Let y represent the amount of time kiran slept, hence:

y = x - (1/10)x = x - 0.1x

y = 0.9x

b) Let y represent the amount of time Mia practice, hence:

y = x - (2/5)x = x - 0.4x

y = 0.6x

c) Let y represent the amount of drink kiran drank, hence:

y = x + (4/3)x = 7x / 3

y = 7x/3

d) Let y represent the money Mai spent, hence:

y = x - (1/4)x  = x - 0.25x

y = 0.75x

e) Let y represent the amount of almond kiran ate, hence:

y = x + 1.5x = 2.5x

f) Let y represent the recycling Mai collected, hence:

y = x - (3/10)x = x - 0.3x

y = 0.7x

g) Let y represent the amount of km kiran walked, hence:

y = x + (3/8)x

y = (11/8)x

h) Let y represent the amount of puzzles mai completed, hence:

y = x + (3/5)x = x + 0.6x

y = 1.6x

a. Calculation of payback period for investment A is: Initial Investment = P400,000Incremental cash flow = Year 1: P100,000 Year 2: P120,000 Year 3: P140,000 Year 4: P120,000 Year 5: P100,000 + P20,000

= P120,000Total cash inflows

= Year 1: P100,000 Year 2: P120,000 Year 3: P140,000 Year 4: P120,000 Year 5: P120,000Therefore, the cumulative cash flow for year 4

= P480,000, and the cumulative cash flow for year 5 is P600,000 (P480,000 + P120,000)Payback period

= Year 4 + Unrecovered amount / Cumulative cash flow in year 5

= 4 + (P220,000 / P600,000)

= 4.37 years

Therefore, the payback period for investment A is 4.37 years.

b) Discounted payback period = Year before recovery + (Unrecovered amount / Discounted cash flow ) Present value of cash flow

= Cash flow / (1 + Discount rate)nYear 0: Initial Investment

= P450,000Year 1: P130,000 / (1 + 0.10)1 = P118,182Year 2: P130,000 / (1 + 0.10)2

= P107,439Year 3: P130,000 / (1 + 0.10)3 = P97,672Year 4: P130,000 / (1 + 0.10)4

= P89,000Year 5: (P150,000 + P20,000) / (1 + 0.10)5

= P95,425Therefore, the discounted cash flows are as follows: Year 1: P118,182 Year 2: P107,439 Year 3: P97,672 Year 4: P89,000 Year 5: P95,425 Therefore, the cumulative discounted cash flow for year 4 = P412,293, and the cumulative discounted cash flow for year 5 is P507,718 (P412,293 + P95,425) The discounted payback period is as follows: Discounted payback period = Year before recovery + (Unrecovered amount / Discounted cash flow of the year)Discounted payback period

= 4 + (P42,282 / P95,425)

= 4.44Therefore, the discounted payback period for investment B is 4.44 years.

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Step-by-step explanation:

3x = 12 - 18

3x = (- 6)

X = (-6)/3

x = (-3)

Answer:

1.) y > - 1/5

2.) y < -2

Step-by-step explanation:

-5y < 1

y > - 1/5

6y < -12

y < - 12/6

y < -2

Please mark me the brainliest!?!

Answer:

( − ∞ , − 12 )

Step-by-step explanation:

The result can be shown in multiple forms.

Inequality Form:

−  5  <  1  and  6 y  <  − 12

Interval Notation:

( − ∞ , − 12 )

Answer:

\(R(x) = (1.3)^{3x-8}\)

Step-by-step explanation:

Given

\(A(x) = (1.3)^{x + 9}\)

\(B(x) = (1.3)^{4x + 1}\)

Required

Ratio B(x) to A(x)

This is calculated as:

\(R(x) = B(x) : A(x)\)

Express as fraction

\(R(x) = \frac{B(x) }{A(x)}\)

Substitute: \(A(x) = (1.3)^{x + 9}\) and  \(B(x) = (1.3)^{4x + 1}\)

\(R(x) = \frac{(1.3)^{4x+1}}{(1.3)^{x+9}}\)

Apply law of indices

\(R(x) = (1.3)^{4x-x+1-9}\)

\(R(x) = (1.3)^{3x-8}\)

Answer:

7.1

Step-by-step explanation:

Once again we can use trig ratios to solve for ST

First we must recall the trig function

Sin = Opposite over Hypotenuse

Cos = Adjacent over Hypotenuse

Tan = Opposite over Adjacent

We are given the measure of an angle and the length of the hypotenuse

Of the given angle we need to find the adjacent side length

When working with the hypotenuse and adjacent we use trig function cosine

That being said we want to create an equation ( remember cos = adjacent over hypotenuse ) ( let ST = x)

\(cos(42)=\frac{x}{9.5}\)

now we solve for x

Step 1 multiply each side by 9.5

\(cos(42)*9.5=9.5cos(42)=7.059875842\\\frac{x}{9.5} *9.5=x\)

we're left with x = 7.059875842

Finally we round to the nearest tenth and get that the answer is 7.1

Numbers in scientific notation are said to be in their standard form

The size of the larger cell is \(5.7 * 10^{-3}m\)

The size of the cell is given:

\(Cell = 4.75 * 10^{-7}m\)

The larger cell is:

\(Larger = 1.2 * 10^{4} * Cell\)

So, we have:

\(Larger = 1.2 * 10^{4} * 4.75 * 10^{-7}m\)

Rewrite as:

\(Larger = 1.2 * 4.75 * 10^{4} * 10^{-7}m\)

Evaluate the product

\(Larger = 5.7 * 10^{-3}m\)

Hence, the size of the larger cell is \(5.7 * 10^{-3}m\)

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