A scientist wishes to estimate the average depth of a river. he wants to be 99% confident that the estimate is accurate within 2 feet. from previous studies, the standard deviation of the depths measure was 4.33 feet. how large a sample is required.

The function has a local minimum at (-2,-7) and no local maxima or saddle points.

To find the local maxima, local minima, and saddle points of the function f(x,y) = x² + xy + 3x + 2y + 2, we need to find its critical points and use the second derivative test to determine their nature.

First, we find the partial derivatives:

fx(x,y) = 2x + y + 3

fy(x,y) = x + 2

Setting these equal to zero and solving for x and y, we get:

2x + y + 3 = 0

x + 2 = 0

Solving for x and y, we get:

x = -2

y = -7

So the only critical point is (-2,-7).

Next, we find the second partial derivatives:

fₓₓ(x,y) = 2

fxy(x,y) = 1

fyx(x,y) = 1

fyy(x,y) = 0

At the critical point (-2,-7), we have:

fₓₓ(-2,-7) = 2

fxy(-2,-7) = 1

fyx(-2,-7) = 1

fyy(-2,-7) = 0

The discriminant of the second derivative test is:

D = fₓₓ(-2,-7)fyy(-2,-7) - fxy(-2,-7)fyx(-2,-7) = 2(0) - 1(1) = -1

Since D < 0 and fₓₓ(-2,-7) > 0, we conclude that the critical point (-2,-7) is a local minimum.

Therefore, the function has a local minimum at (-2,-7) and no local maxima or saddle points.

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The probability that a customer did not order a starter is 9/10.

We have,

To find the probability that a customer did not order a starter, we can use the concept of set theory and probability.

Let's define the events:

A: Customer ordered a starter

A' (read as "A compliment"): Customer did not order a starter

Given information:

Total number of customers = 30

Customer that Ordered a starter = 3

Customer that Ordered a dessert = 5

Customer who ordered Both starter and dessert = 14

To find the probability that a customer did not order a starter (A'), we can subtract the probability of event A (customer ordered a starter) from 1.

Probability of A = Customer that Ordered a starter / Total number of customers

= 3 / 30

= 1 / 10

Probability of A' (customer did not order a starter) = 1 - Probability of A

= 1 - 1/10

= 9/10

Therefore,

The probability that a customer did not order a starter is 9/10.

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9 block rhombuses would create 3 hexagons.

In order to increase the total number by three, a hexagon can be divided into a minimum of three rhombuses, each of which can be further divided into four rhombuses. With n being a positive integer, the result is 3n. The top two hexagons in this image are each divided into 8 and 10 rhombuses. The total number of rhombuses that can fit in a hexagon is not limited to multiples of three, given that the total number of rhombuses dividing a hexagon can be raised by three by quartering a single component rhombus. The amount might actually be any integer larger than 7.

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Answer:

Start at origin (0,0)

Move 1/2 units left

Move 1 and 1/2 units down

Place your point

Step-by-step explanation:

Start at the origin (0,0)

Move 1/2 units to the left

Then move 1 1/2 units down, and place your point.

The first coordinate is locating the position horizontally, or on the x axis

The second coordinate is locating the position vertically, or on the y axis.

If there is a negative number on the x coordinate, the first one, you move left.

If positive, you move right.

If there is a negative number on the y coordinate, the second one, you move down.

If positive, you move up.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

move toward left of the horizontal x axis then plot the point in between o and -1.For next point then move down the vertical y axis and plot the point in between -1 and -2 .

Step-by-step explanation:

Hope this helps u!!

Answer:

18

Step-by-step explanation:

(3a+16)+38=6a

54=3a

18=a

The probability that the tiles are arranged in the order RBP is 8/495.

Probability that the first tile is red:

There are a total of 11 tiles, out of which 4 are red. Therefore, the probability that the first tile is red is:

P(Red on 1st draw) = 4/11

Probability that the second tile is blue given that the first tile was red:

If the first tile is red, then there are 10 tiles left, out of which 4 are blue. Therefore, the probability that the second tile is blue given that the first tile was red is:

P(Blue on 2nd draw given Red on 1st draw) = 4/10 = 2/5

Probability that the third tile is purple given that the first two tiles were red and blue, respectively:

If the first two tiles were red and blue, then there are 9 tiles left, out of which 3 are purple. Therefore, the probability that the third tile is purple given that the first two tiles were red and blue is:

P(Purple on 3rd draw given Red on 1st draw and Blue on 2nd draw) = 3/9 = 1/3

Probability that the tiles are arranged in the order RBP:

To find the probability that the tiles are arranged in the order RBP, we need to multiply the probabilities of each individual event:

P(RBP) = P(Red on 1st draw) x P(Blue on 2nd draw given Red on 1st draw) x P(Purple on 3rd draw given Red on 1st draw and Blue on 2nd draw)

P(RBP) = (4/11) x (2/5) x (1/3) = 8/495

Therefore, the probability that the tiles are arranged in the order RBP is 8/495.

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Answer:

y=x-10

Step-by-step explanation:

y=ax+b - linear equation

y=-x+7

a=-1

y=cx+d - perpendicular equation to y=ax+b

a*c=-1

(-1)*c=-1

c=1

y=x+d

(4,-6) => x=4, y=-6

y=x+d => -6=4+d

d=-10

y=x-10

The day the two bags will have the same weight is the 24th day.

The linear equation that can be used to determine the pound of dog food left is:

Amount of dog food left = capacity of the bag - (number of days x amount the dog eats per day)

Amount of dog food left = 34 - (1 x p)

Amount of dog food left = 34 - 1p

The linear equation that can be used to determine the pound of cat food left is:

Amount of cat food left = capacity of the bag - (number of days x amount the cat eats per day)

Amount of cat food left = 16 - (1/4 x p)

Amount of cat food left = 16 - 1/4p

On the day the two bags will have the same weight, the two above equations would be equal:

16 - 1/4p = 34 - 1p

p - 1/4p = 34 - 16

3/4p = 18

p = (18 x 4) / 3

p = 24 days

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Answer:

Hey there!

10x+12+4x-15=2x+21

14x-3=2x+21

12x=24

x=2

DF= 2x+21

DF=4+21

DF=25

Let me know if this helps :)

"Centripetal is the word used to describe a vector that always points toward the centre of a circular path."

The centripetal acceleration vector is an acceleration in the radial direction that is directed towards the centre of the circular line of motion. It runs perpendicular to the linear motion, or v.

The direction of the velocity shift for a ball travelling around a curve is in the direction of the curve's centre. Centripetal acceleration is the acceleration that is directed towards the centre of a curved or circular route.

Any force that changes the path of motion towards the centre of a circular motion is known as a centripetal force. The portion of the force that produces the centripetal force is the part that is perpendicular to the velocity.

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Answer:

The answer is Table B. Because only table B. doesn't have repeating x or domain.

Answer:

\(\displaystyle x \approx 9.2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:  

Step 1: Define

Angle θ = 35°

Opposite leg = x

Hypotenuse = 16

Step 2: Solve for x

Answer:

See below.

Step-by-step explanation:

Is the equation written correctly?

y = 3×2¹ +4 has no variable, unless the "3×2" is supposed to be "3x*2^1"

If so,

y = 3x*2¹ +4 for x = 1 would be

y = 3(1)2¹ +4

y = 3*2 +4

y = 10

⊰________________________________________________________⊱

Answer:

See Below.

Step-by-step explanation:

\(\large\begin{gathered} \sf{Start \ by \ plugging \ in \ the \ number \ that \ x \ is: 1} \\ \sf{Now, \ evaluate: y=3*1*2^1+4} \\ \sf{y=3*2+4} \\ \sf{Multiply \ 3 \times 2 \ first: y=6+4} \\ \sf{Now, \ just \ add: y=10}{ \end{gathered}\)

Done!!

⊱________________________________________________________⊰

\(\bf{\overbrace{C}\underbrace{A}\overbrace{LL}\underbrace{I}\overbrace{G}\underbrace{R}\overbrace{A}\underbrace{P}\overbrace{H}\underbrace{Y}}\)

Answer:

1. 4x3<7×3

12×2<21×2

24×4<42×4

96×9<168×9

864<1512

2. 11+3>-2+3

14+3>1+3

17_4>4-4

13>0

3. -2/leg-2

-18/leg-18

4. -4<8

0<2

Answer:

758803.5

Step-by-step explanation:

that's what i got- no idea if it's right though-

The measure of angle A, B, C are 60°,60°,60°

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The sum of angle in a polygon is 180°. i.e

A+B + C = 180°

therefore we can say that;

2x+2x + 3x-30 = 180

7x -30 = 180

7x = 180+30

7x = 210

divide both sides by 7

x = 210/7 = 30

therefore ;

angle A = 2× 30 = 60°

angle B = 2×30 = 60°

angle C = 3×30-30 = 90-30 = 60°

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Answer:

a = 127° , b = 12° , c = 115°

Step-by-step explanation:

a and 53° are same- side interior angles and sum to 180° , that is

a + 53° = 180° ( subtract 53° from both sides )

a = 127°

c and 115° are alternate angles and are congruent , then

c = 115°

53° , b and c lie on a straight line and sum to 180°

53° + b + c = 180°

53° + b + 115° = 180°

b + 168° = 180° ( subtract 168° from both sides )

b = 12°

then a = 127° , b = 12° , c = 115°

Answer:

a = 127; b = 12; c = 115

Step-by-step explanation:

c =115

b = 180 - 115 - 53

b = 12

a = b + c

a = 12 + 115

a = 127

Answer:

gra,

Step-by-step explanation:

The standard deviation of the given data is approximately 1.32. The Standard Deviation is the measure of variability or dispersion of a group of values from its mean or average. It is a metric of the degree of deviation or fluctuation of data set values from the mean value.

To find the standard deviation of the given data, use the formula,

σ = √∑\([x - E(X)]^2 P(X)\)

Where, x = data points,

E(X) = mean of the data set, and

P(X) = the probability of each value.

xP(X)0(0.2) = 0.01(1) = 0.10(0.1) = 0.02(2) = 0.10(0.2) = 0.20(3) = 0.10(0.1) = 0.01(4) = 0.10(0.1) = 0.01(5) = 0.30

The expected value is calculated as follows:

E(X) = Σ (xP(X)) = 0 + 0.1 + 0.4 + 0.3 + 0.4 + 1.5 = 3.2

Using this value in the standard deviation formula, we get,

σ = √∑\([x - E(X)]^2\) P(X) = √\([(0 - 3.2)^2\)(0.2) + \((1 - 3.2)^2\)(0.1) + \((2 - 3.2)^2\)(0.2) + \((3 - 3.2)^2\)(0.1) + \((4 - 3.2)^2\)(0.1) + \((5 - 3.2)^2\)(0.3)] ≈ 1.32

Thus, the standard deviation of the given data is approximately 1.32. The Standard Deviation is the measure of variability or dispersion of a group of values from its mean or average. It is a metric of the degree of deviation or fluctuation of data set values from the mean value.

The formula to calculate standard deviation is:

σ = √∑\([x - E(X)]^2\)P(X)

Where, x is the data point.

E(X) is the expected value of the data set.

P(X) is the probability of each value. This formula needs the mean or expected value of the data set to work, which can be calculated as:

E(X) = Σ (xP(X))

We are given the following data: x   P(X)  0     0.2  1     0.1  2     0.2  3     0.1  4     0.1  5     0.3

Calculating the expected value as

E(X) = Σ (xP(X)) = 0 + 0.1 + 0.4 + 0.3 + 0.4 + 1.5 = 3.2

Substituting these values into the standard deviation formula, we have,

σ = √∑\([x - E(X)]^2\) P(X) = √\([(0 - 3.2)^2\)(0.2) + \((1 - 3.2)^2\)(0.1) + \((2 - 3.2)^2\)(0.2) + \((3 - 3.2)^2\)(0.1) + \((4 - 3.2)^2\)(0.1) + \((5 - 3.2)^2\)(0.3)] ≈ 1.32

Therefore, the standard deviation of the given data is approximately 1.32.

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6 yards is approximately equal to 5.4864 meters.

To complete the sentence, we need to convert 6 yards to meters.

1 yard is approximately equal to 0.9144 meters.

Therefore, to convert 6 yards to meters, we can multiply it by the conversion factor:

6 yards x 0.9144 meters/yard ≈ 5.4864 meters.

To convert 6 yards to meters, we need to use the conversion factor that defines the relationship between yards and meters.

The conversion factor states that 1 yard is approximately equal to 0.9144 meters. This value is derived from the exact conversion factor of 1 yard = 0.9144 meters, rounded to four decimal places for convenience.

To convert 6 yards to meters, we multiply 6 by the conversion factor:

6 yards x 0.9144 meters/yard = 5.4864 meters.

This calculation shows that 6 yards is approximately equal to 5.4864 meters. The result is rounded to four decimal places to match the precision of the conversion factor.

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Events A and B are independent with P(A) = 0.15 and P(An B) = 0.096 Rounding to the nearest thousandth, the value of P(B)  (the probability of B) is approximately 0.640.

To determine the value of P(B), we can use the formula for the probability of the intersection of two independent events:

P(A ∩ B) = P(A) * P(B)

Given that P(A) = 0.15 and P(A ∩ B) = 0.096, we can rearrange the formula to solve for P(B):

P(A ∩ B) = P(A) * P(B)

0.096 = 0.15 * P(B)

Now, let's solve for P(B):

P(B) = 0.096 / 0.15

P(B) ≈ 0.6

To further explain, when two events are independent, the probability of their intersection is equal to the product of their individual probabilities. In this case, the probability of A and B occurring together is 0.096, which is the product of 0.15 (the probability of A) and P(B) (the probability of B). Solving the equation, we find that P(B) is approximately 0.64.

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Answer:

549 ft

Step-by-step explanation:

take 670ft away from 1,220 ft ( not all the way sure of I'm right)

Answer:

550

Step-by-step explanation:

1,220+(-670)= 550

Thank you! :)

here's the answer :

=》

In similar figures, the ratio of the lengths of their corresponding sides are equal and corresponding angles are congruent.

hence, A. equal and congruent is correct.

Answer:

equal and congruent

Step-by-step explanation:

equal and congruent

Answer:

Positive.

Hope that this helps!

In our model, we put 2 tickets marked "outer" in the box.Since the player has a 2/3 probability of the dart landing in the outer ring

In this box model for the outcome of a game of darts, the player has a 1/3 probability of throwing a dart in the inner ring and a 2/3 probability of the dart landing in the outer ring.

The model consists of two unique tickets, one marked "inner" and the other marked "outer."

To determine the number of tickets marked "outer" that we should put in the box, we need to consider the probabilities of the dart landing in the inner and outer rings.

Since the player has a 1/3 chance of throwing a dart in the inner ring, we put 1 ticket marked "inner" in the box.

To find the number of tickets marked "outer," we can calculate the complementary probability.

The complementary probability is equal to 1 minus the probability of the event occurring. In this case, the complementary probability is equal to 1 - 1/3 = 2/3.

Since the player has a 2/3 chance of the dart landing in the outer ring, we should put 2 tickets marked "outer" in the box.

Therefore, in our model, we put 2 tickets marked "outer" in the box.

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Answer:

Increasing and linear: B

Decreasing and linear: E

Increasing and nonlinear: A

Decreasing and nonlinear: D

The metric system is based on the number 10, which means that each unit of measurement is a multiple or fraction of 10.

The metric system is a decimal-based system of measurement that is used worldwide. It is based on the number 10, which means that each unit of measurement is a multiple or fraction of 10. This makes conversions between different units of measurement much simpler and more intuitive.

For example, in the metric system, there are 10 millimeters in a centimeter, 100 centimeters in a meter, and 1,000 meters in a kilometer. This consistent base of 10 allows for easy scaling and conversion of measurements.

The metric system was first introduced in France in the late 18th century and has since been adopted by most countries around the world. It is used in various fields, including science, engineering, and everyday life.

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B. 10; The metric system is based on the principle of using a multiple of 10.

The metric system is based upon a multiple of 10. It is a decimal-based system of measurement that provides a logical and consistent framework for measuring quantities such as length, mass, volume, and temperature. The system uses prefixes to denote multiples or fractions of the base units.

In the metric system, the base units are defined for each measurement type, such as meter for length, gram for mass, and liter for volume. These base units are then multiplied or divided by powers of 10 to create smaller or larger units. For example, 1 meter is equal to 10 decimeters, 100 centimeters, or 1000 millimeters.

The use of a decimal-based system makes conversions between different units within the metric system straightforward. It also allows for easy scalability and standardization, enabling global consistency in scientific, industrial, and everyday measurements.

The metric system is based on the principle of using a multiple of 10. This characteristic makes it a convenient and efficient system for measuring quantities, as it allows for easy conversions and standardization across various measurement units.

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Answer: The answer is option C: $17,925.00.

Step-by-step explanation: Using the simple interest formula:

I = Prt

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

We can find the interest earned over the 6 years:

I = P * r * t = $15,000 * 0.0325 * 6 = $2,925

Adding the interest to the principal, we get the balance at the end of the 6 years:

Balance = Principal + Interest = $15,000 + $2,925 = $17,925

Therefore, the answer is option C: $17,925.00.

X u y = {z l z ∈ x or z ∈ y} is a valid set builder notation. Yes, this is a valid set builder notation. This specifies the elements of the set.

A set builder notation is a way of expressing a set using a description of its elements. In this particular set builder notation, the set consists of all elements that are either in set x or set y.

The notation is written as {z l z ∈ x or z ∈ y}, where the curly braces denote the set and the statement "z ∈ x or z ∈ y" specifies the elements of the set. This is a valid set builder notation because it correctly expresses the elements of the set.

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