What is 4x+7=39

Solve for two step equation.

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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Step-by-step explanation:

it still remains 125 it doesn't change

The missing side of the right angled triangle is √202.

Given is a right angled triangle as shown in the image attached.

We can write -

(hypotenuse)² = (base)² + (perpendicular)².

x² = 11² + 9²

x² = 121 + 81

x² = 202

x = √202

Therefore, the missing side of the right angled triangle is √202.

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Answer:

5.

Step-by-Step explanation:

Distance = √ [(6-3)^2 + (8-4)^2) ]

= √(9 + 16)

= √25

= 5.

The surface area of the portion of the paraboloid which is in the first octant and bounded above by z=9 is ((4 √13 + π/2 + 243 √10) / 4) square units.

The given equation is z=x²+y². We are to calculate the area of the portion of the paraboloid in the first octant and bounded above by z=9.Thus, for a point in the first octant, x, y and z are all positive.

So we want to find the area of the part of the paraboloid which lies in the first octant and is less than or equal to 9 in z. This means that the range of values of z is from 0 to 9. We can set z=9 in the equation for the paraboloid to get the equation of the circle which forms the boundary of the surface area we want to find:9 = x²+y²Taking the square root of both sides of this equation, we get:x² + y² = 9This is the equation of a circle with radius 3.

We can solve for y and integrate over the region x=0 to x=3:y = sqrt(9 - x²)dy/dx = -x / sqrt(9 - x²)The integral to find the surface area is: A = ∫(0 to 3) ∫(0 to sqrt(9-x²)) √(1 + (∂z/∂x)² + (∂z/∂y)²) dy dx We have that: z = x² + y² so we can calculate the partial derivatives as follows:∂z/∂x = 2x∂z/∂y = 2ySubstituting these values in the expression for the surface area, we get:A = ∫(0 to 3) ∫(0 to sqrt(9-x²)) √(1 + 4x²/4 + 4y²/4) dy dx Simplifying, we get:A = ∫(0 to 3) ∫(0 to sqrt(9-x²)) √(1 + x² + y²) dy dxA = ∫(0 to 3) [(1/2) (y(1 + x² + y²)3/2 + (1/2) arcsin (y/3))]0 dxA = ∫(0 to 3) [(1/2) (3(1 + x² + 9)3/2 + (1/2) arcsin (1))]0 dxA = (1/2) [(1/2) (4 √13 + π/2) + 243 √10/2]A = (1/4) (4 √13 + π/2 + 243 √10) square units

Therefore, the surface area of the portion of the paraboloid which is in the first octant and bounded above by z=9 is ((4 √13 + π/2 + 243 √10) / 4) square units.

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Probability that the number of speeding cars is at least 9: 0.009 Expected number of speeding cars, E[X]: 4.5 Variance of the distribution of X: 2.25 Standard deviation of the distribution of X: 1.5 Expected fines generated by the next 9 cars: R19566.

To solve the given problem, we need to assume that the number of cars on the highways follows a binomial distribution with parameters n = 9 (number of trials) and p = 0.5 (probability of a car being above the speed limit).

Probability that the number of speeding cars is at least 9:

Since the probability of a car being above the speed limit is 0.5, the probability of a car not being above the speed limit is also 0.5.

To find the probability of having at least 9 speeding cars, we sum up the probabilities of having 9, 10, 11, ..., up to 9 cars. Mathematically, it can be represented as P(X ≥ 9) = P(X = 9) + P(X = 10) + P(X = 11) + ... + P(X = 9).

Using the binomial probability formula, P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), we can calculate the probabilities for each value of k and then sum them up:

P(X ≥ 9) = P(X = 9) + P(X = 10) + P(X = 11) + ... + P(X = 9)

= [C(9, 9) * 0.5^9 * 0.5^(9 - 9)] + [C(9, 10) * 0.5^10 * 0.5^(9 - 10)] + [C(9, 11) * 0.5^11 * 0.5^(9 - 11)] + ...

Evaluating this expression, we find that P(X ≥ 9) ≈ 0.009 (rounded to 3 decimal places).

Expected number of speeding cars, E[X]:

The expected value of a binomial distribution is given by the formula E[X] = n * p. Therefore, in this case, the expected number of speeding cars is E[X] = 9 * 0.5 = 4.5 (rounded to one decimal place).

Variance of the distribution of X:

The variance of a binomial distribution is calculated using the formula Var(X) = n * p * (1 - p). Substituting the values, we get Var(X) = 9 * 0.5 * (1 - 0.5) = 2.25 (rounded to one decimal place).

Standard deviation of the distribution of X:

The standard deviation is the square root of the variance. Therefore, the standard deviation of the distribution of X is sqrt(2.25) = 1.5 (rounded to one decimal place).

Expected fines generated by the next 9 cars:

Since the average speeding fine per car is R2174, the expected fines generated by a single car is R2174. Therefore, the expected fines generated by the next 9 cars would be 9 * R2174 = R19566.

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Yes You can buy 24 apples for $0.125 per pound. This price will not available except in festival or discounts sale.

what are ounces ?

An ounce is a unit of weight or mass commonly used in the United States and other countries. It is usually abbreviated as oz. One ounce is equal to 1/16th of a pound or approximately 28.35 grams. Ounces are often used to measure small quantities of food or ingredients in recipes, as well as for measuring the weight of small objects.

According to the question:

To determine whether you can buy 24 apples for $9, we need to find the cost per apple.

If 24 apples cost $9, then the cost per apple is:

$9 / 24 apples = $0.375 per apple

Since each apple weighs about 5 ounces, there are about 3 apples per pound:

16 ounces / 5 ounces per apple ≈ 3.2 apples per pound

Therefore, the cost per pound of apples is:

$0.375 per apple / 3 apples per pound = $0.125 per pound

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Answer:

1: 100

3: 65,610,000

Step-by-step explanation:

Probability which helps Asher to win the the game than Eitan , the possible outcomes should be option c. rolling a sum of dice less than 5.

As given in the question,

Possible outcomes after rolling two dice are:

={( 1,1), (1,2), ....(1,6),(2,1),....(2,6),(3,1),.....(3,6), (4,1),.....(4,6), (5,1) , .....(5,6), (6,1) ,...(6,6)}

Probability for each optional outcome is given by :

Total number of outcomes = 36

a. Rolling a sum of dice to 4

Number of favourable outcomes = 4

Probability = 4/36

                  = 1/9

b. Rolling sum of dice to 9

Number of favourable outcomes = 4

Probability = 4/36

                  = 1/9

c. Rolling sum of dice that is less than 5

Number of favourable outcomes = 6

Probability = 6/36

                  = 1/6

d. Rolling a sum greater than 5 less than 7

Number of favourable outcomes = 5

Probability = 5/36

e. Rolling a sum greater than 9 less than 11

Number of favourable outcomes = 3

Probability = 3/36

                  = 1/12

f. Rolling a sum greater than 2 less than 4

Number of favourable outcomes = 2

Probability = 2/36

                  = 1/18

Therefore, probability which helps Asher to win the game is given by Option C. rolling a sum of dice less than 5.

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Answer:

The answer is B,C,D

Step-by-step explanation:

trust me im him

Answer:

The sale this month = 79

Step-by-step explanation:

Let the amount he needs to sell this month = x

\(Average = \frac{sum\ of\ individual\ data\ }{number\ of\ entries}\)

\(Average= \frac{90\ +\ 45\ +\ 103\ +\ 68\ +\ x}{5}\)

Note that number of entries = number of months = 5

To maintain an average sales of 77, the amount of sale in month 5 is determined as follows:

\(77 = \frac{306\ +\ x}{5} \\cross-multiplying\\77\ \times\ 5\ = 306\ +\ x\\385 = 306\ +\ x\\x =385\ -\ 306\\x = 79\)

Answer:

4

Step-by-step explanation:

To cut a 14-inch pizza into three equal area pieces using two parallel cuts placed symmetrically from the center, each piece will have an area of 150.

As we need to cut a 14-inch pizza into three pieces of equal area using two parallel cuts, we have to follow the steps given below

:Step 1: Cut the pizza with a line that goes through the center of the pizza and marks its diameter. This cut separates the pizza into two equal halves.

Step 2: The second cut needs to be made parallel to the first cut and needs to be at a distance of approximately 1/3 the diameter of the pizza from the first cut.

Step 3: Then, the pizza will be separated into three equal area pieces as required. As we have to cut the pizza into three equal area pieces, the area of each piece will be 150 square inches.

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Answer:

number of cans Raina will be needed in court floor is 14 cans

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW;

Raina is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 46 feet and its width is 35 feet. Suppose each can of wood stain covers 115 square feet. How many cans will she need to cover the court?

CALCULATION;

Given:

length of the rectangular shape =46 feet

width of the the rectangular shape = 35 feet.

The floor of the court room is having a rectangular shape, then we need to calculate the surface Area of the rectangular shape first in order to know the number of cans that Raina will be needed

Surface Area= Length × Width

= 46feet × 35 feet

=1610 square ft

Then to get the number of cans , we need to divide the surface Area by each can of wood stain covers which is 115 square feet,

number of cans Raina will be needed in court = 1610 square ft / 115 square ft = 14

number of cans Raina will be needed in court floor is 14cans

Answer:

1: A career is long-term that lasts your whole life while showing progression in a field of work while an occupation is job duties that have simliar to a task but isn't a full term.

2: True

3: To have and know about the knowledge and skills needed in that career and make informed decisions

4: education that will prepare students for postsecondary education and career success.

5: life long learning

6: They help you during your career transitions

7: aptitude is natural talent while the ability is skills developed with practice

8: job shadowing and career mentorship

9: A certification verifies that a professional has met a certain set of criteria for a skill or job as measured by a third-party assessment.

A liscense is verification by a government agency that a professional is able to perform a particular occupation  

10: Print, Media, and online.

11. y=(3/2)x-2

12. y=x+3

13. y=(3/5)x-4

14. y=3x-1

15. y=(5/4)x

im not 100% sure on 14 but the rest of them should b right :)

The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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Answer:

B

Step-by-step explanation:

The Interquartile Range (IQR) rule is a commonly used quantitative rule to determine univariate outliers and deleting a case may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

The Interquartile Range (IQR) rule is a commonly used method for identifying outliers in a univariate data set. It is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1). Outliers are considered to be any values that fall outside of the range Q1 - 1.5 * IQR to Q3 + 1.5 * IQR. This range encompasses approximately 75% of the data, with outliers being any values that fall outside of this range.

In some cases, deleting a case or participant may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

This decision should be made carefully and only after careful consideration of the implications, as removing data can affect the validity of the results and the conclusions that can be drawn from the analysis. In some cases, it may be better to keep the outlier and consider it a potential error or to conduct further analysis to determine if there is a valid reason for the outlier.

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The probability that at least 2 babies out of a cluster of 5 babies will speak tomorrow is 47/128.

To calculate the probability that at least 2 babies out of a cluster of 5 babies will speak tomorrow, we can use the binomial probability formula. The binomial probability formula is given by:

P(X ≥ k) = 1 - P(X < k) = 1 - ∑(i=k-1)^(n) [C(n, i) * p^i * (1-p)^(n-i)]

Where:

P(X ≥ k) is the probability that X is greater than or equal to k

P(X < k) is the probability that X is less than k

n is the number of trials (number of babies in the cluster) = 5

p is the probability of success (probability that a baby speaks) = 1/4

k is the number of successes we are interested in (at least 2 babies speaking)

Let's calculate the probability using this formula:

P(X ≥ 2) = 1 - P(X < 2) = 1 - [P(X = 0) + P(X = 1)]

P(X = 0) = C(5, 0) * (1/4)^0 * (3/4)^(5-0) = 1 * 1 * (3/4)^5 = 243/1024

P(X = 1) = C(5, 1) * (1/4)^1 * (3/4)^(5-1) = 5 * (1/4) * (3/4)^4 = 405/1024

P(X ≥ 2) = 1 - (243/1024 + 405/1024) = 376/1024 = 47/128

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Answer:

the first one gat to be x=4

Answer: 17

Step-by-step explanation: :)

A triangle that is a right triangle will have a sides that form the basis of Pythagorean triple or theorem, which is given as: c² = a² + b². (see diagram attached below).

A triangle that has one of its angles as right angle or two of its sides are perpendicular is referred to as a right triangle or right-angled triangle.

Thus, a triangle that is a right triangle will have a sides that form the basis of Pythagorean triple or theorem, which is given as: c² = a² + b². (see diagram attached below).

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Answer:

1.48

2.138

3.9

4.99

Step-by-step explanation:

I hoped I helped

The equation of the parabola symmetric about x = -10 is y = a(x - (-10))^2 + a.

To write an equation of a parabola symmetric about x = -10, we can use the standard form of a quadratic equation, which is

\(y = a(x - h)^2 + k\), where (h, k) represents the vertex of the parabola.
In this case, since the parabola is symmetric about x = -10, the vertex will have the x-coordinate of -10. Therefore, h = -10.
Now, let's substitute the values of h and k into the equation. Since the parabola is symmetric, the y-coordinate of the vertex will remain unknown. Let's call it "a".
Please note that without further information or constraints, we cannot determine the specific values of "a" or the y-coordinate of the vertex.

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The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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Answer:

92

Step-by-step explanation: