Rewrite the following equation in slope-intercept form.

19x + 18y = –17

The percentage change in productivity for this worker is -5.9%.

Productivity is the amount of goods and services produced by a worker in a given amount of time.

A worker produced 79 units of output in 38 hours. The previous week, the same worker produced 75 units in 34 hours.

Let's determine the productivity of the worker each week.

Step 1: Calculate productivity of the worker in the first week (week 1)

Productivity in week 1 = Total output produced / Number of hours worked

= 75 units / 34 hours

= 2.21 units per hour

Step 2: Calculate productivity of the worker in the second week (week 2)

Productivity in week 2 = Total output produced / Number of hours worked

= 79 units / 38 hours

= 2.08 units per hour

Step 3: Determine the percentage change in productivity

Percentage change = ((New value - Old value) / Old value) x 100%

Where,Old value = Productivity in week 1New value = Productivity in week 2

Substituting the values,Percentage change = ((2.08 - 2.21) / 2.21) x 100%

                                                                        = (-0.059) x 100%

                                                                        = -5.9%

Therefore, This employee's productivity has decreased by -5.9% as a whole.The negative sign indicates a decrease in productivity.

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Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Answer:

64,890

Step-by-step explanation:

105×3 =315

103×2= 206

315×206= 64,890

Answer:

6.489× 10⁴

Step-by-step explanation:

(3×105)×(2×103)

315× 206

64,890

6.489×10⁴

Answer:

  x = 15

Step-by-step explanation:

The solution to any problem is found by making use of the relations you know between the parts of the problem. Here, values of x relate to the arc measures around a circle. The relation you know is the sum of the arcs around a circle is 360°. Using this relation, you can write the equation ...

  7x° +4x° +6x° +7x° = 360°

The equation can be solved for x by making use of the rules of algebra.

  24x = 360 . . . . . . . . . . . . . . divide by °, collect terms

  x = 15 . . . . . . . . . . . . . . . . divide by 24

The mean of the fitted exponential distribution is 66.67.

To find the mean of the fitted exponential distribution, we first need to estimate the parameter lambda using maximum likelihood estimation.

The probability density function of the exponential distribution is given by

f(x; lambda) = lambda * exp(-lambda * x)

where x is the claim size and lambda is the parameter to be estimated.

The likelihood function for the observed data is the product of the individual probabilities of each claim

L(lambda) = lambda^n * exp(-lambda * sum(x_i))

where n is the number of observed claims and x_i is the i-th claim size.

The log-likelihood function is given by:

ln L(lambda) = n * ln(lambda) - lambda * sum(x_i)

To estimate the parameter lambda, we need to maximize the log-likelihood function with respect to lambda:

d/d(lambda) ln L(lambda) = n/lambda - sum(x_i) = 0

Solving for lambda, we get

lambda = n / sum(x_i)

Substituting the observed values, we get

lambda = 6 / (20 + 45 + 50 + 80 + 100 + 2*100) = 0.015

Therefore, the estimated parameter of the fitted exponential distribution is lambda = 0.015.

The mean of the exponential distribution is given by

E(X) = 1/lambda

Substituting the estimated value of lambda, we get

E(X) = 1/0.015 = 66.67

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Answer:

17×6=102 because he gave 2 boxes to his brother so he have 6 boxes

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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The number of permutations of {1, 2, ..., 7} in which 1, 2, and 3 are not in their natural positions is 720.

The principle of inclusion-exclusion. We start by finding the total number of permutations of {1, 2, ..., 7}, which is 7!.

Next, we need to subtract the number of permutations where at least one of the numbers 1, 2, or 3 is in its natural position. Let's calculate this for each number individually and apply the principle of inclusion-exclusion.

1 in its natural position:

For this case, we fix 1 in the first position, and there are 6! ways to arrange the remaining numbers. So, there are 6! permutations with 1 in its natural position.

2 in its natural position:

Similar to the previous case, we fix 2 in the second position, and there are 6! ways to arrange the rest of the numbers. Thus, there are 6! permutations with 2 in its natural position.

3 in its natural position:

Fixing 3 in the third position, there are again 6! ways to arrange the remaining numbers. Therefore, there are 6! permutations with 3 in its natural position.

Now, we need to subtract the cases where two of these numbers are in their natural positions. Let's consider each combination:

1 and 2 in their natural positions:

Fixing 1 in the first position and 2 in the second position, there are 5! ways to arrange the remaining numbers. Thus, there are 5! permutations with 1 and 2 in their natural positions.

1 and 3 in their natural positions:

Similarly, fixing 1 in the first position and 3 in the third position, there are 5! ways to arrange the remaining numbers. So, there are 5! permutations with 1 and 3 in their natural positions.

2 and 3 in their natural positions:

Fixing 2 in the second position and 3 in the third position, there are 5! ways to arrange the rest of the numbers. Therefore, there are 5! permutations with 2 and 3 in their natural positions.

Finally, we need to add back the case where all three numbers are in their natural positions:

1, 2, and 3 in their natural positions:

Fixing 1 in the first position, 2 in the second position, and 3 in the third position, there are 4! ways to arrange the remaining numbers. Thus, there are 4! permutations with 1, 2, and 3 in their natural positions.

Applying the principle of inclusion-exclusion, the number of permutations where 1, 2, and 3 are not in their natural positions is:

Total permutations - (permutations with 1) - (permutations with 2) - (permutations with 3) + (permutations with 1 and 2) + (permutations with 1 and 3) + (permutations with 2 and 3) - (permutations with 1, 2, and 3)

= 7! - 6! - 6! - 6! + 5! + 5! + 5! - 4!

= 5040 - 720 - 720 - 720 + 120 + 120 + 120 - 24

= 5040 - 2160 - 2160 - 2160 + 360 + 360 + 360 - 24

= 720

Therefore, the number of permutations of {1, 2, ..., 7} in which 1, 2, and 3 are not in their natural positions is 720.

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Answer:

The line that represents a proportional relationship is y3 which is letter C in the Cartesian Plane

Explanation:

The line that goes through the origin of where x-axis and y-axis meet or intersect at the same point is called a proportional relationship

Answer:

Step-by-step explanation:

you do base times height

Answer:

110.5 cm²

Step-by-step explanation:

The figure is composed of a rectangle with a triangle on top.

Area of rectangle = 13 × 6 = 78 cm²

Area of triangle = \(\frac{1}{2}\) bh ( b is the base and h the height )

Here b = 13 and h = 11 - 6 = 5 cm , then

A = \(\frac{1}{2}\) × 13 × 5 = 32.5 cm°

Thus

total area = 78 + 32.5 = 110.5 cm²

Answer:

Tessa receives £60

Step-by-step explanation:

The ratio is 5:3 so 5+3=8 which is then what you use to divide 96

96/8=12

12x5(the 5 comes from the ratio for Tess) is 60 therefore she receives £60

Answer:

Step-by-step explanation:

Tesa and Vivienne share £96 in the ratio 5:3. How much does Tesa receive?​

96 : (5 + 3) = 12

12 * 5 = 60

The equation that shows the cost of salsa is (c) d = 5p

From the question, we have the following parameters that can be used in our computation:

p  4      6     8

d  20   30   40

The equation that shows the cost of salsa. is calculated as

p : d = 4 : 20

Express the ratio as fraction

So, we have the following representation

p/d = 4/20

Take the inverse of both sides

d/p = 20/4

Evaluate

d/p = 5

So, we have

d = 5p

Hence, the equation is (c) d = 5p

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Answer:

If this is your question: john and jack divided there math homework.John solved twice as many problems as jack plus 1 more problem how many problems did each boy solve if there are 28 assigned problems?

Answer:

John: 19

Jack: 9

Step-by-step explanation:

Hope it helps! God bless!

ANSWER

True

EXPLANATION

We have that:

f(6) = 60

That means whatever f(x) is, when we put the value of x to be 6, we will get f(x) = 60.

So, to see if f(x) = 14x - 24 is a possible function, we will replace x with 6 and find out if we get 60:

f(6) = 14(6) - 24

f(6) = 84 - 24

f(6) = 60

As we can see, we got that f(6) = 60, so, it is true that it is a possible function.

Answer:

inside the c circle put 12 inside the d circle put 7 and inside the middle put 19 or 15 and inside rectangle put 30

To perform the operation (DE)F, we need to multiply matrices D and E first, and then multiply the resulting matrix by matrix F.

Matrix multiplication is defined when the number of columns in the first matrix matches the number of rows in the second matrix. Let's assume that D is a matrix of size m x n, E is a matrix of size n x p, and F is a matrix of size p x q. The resulting matrix (DE) will have a size of m x p. If p and q are not equal, the operation is undefined.

In matrix multiplication, each element of the resulting matrix is computed by taking the dot product of a row from the first matrix and a column from the second matrix. The dot product is obtained by multiplying corresponding elements and summing them up. To perform (DE)F, we first multiply matrices D and E. If the dimensions allow, let's say the resulting matrix is G with dimensions m x p. Then, we multiply G by matrix F.

Let's say D is a 3x2 matrix, E is a 2x4 matrix, and F is a 4x3 matrix. The product of D and E is matrix G, with dimensions 3x4. If matrix F is a 4x3 matrix, then the operation (DE)F is defined. To compute (DE)F, we multiply G and F. If the dimensions are valid, the resulting matrix will have dimensions 3x3. Each element in the resulting matrix is obtained by taking the dot product of a row from G and a column from F.

If the dimensions allow, we can perform the operation (DE)F by first multiplying matrices D and E to obtain matrix G, and then multiplying G by matrix F to get the final result.

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Answer:

a=10

Step-by-step explanation:

Answer:

\(8x-36\)

Step-by-step explanation:

\(4(2x-9)\)

Through distributing the \(4\) into \(2x\) and \(-9\) (multiply), \(4(2x-9)\) is equivalent to:

\(8x-36\)

There are other solutions for this problem, but this is the most easily reachable solution.

-

You can check if the solution is equivalent & correct by first dividing it by 2:

\(\frac{8x-36}{2} =\)

\(4x-18\)

With that, you can factor out a 2 from both \(4x\) and \(-18\) to get:

\(4(2x-9)\)

Therefore, this solution is correct!

Answer: y = 45x + 345

Step-by-step explanation:

Hope this helps!!! :)

The answers are:

a. The correlation between lunch and helmet is 84.8%.

b. The slope is 0.538 and the intercept is 22.1.

c. It means that even if no children receive reduced-fee lunches, there would still be a baseline percentage of 22.1% of bike riders wearing helmets.

d. It means that for every 1% increase in the percentage of children receiving reduced-fee lunches, there is an expected increase of 0.538% in the percentage of bike riders wearing helmets.

e. The residual is 40 - 41.9 = -1.9%. In this context, the negative residual suggests that the actual percentage of bike riders wearing helmets is slightly lower than the predicted value, given the percentage of children receiving reduced-fee lunches.

(a) The correlation coefficient (r) between lunch and helmet can be calculated using the formula: r = (R^2)^(1/2). Given that R^2 is 72%, we can find r = sqrt(0.72) = 0.848.

(b) The slope (b) and intercept (a) for the least-squares regression line can be calculated using the formulas: b = r * (SDy / SDx) and a = mean_y - b * mean_x. With SDy = 16.9%, SDx = 26.7%, mean_y = 38.8%, and mean_x = 30.8%, we can find b = 0.848 * (16.9 / 26.7) = 0.538 and a = 38.8 - 0.538 * 30.8 = 22.1.

(c) The intercept (a) represents the predicted percentage of bike riders wearing helmets when the percentage of children receiving reduced-fee lunches is 0.

(d) The slope (b) represents the change in the percentage of bike riders wearing helmets for each 1% increase in the percentage of children receiving reduced-fee lunches.

(e) To calculate the residual for a neighborhood where 40% of children receive 0% reduced-fee lunches and 40% of bike riders wear helmets, we can use the formula: residual = observed_y - predicted_y. Given that observed_y is 40% and predicted_y can be calculated as a + b * x, where x is 40%, we have predicted_y = 22.1 + 0.538 * 40 = 41.9%.

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Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

B postulates and C axioms are accepted without proof in a logical system.

A theorem is a statement that can be proven true using standard mathematical operations and reasoning. A theorem, in general, is an embodiment of a general principle that is part of a larger theory. A proof is the process of demonstrating that a theorem is correct.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

Step-by-step explanation:

3.2 + 2 ( y - 1.2 ) = ?

3.2 + 2 ( 6 - 1.2 ) = ?

3.2 + 2 ( 5.8 ) = ?

3.4 ( 5.8 ) =

12.8

Hope this helps! <3

Answer:

y>=-2x-5 is the answer. Just to be sure, check the points of the equation with an ordered pair shaded that should reveal if this answer is valid.

Step-by-step explanation:

Answer:

Maybe just 26 cause when you do 26/1 as a fraction that’s indicating it’s a whole number so just try 26, I’m not completely sure though. Sorry wish I could help more

Step-by-step explanation:

The theoretical probability is 0.5

the practical probability is 0.5

Given, A coin is tossed 50 times, and it lands on heads 28 times. Theoretically, when a coin is tossed the probability of getting a head is 0.5 since in this question we tossed the same coin so the theoretical probability of the given question is 0.5. as per the given data, the Practical probability of getting a head is event happen divided by total events.

Practical probability = 28/50 = 0.56

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The number of points Jim scored is 15 points.

The number of cars given the ratio of car to boat is 140 cars

Total points = Number of points Kevin has + Number of points Jim has

22 = x + (8 + x)

22 = x + 8 + x

22 = 2x + 8

22 - 8 = 2x

14 = 2x

divide both sides 2

x = 14/2

x = 7

Number of points Jim has = 8 + x

= 8 + 7

= 15 points

Part B:

Boat : car

2 : 5 = 56 : x

2/5 = 56/x

cross product

2 × x = 56 × 5

2x = 280

divide both sides by 2

x = 280/2

x = 140

Therefore, the number of points Jim scored is 15 points and the number of cars is 140

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