During the holiday, students went swimming in a local rectangular pool. The pool measures 20 feet by 35 feet. It is surrounded by a patio that is uniform width. Find the width of the patio if the total area of the pool and patio is 1350 sqr feet. Write a quadratic equation to solve the problem.

Answer:

Yes.

Step-by-step explanation:

Because

6*4 =24

and 4*0 = 0,

24+0=24

have a nice day!!!

Given the marginal willingness to pay for oil, the constant marginal cost of extraction, and a discount rate of 1%, the oil reserve will last for approximately 10.8 periods.



To determine how long the oil reserve will last, we need to find the point at which the marginal cost of extraction equals the marginal willingness to pay for oil. In this case, the marginal cost is constant at $4 per unit. The marginal willingness to pay is given by the equation P = 7 - 0.40q, where q represents the quantity of oil extracted.

Setting the marginal cost equal to the marginal willingness to pay, we have:4 = 7 - 0.40q

Simplifying the equation, we get:0.40q = 3

q = 3 / 0.40

q ≈ 7.5So, at q ≈ 7.5, the marginal cost and marginal willingness to pay are equal. We can interpret this as the point at which the country would extract the oil until the quantity reaches 7.5 units. To determine how long this would last, we need to divide the total oil reserve (5 units) by the extraction rate (7.5 units per period):5 / 7.5 ≈ 0.67

Since the extraction rate is less than 1 unit per period, it means that the oil reserve will last for approximately 0.67 periods. However, the discount rate of 1% needs to be taken into account. To calculate the present value of the oil reserve, we discount each period's value. Using the formula for present value, we find that the oil reserve will last for approximately 10.8 periods.

To learn more about interpret click here

brainly.com/question/29671241

#SPJ11

An ensemble approach called bagging combines the predictions from all models after fitting each one to a distinct portion of a training dataset.

When the standard deviation is low, the data tend to cluster around the mean; when it is large, the data are more spread. Calculated using the standard deviation, the data's divergence from the mean value is determined. It is useful for contrasting data sets with possibly the same mean but a distinct range. For instance, the mean of the two following numbers is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. But it's clear that the second is more diffused. The standard deviation shows how erratic the data is. It conveys the difference between each observed value and its mean.

given

An variation of bagging called random forest additionally randomly chooses the subsets of features that are applied to each data sample.

With the addition of splitting on a random subset of characteristics, random forest outperforms bagging by decorrelating the trees.

As a result, the model only takes into account a small subset of its properties at each branch in the tree rather than all of them.

To know more about standard deviation visit :-

https://brainly.com/question/23907081

#SPJ1

Answer:

image below

Step-by-step explanation:

The rejection region for the given combinations of Ha, alpha, and n is given below:c. Ha: μ > 10;

alpha = 0.01

n = 12

Level of significance, α = 0.01

Since it is a right-tailed test, the critical value zα is obtained from the z-table as follows:

z0.01 = 2.33

The rejection region is z > 2.33.If z-calculated > 2.33, reject the null hypothesis; otherwise, fail to reject it.d.

Ha: μ < 10;

alpha = 0.10

n = 11

Level of significance, α = 0.10

Since it is a left-tailed test, the critical value zα is obtained from the z-table as follows:

z0.10 = -1.28

The rejection region is z < -1.28.If z-calculated < -1.28, reject the null hypothesis; otherwise, fail to reject it.e.

Ha: μ ≠ 10

alpha = 0.01

n = 19

Level of significance, α = 0.01

Since it is a two-tailed test, the critical value zα/2 is obtained from the z-table as follows:

z0.005 = 2.58

The rejection region is z > 2.58 and z < -2.58.If |z-calculated| > 2.58, reject the null hypothesis; otherwise, fail to reject it.f. Ha: μ < 10;

alpha = 0.05

n = 5

Level of significance,

α = 0.05

Since it is a left-tailed test, the critical value tα is obtained from the t-table with (n-1) degrees of freedom as follows: t

0.05,4 = -2.78

The rejection region is t < -2.78.If t-calculated < -2.78, reject the null hypothesis; otherwise, fail to reject it.

To know more about value visit :

https://brainly.com/question/30145972

#SPJ11

With the volume of water poured at rate 8 m³/minute, when the height of water is 5 meters, the water will be rising at rate 0.23 m/minute.

Let:

r = radius of water at an instant

h = level of water at an instant

Then,  due to similarity property:

r/h =  4/6 = 2/3

Or,

r = 2/3 . h

The volume of the poured water is:

V = 1/3. πr².h

Substitute r = 2/3 . h into the formula:

V = 1/3. π(2/3. h)².h

V = 4/27. πh³

Take the derivative with respect to t:

dV/dt = 4/27 . 3πh² . dh/dt

dV/dt = 4/9 . πh² . dh/dt

Substitute: dV/dt = 8 m³/minute and h = 5 m:

8 = 4/9 .  π .5² . dh/dt

dh/dt = 0.23 m/minute.

Learn more about derivative here:

https://brainly.com/question/28780341

#SPJ4

5(p+5) + 6(p+6)

First step: Distribute  (PEMDAS --> Parenthesis)

5p + 25 + 6p + 36       Now, combine like terms

11p + 61

Thus, the answer is 11p + 61

\(5(p+5)+6(p+6)\\\\=5p+25+6p+36\\\\=11p+61\)

Answer:

The number is 15

Step-by-step explanation:

x = a number

4/3 x - 12 = 8

Rearrange the equation so that the integers are on one side - in the format Ax = B

4/3 x - 12 = 8

4/3 x = 8 + 12

4/3 x = 20

Simplify the equation - in the format x = A - then solve for x

4/3 x = 20

4 x = 20 * 3

4 x = 60

x = 60 / 4

x = 15

\( \large \bf \implies{A\: number\: is\:15}\)

A number is x

then we have \(\frac{4}{3}\)x - 12 = 8

\( \bf \longrightarrow \frac{4}{3}x - 12 = 8 \\ \\ \bf \longrightarrow \frac{4}{3}x = 8 + 12 \\ \\ \bf \longrightarrow \frac{4}{3}x = 20 \\ \\ \bf \longrightarrow 4x = 20 \times 3 \\ \\ \bf \longrightarrow4x = 60 \\ \\ \bf \longrightarrow x = \frac{ \cancel{60}}{ \cancel{4} } \\ \\ \bf \longrightarrow \: x = 15\)

'Four thirds of the number is \(\frac{4}{3}x\) then decreased by 12 is \(\frac{4}{3}x - 12\) then gives the result 8. That is \(\bf\frac{4}{3}x - 12 = 8\)'

The following statements are TRUE about hypothesis testing ;

hypothesis testing is known as statistical inference type that uses data from a sample to develop inferences about a population parameter or population probability distribution. An educated guess is first made on the parameter or distribution.

To learn more about hypothesis testing

https://brainly.com/question/17099835

#SPJ4

The table of values for the function y = -4x.

The table is attached below-

Hence, the values for the function is giiven below

To understand more about Simple equations refer -

https://brainly.com/question/25020119

#SPJ1

Answer:

Can you be more specific, like y is what and k is what because it tells us what x is but not the rest.

Step-by-step explanation:

Answer:

d≤69

Step-by-step explanation:

The sum of the series converges to 7 / (1 + 2z), and the domain for which it converges is -1/2 < z < 1/2.

To find the sum of the given geometric series\(7−14z+28z^2−56z^3+\)⋯, we need to first identify the first term (a) and the common ratio (r).
Step 1: Identify the first term (a)
The first term is 7.
Step 2: Identify the common ratio (r)
Observe the series and find the ratio between consecutive terms:
-14z / 7 = -2z
\(28z^2 / -14z = -2z\)
\(-56z^3 / 28z^2 = -2z\)
The common ratio is -2z.
Step 3: Determine the convergence of the series
A geometric series converges when the absolute value of the common ratio (|r|) is less than 1:
| -2z | < 1
To solve for the domain of z, we need to find the values for which this inequality holds:
-1 < -2z < 1
Divide all parts of the inequality by -2, and remember to reverse the inequality signs when dividing by a negative number:
1/2 > z > -1/2
Step 4: Find the sum of the converging series
For a converging geometric series, the sum can be calculated using the formula:
sum = a / (1 - r)
Plug in the values of a and r:
sum = 7 / (1 - (-2z))

for such more question on  converges

https://brainly.com/question/30583079

#SPJ11

The margin of error for a 95 percent confidence interval estimate for the true population mean is approximately 2.29 miles.

To calculate the margin of error, we need to use the formula:

Margin of Error = (Critical Value) x (Standard Deviation / √Sample Size)

For a 95 percent confidence level, the critical value can be obtained from the standard normal distribution table. The critical value corresponding to a 95 percent confidence level is approximately 1.96.

Given:

Sample Standard Deviation (s) = 5.30 miles

Sample Size (n) = 20

Using the formula:

Margin of Error = 1.96 x (5.30 / √20) ≈ 1.96 x (5.30 / 4.47) ≈ 1.96 x 1.18 ≈ 2.29 miles

Therefore, the margin of error for a 95 percent confidence interval estimate for the true population mean is approximately 2.29 miles.

The margin of error represents the range within which we can reasonably expect the true population mean to fall. In this case, with a 95 percent confidence level, we estimate that the true mean number of miles downtown employees commute to work roundtrip each day is within 2.29 miles of the sample mean.

To know more about mean follow the link:

https://brainly.com/question/1136789

#SPJ11

The required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
3 1/2+(-7 1/5) = 3+(-7) + 2/5 + (-1/5)
7/2 - 34/5 = -4 + 2/5 + -1/5
-33/10 =  -4 + 1/5
-33/10 ≠ -19/5

Thus, the required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1

The cost of each printer is $568.

To find the cost of each printer, we need to use a system of equations.

Let's call the cost of each printer "p" and the cost of each camera "c".

The first equation we can create is: 6p + 3c = 4773

The second equation we can create is: 4p + 6c = 5002

Now we can use the elimination method to solve for one of the variables.

Let's eliminate the "c" variable by multiplying the first equation by -2: -12p - 6c = -9546

And then add the two equations together: -8p = -4544

Now we can solve for "p" by dividing both sides by -8: p = 568

So the cost of each printer is $568.

To find the cost of each camera, we can plug the value of "p" back into one of the original equations and solve for "c":

6(568) + 3c = 4773

3408 + 3c = 4773

3c = 1365

c = 455

So the cost of each camera is $455.

Therefore, the cost of each printer is $568 and the cost of each camera is $455.

Learn more about unit cost at https://brainly.com/question/29355214

#SPJ11

Answer:

48 ft

Step-by-step explanation:

4 + 8 + 13 + 5 + 11 + x =

12 + 18 + 11 + x =

30 + 11 + x =

41 + x =

NOW TO SOLVE FOR X:

The width of the bottom and the top are equal. 11 - 4 = 7. The missing number is 7.

41 + 7 = 48 ft

Answer:

1 - 109 degrees

2- 71 degrees

3 - 109 degrees

Step-by-step explanation:

Opposite angles are equivalent.

A straight angle is 180 degrees. Subtract 71 from 180 and you'd get 109. Therefore, the Angle 1 is 109 degrees.

Since Angle 3 is the opposite of Angle 1, they are equivalent.

Angle 2 is the opposite of Angle 4, so they are equivalent as well!

Answer:

∠1= 109°, ∠2=71°, ∠3=109°, ∠4=71°

Step-by-step explanation:

Angles 4 and 2 are vertical angles therefore are congruent and have equal measure; because is given m∠4=71° then m∠2 = 71°

Angle 4 and 3 are a linear pair so m∠4+m∠3 =180° so m∠3 = 180 -71 =109°

Angles 1 and 3 are vertical angles therefore are congruent and have equal measure; because we found that  m∠3=109° then m∠1 = 109°

Solution:

y=mx^2-5x-2

To find x-intercepts we must equal y to zero:

y=0→mx^2-5x-2=0

This is a quadratic equation, and we can solve it using the quadratic formula:

ax^2+bx+c=0; a=m, b=-5, c=-2

x=[-b +- sqrt( b^2-4ac) ] / (2a)

x=[-(-5) +- sqrt( (-5)^2-4(m)(-2) ) ] / (2(m))

x=[5 +- sqrt(25+8m)] / (2m)

This equation doesn't have solution (no x-intercepts) if:

25+8m<0

This is an inequality. Solving for m: Subtracting 25 both sides of the inequality:

25+8m-25<0-25

8m<-25

Dividing both sides of the inequality by 8:

(8m) / 8 < (-25) / 8

m<-25/8

Answer: The graph of y=mx^2-5x-2 have no x-intercepts for m<-25/8

Number 21.8

21.849 This number is rounded to 21.8

O 21.749 This number is not rounded

O 21.761 This number is rounded to 21.8

O 21.850 This number is not

21.708 This number is not



The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

for more questions on traction control system

https://brainly.com/question/32581998

#SPJ8

Answer:

mean ( averege) is the sum of the value divided by the number of value

mean= (5+12+17+7+7) / 5

=48/5

= 9.6

Answer:

The mean is the sum of the value divided by the number of the values.

i.e. mean = (5+12+17+7+7) / 5

=48/5

= 9.6

Answer:

Part A: 1

Explain: The solution for a pair of lines is where they intersect.

Part B: (3,4)

Explain: (3,4) is the place where the lines intersect.

Answer:

Step-by-step explanation: How do you find the 3rd angle of a triangle?

Image result for im not sure on how to do this If one angle of a triangle is 30° more than twice another angle, and the third angle is equal to the sum of the first two angles, find the measure of each angle.

The three angles of any triangle add up to 180 degrees. Since you know two angles (35 and 40), add them together, then subtract the total from 180 to determine the degree of the third angle.

The smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

The nullity of a matrix is the dimension of its null space, which represents the set of vectors that satisfy the equation A * x = 0, where A is the matrix and x is a vector.

The nullity of a matrix can range from 0 to the number of columns in the matrix. In this case, since A is a 3 x 8 matrix, the minimum possible value of nullity(A) is 0, indicating that the null space is trivial and contains only the zero vector. This occurs when the matrix is full rank, meaning that its columns are linearly independent.

On the other hand, the maximum possible value of nullity(A) is 8, which would occur if the matrix has rank 0. In this case, all the columns of the matrix are linearly dependent, and the null space spans the entire vector space of size 8.

Therefore, the smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

Learn more about nullity and rank of matrices here: brainly.com/question/31051373

#SPJ11

The value of S, which represents the length of each side of the square, is 4 miles.

To find the value of S, we need to determine the length of each side of the square. Given that the perimeter of the square is 16 miles, we can use the formula for the perimeter of a square, which is 4 times the length of a side.

Perimeter = 4 × S

Given that the perimeter is 16 miles, we can substitute this value into the equation:

16 = 4 × S

To solve for S, we divide both sides of the equation by 4:

16 ÷ 4 = S

4 = S

Therefore, S, which stands for the square's side lengths, has a value of 4 miles.

So, S = 4 miles.

This means that each side of the square measures 4 miles, and the square has equal sides and right angles at each corner.

for such more question on value

https://brainly.com/question/4344214

#SPJ8

Answer:

x-1=y

Step-by-step explanation:

Is this what you need?

a. The z-score is approximately 0.43.

Draw the Normal curve and shade the area to the left of the z-score.

b. The corresponding z-score is approximately -1.10.

Draw the Normal curve and shade the area to the left of the z-score.

A standard Normal distribution means that we have a bell-shaped curve with a mean of 0 and a standard deviation of 1. A Normal curve, we can use a graphing calculator or a standard Normal distribution table.
a. The z-score that gives a left area of 0.6768, we need to look up the value in the Standard Normal distribution table. A printed table or an online calculator to find that the z-score is approximately 0.43.

Draw the Normal curve and shade the area to the left of the z-score.
b. To find the z-score that gives a left area of 0.1332, we can again use the Standard Normal distribution table.

This time, we look up the area that corresponds to 0.1332 and find that the closest value is 0.1335.

The corresponding z-score is approximately -1.10.

We can then draw the Normal curve and shade the area to the left of the z-score.
To draw a well-labeled Normal curve for each part, we first need to find the corresponding z-score using a Standard Normal distribution table.

The z-score to shade the area to the left of the curve and label the mean and standard deviation on the x-axis.

Drawing the Normal curve helps us visualize the distribution and calculate probabilities for various events.

For similar questions on Normal Curve

https://brainly.com/question/27271372

#SPJ11

The general term an of the sequence is given by:\(a_n = (-1)^{(n+1)} * 2 / (3^{(n-1)})\)

A list of numbers in a specific order is called a sequence. The terms of the sequence are the various numbers that appear in it.

To find a formula for the general term of the sequence, we can observe the pattern in the given terms.

We have:

a₁ = 2

a₂ = -2 / (1 + (-2)) = -2/(-1) = 2

a₃ = 2 / (1 + 2) = 2/3

a₄ = 2/3 / (1 + 2/3) = 2/3 / (3/3 + 2/3) = 2/3 / 5/3 = 2/3 * 3/5 = 2/5

a₅ = 2/5 / (1 + 2/5) = 2/5 / (5/5 + 2/5) = 2/5 / 7/5 = 2/5 * 5/7 = 2/7

From the pattern we can observe that the sign alternates between positive and negative, and the denominator increases by multiplying by 3 each time. The numerator remains constant as 2.

Therefore, the formula for the general term of the sequence is:

\(a_n = (-1)^{(n+1)} * 2 / (3^{(n-1)})\)

So, for the given sequence, we have:

\(a_1 = 2\\a_2 = (-1)^{(2+1)} * 2 / (3^{(2-1)}) = 2\\a_3 = (-1)^{(3+1)} * 2 / (3^{(3-1)}) = -2/3\\a_4 = (-1)^{(4+1)} * 2 / (3^{(4-1)}) = 2/9\\a_5 = (-1)^{(5+1)} * 2 / (3^{(5-1)}) = -2/27\)

Therefore, the general term an of the sequence is given by:\(a_n = (-1)^{(n+1)} * 2 / (3^{(n-1)})\)

Learn more about sequence on:

https://brainly.com/question/30194025

#SPJ4