5х2 – 5х
Combine like terms

The number of units of electricity used in one hour is 1.6

An oven uses 8.24 units of electricity in 5 hours

The number of unit used in one hour can be calculated as follows

= 8.24/5

= 1.6

Hence 1.6 units of electricity was used in one hour

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The area of the field is 10,765.44 square meters.

Given that:

Diameter, d = 72 m

Width, W = 72 m

Length, L = 93 m

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the field is calculated as,

A = (π/4)d² + W·L

A = (3.14 / 4) x 72² + 72 x 93

A = 4,069.44 + 6,696

A = 10,765.44 square meters

The area of the field is 10,765.44 square meters.

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Therefore , the solution to the given problem of the test statistics comes out to be Z =1.801.

A test statistic statistic illustrates how closely the distribution of your data matches the hypothesis  of the test statistic you are using. It is possible to figure out the distribution of the data, or how regularly an observation occurs, by looking at the confidence interval and variability around it.

Here,

Given : p' =210/400 = 0.525

p=0.48 , n=400

Test statistics:

=> Z = \(\frac{p'-p}{\sqrt{p(1-p)}/n }\)

=>Z=\(\frac{0.525-0.48}{\sqrt{0.48(1-0.48)}/400 }\)

=> Z = 1.801

Therefore , the test statistics comes out to be Z =1.801.

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Answer:

d = 637 ft below the surface

Step-by-step explanation:

Given

P = 14 + \(\frac{6}{13}\) d

To find d when P = 308, then

14 + \(\frac{6}{13}\) d = 308 ( subtract 14 from both sides )

\(\frac{6}{13}\) d = 294 ( multiply by 13 to clear the fraction )

6d = 3822 ( divide both sides by 6 )

d = 637 ft

Answer:

Step-by-step explanation:

\(P=14+\dfrac6{13}d\\\\\\P=308\,,\qquad\qquad d=??\\\\\\308=14+\dfrac6{13}d\\\\ 308-14=\dfrac6{13}d\\\\294=\dfrac6{13}d\\\\d=294:\frac6{13}\\\\ d=294\cdot\frac{13}6\\\\d=637\,ft\)

Answer:

7.5

Step-by-step explanation:

100 = 36 + x^2

64 = x^2

x = 8

To build a garden of 4 feet Deja needs 12 small bricks.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The first garden is 4 feet long the bricks Deja is using are each 1/3 of a foot long.

Therefore, the number of bricks required is,

= 4/(1/3).

= 4×(3/1).

= 12 bricks.

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Answer:

swap the bottom two. it should be, in this order, 32+c, 0.25, 8, 0.25c

Step-by-step explanation:

The correct option of the given question is option (c)  fissure.

When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is c. fissure.

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The main term to reference in the index when coding the phrase "supravesical fissure of urinary bladder" is c. fissure.

In medical coding, the index is typically organized alphabetically based on the main terms or significant words within medical terminology. In this case, "fissure" is the main term that represents the specific condition or anatomical feature being coded.

The other terms, such as "urinary," "bladder," and "supravesical," provide additional context but are not the primary focus when searching for the appropriate code in the index.

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The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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Differences with in number of volunteers can explain  60.01% of the variation in the amount of trash bags collected.

The coefficient of correlation (r) between both the number of volunteers x and also the number of trash bags collected y is 0.775.

To calculate the percentage of variation for one derivative contract by the other, simply square the correlation coefficient.

Here, r = 0.775

Squaring both side.

r² = 0.775²

r² = 0.600625

Simply multiply with 100 to get the percent.

r² = 60.0625

r² = 60.01

Thus, differences in the number of volunteers can explain 60.01% of the variation in the number of trash bags collected.

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ACTIVITY 3 :Spot the difference

Direction:Below are two sets of mathematical statements. Use these to answer the question and statements that follow. ​

The requirements for a one-sample t-test are generally satisfied assuming a simple random sample and a large enough sample size. However, we cannot determine if the normality requirement is met without examining the data.

To test the claim that the sample is from a population with a mean greater than 80 sec, we need to perform a one-sample t-test. The following requirements must be satisfied to use the one-sample t-test:

The sample must be a simple random sample from the population.

The variable under study must be continuous or approximately continuous.

The population must be normally distributed or the sample size should be large (n > 30).

To determine if the requirements are satisfied for the given data, we need to check if the sample is a simple random sample, the variable (duration times of drug use) is continuous or approximately continuous, and if the population is normally distributed or the sample size is large enough.

Assuming that the sample is a simple random sample, we can check the other requirements:

Continuity: The variable (duration times of drug use) is continuous.

Normality: We can examine a histogram, a normal probability plot, or conduct a normality test such as the Shapiro-Wilk test. If the data is approximately normally distributed, we can proceed with the t-test. If not, we can use a non-parametric test.

Without the data, we cannot determine if the normality requirement is met. However, if the sample size is large (n > 30), we can use the central limit theorem to assume normality. In that case, we can proceed with the t-test.

Therefore, the requirements for a one-sample t-test are generally satisfied assuming a simple random sample and a large enough sample size. However, we cannot determine if the normality requirement is met without examining the data.

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Step-by-step explanation:

X = 10 (use pyth)

Y = 11.18(use pyth)

Answer:

R and s are parallel as they are the same size and length

i would think 2 and 5 or 2 and 6

hope this helps! (:

Normal quantile plot is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution.

What is a Normal Quantile Plot?

A normal quantile plot is a graphical tool used to determine whether a data set is normally distributed or not.

It plots sample data versus a theoretical normal distribution.

In general, the points on the plot should form a straight line if the data is normally distributed. If the data is not normally distributed, the points on the plot will not form a straight line.

A normal quantile plot can be used to evaluate the following:

The normal quantile plot of the residuals is the most important diagnostic tool for examining whether the assumptions of a linear regression model have been met.

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posting answer as a picture because it was "inappropriate"

According to the equation we have After simplifying, the equation in spherical coordinates is: 5ρ^2 - 3ρ sin(θ) cos(φ) = 0 .

To write the given equation in spherical coordinates, we first need to express x, y, and z in terms of rho (ρ), theta (θ), and phi (φ), which are the spherical coordinates.

We know that:

x = ρsinφcosθ
y = ρsinφsinθ
z = ρcosφ

Substituting these values in the given equation, we get:

5(ρsinφcosθ)² - 3(ρsinφcosθ) + 5(ρsinφsinθ)² + 5(ρcosφ)² = 0

Simplifying further, we get:

5ρ²sin²φcos²θ + 5ρ²sin²φsin²θ + 5ρ²cos²φ - 3ρsinφcosθ = 0

Now, we can use the trigonometric identities:

sin²θ + cos²θ = 1
sin²φ + cos²φ = 1

Substituting these in the equation, we get:

5ρ²sin²φ + 5ρ²cos²φ - 3ρsinφcosθ = 0

To rewrite the given equation 5x^2 - 3x + 5y^2 + 5z^2 = 0 in spherical coordinates, we need to use the conversions:

x = ρ sin(θ) cos(φ)
y = ρ sin(θ) sin(φ)
z = ρ cos(θ)

Substitute these conversions into the equation:

5(ρ sin(θ) cos(φ))^2 - 3(ρ sin(θ) cos(φ)) + 5(ρ sin(θ) sin(φ))^2 + 5(ρ cos(θ))^2 = 0

After simplifying, the equation in spherical coordinates is:

5ρ^2 - 3ρ sin(θ) cos(φ) = 0

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Answer:

60

Step-by-step explanation:

the total cupcakes are:

(57/95) . 100 = 60

The given statements are correct or incorrect is given below:

1) Correct.

2) Correct.

3) Correct.

4) Correct.

5) Correct.

6) Incorrect.

7) Correct.

8) Correct.

9) Correct.

10) Incorrect.

Here, we have,

1) Correct. In a simple graphical method, a graph is plotted to show the relationship between water usage and population.

2) Correct. The pressure in a distribution system needs to be sufficient to allow for adequate hydrant flows in case of a fire.

3) Correct. The term "distribution system" refers to the infrastructure and facilities used to supply water from its source to the point of usage.

4) Correct. Brackish water is water that has a higher salinity level than fresh water and even higher than seawater.

5) Correct. Monthly variation in water usage can impact the design and capacity requirements of storage reservoirs.

6) Incorrect. Jordan is considered a "Water Scarce" country, as it faces significant challenges in terms of water availability and scarcity.

7) Correct. During a fire, a significant quantity of water needs to be supplied over an extended period, necessitating a high rate of hourly supply.

8) Correct. The Manning equation is commonly used in the design and evaluation of sanitary sewers.

9) Correct. If the diameter (d) is less than 200 mm, the pipe's final diameter (D) is set at 200 mm.

10) Incorrect. The diameter of the interceptor pipe is typically larger than the diameter of the lateral pipe. The interceptor pipe carries wastewater from multiple lateral pipes.

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The actual dimensions of the rectangular stamp with width 1.4 cm greater than the length are 3.5 cm by 4.9 cm.

It is given that if both the length and width of the rectangular stamp are increased by 1 cm each, the stamp would have a perimeter equal to 20.80 cm.

We have to find the original dimensions of the rectangular stamp.

Let the length of the rectangular stamp be x cm.

Hence, according to the question,

Width of the stamp = (x + 1.4) cm.

If 1 cm is increased in each of the length and width of the stamp,

the increased length and breadth will become,

Width = (x + 1.4) + 1 = (x + 2.4) cm

Length = x + 1 = (x + 1) cm

We know that,

Perimeter of rectangle = 2*(Length + Breadth)

Hence,

Perimeter of rectangular stamp = 2*[(x + 2.40) + (x + 1)]

Perimeter of rectangular stamp = 2*[(x + x) + (2.40 + 1)]

Perimeter of rectangular stamp = 2*[2x + 3.40]

Perimeter of rectangular stamp = (4x + 6.80) cm

We have,

Perimeter = 20.80 cm = (4x + 6.80) cm

Hence,

20.80 - 6.80 = 4x

14 = 4x

x = 14/4

x = 3.5cm

Hence,

x + 1.4 = 3.5 + 1.4 = 4.9cm

Hence,

Original width of the rectangular stamp = 4.9cm

Original length of the rectangular stamp = 3.5cm

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Answer:

1.65

Step-by-step explanation:

Divide 6.6 by 4

Answer: x^2 + y^2 - 4x + 18y = 76 = 0

The center of the circle given is (2, 9)

radius = r

The equation of a circle for a given point is

(x - h)^2 + (y - k)^2 = r^2

Where h = 2, and y = 9

(x - 2)^2 + (y - 9)^2 = 3^2

Expand the parentheses

(x - 2) (x - 2) + (y - 9) (y - 9) = 9

(x - 2) (x - 2 ) = x* x - 2*x - 2*x + 2* 2

= x^2 - 4x + 4

(x - 2) (x - 2) = x^2 - 4x + 4

(y - 9) (y - 9) = y*y - y*9 - 9*y + 9*9

= y^2 - 18y + 81

(y - 9) (y - 9)= y^2 - 18y + 81

Therefore, the equation becomes

x^2 - 4x + 4 + y^2 - 18y + 81 = 9

Re-arrange the equation

x^2 + y^2 - 4x - 18y + 4 + 81 = 9

x^2 + y^2 - 4x - 18y = 9 - 81 - 4

x^2 + y^2 - 4x - 18y = -76

x^2 + y^2 - 4x - 18y + 76 = 0

The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0

Answer:

The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0

Step-by-step explanation:

2-1. a) The shear stress τ is constant across the flow. b) The velocity is maximum at the center (r = 0) and decreases linearly as the radial distance increases. c)v_max = (P₁ - P₂) / (4μL) * \(R^{2}\) and v_avg = (1 / (π(\(R^{2} -a^{2}\)))) * ∫[a to R] v * 2πr dr 2-2.a) The shear stress is constant for parallel plates. b) The velocity profile shows that the velocity is maximum at the centerline and decreases parabolically .c)v_max = (P₁ - P₂) / (2μh) and v_avg = (1 / (2h)) * ∫[-h to h] v dr.

2-1. Flow in an annular region between concentric cylinders:

(a) Shear stress profile:

In an incompressible fluid flow between concentric cylinders, the shear stress τ varies with radial distance r. The shear stress profile can be obtained using the Navier-Stokes equation:

τ = μ(dv/dr)

where τ is the shear stress, μ is the dynamic viscosity, v is the velocity of the fluid, and r is the radial distance.

Since the flow is at steady state, the velocity profile is independent of time. Therefore, dv/dr = 0, and the shear stress τ is constant across the flow.

(b) Velocity profile:

To determine the velocity profile in the annular region, we can use the Hagen-Poiseuille equation for flow between concentric cylinders:

v = (P₁ - P₂) / (4μL) * (\(R^{2} -r^{2}\))

where v is the velocity of the fluid, P₁ and P₂ are the pressures at the outer and inner cylinders respectively, μ is the dynamic viscosity, L is the length of the cylinders, R is the outer radius, and r is the radial distance.

The velocity profile shows that the velocity is maximum at the center (r = 0) and decreases linearly as the radial distance increases, reaching zero at the outer cylinder (r = R).

(c) Maximum and average velocities:

The maximum velocity occurs at the center (r = 0) and is given by:

v_max = (P₁ - P₂) / (4μL) * \(R^{2}\)

The average velocity can be obtained by integrating the velocity profile and dividing by the cross-sectional area:

v_avg = (1 / (π(\(R^{2} -a^{2}\)))) * ∫[a to R] v * 2πr dr

where a is the inner radius of the annular region.

2-2. The flow between parallel plates:

(a) Shear stress profile:

For flow between very wide or broad parallel plates, the shear stress profile can be obtained using the Navier-Stokes equation as mentioned in problem 2-1. The shear stress τ is constant across the flow.

(b) Velocity profile:

The velocity profile for flow between parallel plates can be obtained using the Hagen-Poiseuille equation, modified for this geometry:

v = (P₁ - P₂) / (2μh) * (1 - (\(r^{2} /h^{2}\)))

where v is the velocity of the fluid, P₁ and P₂ are the pressures at the top and bottom plates respectively, μ is the dynamic viscosity, h is the distance between the plates, and r is the radial distance from the centerline.

The velocity profile shows that the velocity is maximum at the centerline (r = 0) and decreases parabolically as the radial distance increases, reaching zero at the plates (r = ±h).

(c) Maximum and average velocities:

The maximum velocity occurs at the centerline (r = 0) and is given by:

v_max = (P₁ - P₂) / (2μh)

The average velocity can be obtained by integrating the velocity profile and dividing by the distance between the plates:

v_avg = (1 / (2h)) * ∫[-h to h] v dr

These formulas can be used to calculate the shear stress profile, velocity profile, and maximum/average velocities for the given geometries.

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T-test is commonly used to examine whether two groups are significantly different from each other or not.

A t-test is an inferential statistic used to determine if there is a significant difference between the means of two groups and how they are related. T-tests are used when the data sets follow a normal distribution and have unknown variances, like the data set recorded from flipping a coin 100 times.

It is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another.

T-test is used to determine whether two groups are different or not.

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The T-test is commonly used to examine whether two groups are significantly different from each other or not.

A T-test is used to determine if two groups are different.

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Answer: A, B

Step-by-step explanation:

Answer:

5.047 and 5.009

el gato?

If we draw a vertical line and it crosses the figure more than once, then it is not a function.

So, the only graph that a vertical line will intersect the line once is graph A:

B, C and D are intersected more than 1 time, so they are not functions.

Answer: A

Answer:

71701,71702, 71703 etc

Step-by-step explanation:

Given :

\(7.17\)×\(10^{4}\) and 8.17×\(10^{5}\)

Now

\(7.17\)×\(10^{4}\)=71700 and

8.17×\(10^{5}\)=817000

There are so many numbers between 71700 and 817000

Like: 71701,71702, 71703 etc