The area of the rectangle is 3x² + 7x + 2 with a width of (x + 2) meters, write the
expression that would represent the length of the rectangle. Hint: A=l. W
O (3x + 1)
O (1-7)
O (2+7)
O (3x - 1)

Answer:

The answer is 15

Step-by-step explanation:

add 5 plus 2 equals 7 then divide 10 with 5 equals 2 then 2 times 2 times 2 equals 8 then you have your answer 8 plus 7 equals 15

and the reason I said 2 times 2 times 2 was because there is a 3 and you have to do that 3 times

Hope it helps plz give me brainlist

The Correct answer is option a. 7-9.42, P-value = 0.002 which is derived based on the given data about alcohol consumption.

The chi-square test of homogeneity is a statistical test used to determine whether there is a significant difference between the observed frequencies of two categorical variables.

In this case, the test statistic would be the chi-square value calculated using the observed frequencies of alcohol consumption in the sample of smokers and non-smokers, and the P-value would be the probability of obtaining a chi-square value as extreme or more extreme than the calculated value under the assumption that the null hypothesis is true (i.e. no difference in alcohol consumption between smokers and non-smokers).

In this case, the test statistic would be 7.942 and the P-value would be 0.002 which implies that there is a significant difference in alcohol consumption between smokers and non-smokers.

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Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

In this scenario, there are four people in a room. Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

The remaining person is a foreign agent who has chosen a pair randomly. Thus, if any two of the three people with the valid pairs collaborate, they can successfully uncover the secret, as per the properties of the Shamir secret sharing scheme.

The presence of the foreign agent does not affect the security of the scheme unless they collaborate with another person possessing a valid pair.

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Answer:

1

Step-by-step explanation:

|x| means the absolute value, which is 4 and -4

Answer:

A

Step-by-step explanation:

So we have the equation:

\(|x|=4\)

Solve for x. Use the definition of absolute value:

\(|x|=4\)

This means that:

\(x=4\text{ or } x=-4\)

And... we're done :)

The answer is A.

The expression does not exist when x = 1/√3, or x = -1/√3

The given quotient is \(3x^2 - 27x^2/x^2 - 13x - 7 / 3x^4x^2 - 1\).

To simplify the quotient, we need to factor the numerator and denominator.
The numerator \(3x^2 - 27x^2\) can be factored as \(-24x^2.\)
The denominator \((x^2-13x-7)\) cannot be factorised.  

The denominator \((3x^6-1)\) can be factored as \((\sqrt3x^3 - 1)(\sqrt3x^3 + 1).\)
Therefore, the simplified form of the quotient is\(-24x^2/(x^2-13x-7)(3x^6-1)\)

The numerator of the simplified form is \(-24x^2.\)and the denominator is \((x^2-13x-7)(\sqrt3x^3 - 1)(\sqrt3x^3 + 1).\).

The expression does not exist when  x = 1/√3, or x = -1/√3 because these values would result in a division by zero, which is undefined.

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Answer:

see photo#5

Step-by-step explanation:

The one-sided p value for a z-statistic of 1.72 is approximately 0.0427.

To calculate the one-sided p value for a z-statistic of 1.72:

Step 1: Identify the z-statistic (zstat) given in the question, which is 1.72.

Step 2: Look up the z-statistic in a standard normal (z) table or use an online calculator to find the area to the left of the z-statistic. For a z-statistic of 1.72, the area to the left is approximately 0.9573.

Step 3: Since we want the one-sided p-value, and our z-statistic is positive, we'll calculate the area to the right of the z-statistic. To do this, subtract the area to the left from 1:

P-value (one-sided) = 1 - 0.9573 = 0.0427

The one-sided p-value for a z-statistic of 1.72 is approximately 0.0427.

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Answer:

Step-by-step explanation:

1. Verticutting - Removes soil about 4 inches deep and makes a mess 2. Aeration - Makes holes in soil without removing soil 3. Topdressing - Used mostly for renovation rather than routine maintenance 4. Leveling - Can be used to fill in holes and provide a smoother surface 5. Reel mowing - Trues turf surface by removing grain.

1. Verticutting is a cultural practice that involves removing soil about 4 inches deep and creates a messy appearance. It is commonly used to control thatch buildup and promote healthy turf growth.

2. Aeration is a technique that creates holes in the soil without removing the soil itself. It helps alleviate soil compaction, improve air and water movement, and enhance root development.

3. Topdressing is primarily utilized for renovation purposes rather than routine maintenance. It involves applying a thin layer of sand, soil, or organic material to the turf surface, which helps improve soil composition, level uneven areas, and enhance turf health.

4. Leveling is a process that can be employed to fill in holes and provide a smoother surface. It aims to eliminate unevenness and create a more uniform and aesthetically pleasing turf.

5. Reel mowing is a practice that trues the turf surface by removing grain. It involves cutting grass using a reel mower, which delivers a precise and uniform cut, resulting in a smoother appearance and improved playability.

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Answer:

A) The total length of each edging in her scale drawing would be 19.2 centimeters.

B) Square or rectangle

C) angle  α= 53.13 degrees

angle β=  36.87 degrees

height=  32 inches

base= 24 inches

hypotenuse 40 inches.

Step-by-step explanation:

Part A:

If the roll edging is 96 inches long and the scale chosen is

5inches = 1 cm

96inches /5= 19.2cm

The total length of each edging in her scale drawing would be 19.2 centimeters.

Part B:

The quadrilaterals such rectangle square right  trapezoid have a pair of 90 degrees angles.

If we choose a square shape then all sides must be equal. And we have a length of 19.2 centimeters.

Dividing 19.2 by 4  gives 4.8 cm for each side.

Figure A  shows a square and has 4 sides equal and 4 right angles.

If we choose a rectangle shape then 2 sides must be equal. We have a length of 19.2 centimeters.

Suppose the length is 2 times more than the width

which will give the dimensions as

2*2 x+ 2x= 6x   ( length and width denoted by x)

Dividing 19.2 by 6  gives 3.2 cm for each width and  6.4 for the lengths.

Figure B shows a rectangle  and has 2 sides equal and 4 right angles.

It depends on which quadrilateral you wish to choose.

Part C:

Using Pythagorus theorem if the base and altitude are given then the hypotenuse can be found out using the following formula.

c²= a² +b²

c²= 6.4² +4.8²

c²= 40.96+23.04= 64

c= √64 = 8

The third side must be equal to 8 centimeters.

Using the formula

Cos α= base / hypotenuse

Cos α=4.8/8

α= Cos (inverse) 4.8/8

α= Cos (inverse) 0.6

α= 53.13 degrees

So angle α= 53.13 degrees

All the angles in the triangle must be 180 degrees.

α + β +  90°= 180°

And angle β= 180-90-53.13= 36.869= 36.87 degrees

The actual dimensions of this triangle are

height= a= 6.4* 5= 32 inches

base= b= 4.8*5= 24 inches

hypotenuse= 8*5= 40 inches.

The radius of each circle is approximately 3.46 units.

Since the two circles are congruent and tangent to each other, their centers are located on the same line perpendicular to the side of the square.

Let the center of each circle be O and the point where the circles are tangent be T. Then, the radius of each circle is equal to the distance from O to T.

Drawing a line from O to T, we can see that it forms a right triangle with one leg equal to the radius of the circle and the other leg equal to half the side length of the square. Using the Pythagorean theorem, we can solve for the radius:

\(r^2 + (2)^2 = (4)^2r^2 = 12\\\)

r ≈ 3.46

Therefore, the radius of each circle is approximately 3.46 units, rounded to the nearest hundredth.

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Hello there! :)

Answer:

y = -4x.

Step-by-step explanation:

Begin by finding the slope of the line using the slope formula:

\(m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

Plug in two points on the graph. We can use the points (-1, 4) and (0, 0):

\(m = \frac{0 - 4}{0 - (-1)}\)

Simplify:

m = -4.

Therefore, the equation of this line in slope-intercept form (y = mx + b) is:

y = -4x.

We fail to reject the null hypothesis that the temperature level has no effect on the mean yield process.

Summary of Result:

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

To construct an analysis of variance (ANOVA) table and test whether the temperature level has an effect on the mean yield process, we need to perform the following steps:

Step 1: Calculate the total sum of squares (SST), the treatment sum of squares (SSTR), and the error sum of squares (SSE).

SST = ΣΣ(yij - ȳ)^2 = 359.2

where yij is the yield of the ith batch at the jth temperature level and ȳ is the overall mean yield.

SSTR = Σ(nj(ȳj - ȳ)^2) = 118.2

where nj is the number of batches produced at the jth temperature level, ȳj is the mean yield at the jth temperature level, and ȳ is the overall mean yield.

SSE = SST - SSTR = 241.0

Step 2: Calculate the degrees of freedom (df) for SST, SSTR, and SSE.

df(Total) = N - 1 = 14

where N is the total number of observations.

df(Treatment) = k - 1 = 2

where k is the number of treatment levels.

df(Error) = df(Total) - df(Treatment) = 12

Step 3: Calculate the mean square (MS) for SSTR and SSE.

MS(Treatment) = SSTR / df(Treatment) = 59.1

MS(Error) = SSE / df(Error) = 20.1

Step 4: Calculate the F-statistic.

F = MS(Treatment) / MS(Error) = 2.94

Step 5: Determine the critical value of F for a 0.05 level of significance with df(Treatment) = 2 and df(Error) = 12.

From a table of F-distributions, the critical value of F is 3.89.

Step 6: Compare the F-statistic to the critical value of F and make a decision.

Since 2.94 < 3.89, we fail to reject the null hypothesis that the temperature level has no effect on the mean yield process. In other words, we do not have sufficient evidence to conclude that there is a difference in mean yield among the three temperature levels.

Step 7: Summarize the results in an ANOVA table.

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

Note: The p-value is calculated as P(F > 2.94) = 0.095, which is greater than the significance level of 0.05. Therefore, we do not reject the null hypothesis.

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Answer:

Two triangles are similar if they have:

Step-by-step explanation:

all their angles equal

corresponding sides are in the same ratio

But we don't need to know all three sides and all three angles ...two or three out of the six is usually enough.

There are three ways to find if two triangles are similar: AA, SAS and SSS:

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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\(v = 120 \: {cm}^{3} \)

\(h = 4.5 \: cm\)

the radius of the cone.

\(r = \sqrt{3 \frac{v}{\pi \: h} } \)

\(r = \sqrt{3 \times \frac{120}{\pi \times 4.5} } \)

\(r = 5.04627 \: cm\)

\(r = 5.05 \: cm\)

hence, the radius of the given cone is 5.05 centimeters.

Answer:

see explanation

Step-by-step explanation:

The hypotenuse is the longest side thus is (4x + 1)

The legs are 2x and (4x - 1)

Using Pythagoras' theorem, then

(4x + 1)² = (2x)² + (4x - 1)² ← expanding factors

16x² + 8x + 1 = 4x²  + 16x² - 8x + 1 , that is

16x² + 8x + 1 = 20x² - 8x + 1 ( subtract 20x² - 8x + 1 from both sides )

- 4x² + 16x = 0 ( multiply through by - 1 )

4x² - 16x = 0 ← factor out 4x from each term

4x(x - 4) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

x - 4 = 0 ⇒ x = 4

Now x > 0, thus x = 4

2x = 2(4) = 8

4x - 1 = 4(4) - 1 = 16 - 1 = 15

4x + 1 = 4(4) + 1 = 16 + 1 = 17

Thus

perimeter = 8 + 15 + 17 = 40 cm

Answer:

23°

Step-by-step explanation:

As We All Know Sum Of Angles In A Straight Line is 180° so,

157° + a = 180°

or, a = 180° - 157°

or, a = 23°

(a) To find the value of a, we can use the standard deviation formula:

Standard deviation = (Upper specification limit - Lower specification limit) / (6 * Sigma)

Given that the diameter specification is between 0.98 and 1.01 inches, and we want the standard deviation to be a, we can set up the equation:

a = (1.01 - 0.98) / (6 * Sigma)

Simplifying the equation, we get:

a = 0.03 / (6 * Sigma)

a = 0.005 / Sigma

Therefore, the value of a is 0.005 / Sigma.

(b) To find the diameter at which one elevator rail in 1000 will be at least, we need to find the z-score corresponding to a cumulative probability of 0.999.

Using the standard normal distribution table or a calculator, we find that the z-score corresponding to a cumulative probability of 0.999 is approximately 3.090.

Since the mean diameter is 1 inch and the standard deviation is a, we can calculate the minimum diameter as:

Minimum diameter = Mean - (z-score * Standard deviation)

Minimum diameter = 1 - (3.090 * a)

Substituting the value of a from part (a), we get:

Minimum diameter = 1 - (3.090 * 0.005 / Sigma)

Minimum diameter = 1 - (0.01545 / Sigma)

Round the answer to three decimal places if necessary.

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a. The perimeter of the triangle is 12+4√3

b. The area of the sector AOB and length of arc AB are 29.4 and 11.8 respectively

Arc length is defined as the distance along the part of the circumference of any circle or any curve (arc).

The perimeter of a shape is the addition of all the sides of a shape.

A sector is the space bounded by an arc and the radii of a circle.

a. The other two sides of the triangle is calculated as,

sin 30 = x/ 8

1/2 = x/8

x = 4

cos 30 = y/8

√3/2 = y/8

8√3 = 2y

y = 4√3

The perimeter of the triangle = 4+4√3+ 8

= 12+4√3 unit

b. The area of sector = (tetha)/360 × πr²

= 135/360 × 3.14× 5²

= 10597.5/360

= 29.4 unit²

The length of the arc = (tetha)/360 × 2πr

= 135/360 × 2 × 3.14 × 5

= 4239/360

= 11.8units

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Answer:

A. The sampling distribution follows a normal distribution

B. With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between 17.04 and 19.28

C. If many groups of 55 randomly selected people were surveyed, then a different confidence interval would be produced for each group. About 90 percent of these confidence intervals will contain the true population mean number of names remembered and about 10 percent will not contain the true population mean number of names remembered  

Step-by-step explanation:

The given parameters are;

The known population standard deviation of the number of names that people can recall after being introduced to 40 people in a party, σ = 6.34 names

The number of people randomly selected in the survey, n = 55 people

The average number of names correctly remembered, \(\overline x_1\) = 18.16

The standard deviation of the group surveyed, s = 4.28

A. Based on the Central Limit Theorem CLT, the sampling distribution follows a normal distribution

B. The 90% confidence interval is given as follows;

\(C.I.=\bar{x}\pm z_{\alpha /2}\cdot \dfrac{\sigma}{\sqrt{n}}\)

Where \(z_{\alpha /2}\) at 90% = 1.65, we have;

\(C.I.=18.16\pm 1.65 \times \dfrac{4.28}{\sqrt{55}}\)

C.I. ≈ 17.20 < μ < 19.11

With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between 17.04 and 19.28

C. The 90% confidence interval gives the certainty that if different groups of 55 randomly selected people were surveyed, then about 90 percent of the confidence intervals will contain the true population mean number of names remembered and about 10 percent will not contain the true population mean number of names remembered.

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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1. We can conclude that T(n) = 1 + 5(n-1).

2. This recurrence relation can be solve as  T(n) = O(n²).

(1) T(n) = {1, T(n-1) + 5} for n = 1, and for n ≥ 2

To solve this recurrence relation, we can use the substitution method.

We'll start by finding the pattern for a few values of n:

T(1) = 1

T(2) = T(1) + 5 = 1 + 5 = 6

T(3) = T(2) + 5 = 6 + 5 = 11

T(4) = T(3) + 5 = 11 + 5 = 16

From the pattern, we can observe that T(n) = T(n-1) + 5 = T(n-2) + 5 + 5 = T(n-3) + 5 + 5 + 5 = ... = T(1) + 5(n-1).

Therefore, we can conclude that T(n) = 1 + 5(n-1).

(2) T(n) = {1, 3T(n/2) + n^2} for n = 1, and for n ≥ 2

To solve this recurrence relation, we can use the recursion tree method.

First, let's build the recursion tree:

                       T(n)

                 /                 \

             T(n/2)          T(n/2)

              /   \                /   \

          T(n/4) T(n/4) T(n/4) T(n/4)

           /   \     /   \     /   \     /   \

        ...      ...  ...     ...    ...  ... ...

The height of the recursion tree is log₂n, and at each level, the work done is n². Therefore, the total work done can be calculated by multiplying the work done at each level by the number of nodes at that level.

Total work = n² + 2(n/2)² + 4(n/4)² + ... + 2ᵏ(n/2ᵏ)²

The recursion tree terminates when n/2ᵏ = 1, which implies k = log₂n.

Using the formula for the sum of geometric series, we can simplify the total work:

Total work = n²(1 + 1/2² + 1/4² + ... + 1/(2^(log₂n))²)

= n²(1 + 1/4 + 1/16 + ... + 1/n²)

= n²(1 - 1/(4^log₂n))/(1 - 1/4)

= n²(1 - 1/n²)/(3/4)

= 4/3 n² - 4/3

Therefore, T(n) = O(n²).

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The factor that most directly affects the amount of money borrowers must repay to lenders is d) the annual percentage rate.

This rate represents the cost of borrowing money and includes interest and other fees. The higher the APR, the more money borrowers will have to repay over time. The currency exchange rate, unemployment rate, and inflation rate can indirectly affect borrowing costs but are not as directly linked as the APR. The factor that most directly affects the amount of money borrowers must repay to lenders is d. the annual percentage rate (APR). The APR represents the total cost of borrowing, including interest and any additional fees, expressed as a percentage. A higher APR means a higher cost for borrowers, making it an essential factor to consider when repaying loans.

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Answer:

Step-by-step explanation:

plug in 4 for x then simplify

= 2(4) + 1

= 8 + 1

= 9

hope this helps <3

Answer: f (4) = 9

Step-by-step explanation:

f (x) = 2x + 1

f (4) = 2 (4) + 1

f (4) = 8 + 1

f (4) = 9

Answer:

If x = 5 then, y = 10

Answer:

y = 5x-14

Step-by-step explanation:

We should use point-slope form to form our equation:

y-1 = 5(x-3)

y-1 = 5x-15

y = 5x-14

Our equation is now in slope-intercept form.

HTH :)

Answer:

0.4

Step-by-step explanation:

hegarty maths