Five machines are cutting 1.25-foot long
metal sheets. The machines are being
calibrated to ensure that they are cutting
the accurate length. The previous batches
for each machine are shown in the table.
Select all of the statements that are valid
for the data.

Answer:

x=-23

Step-by-step explanation:

Since 180° is a straight line you must find a way to get 180 by adding 97°,106°, and x.

Therefore, x must be equal to -23.

Answer:

y<-2x-4

Step-by-step explanation:

when x=0 then y is equal to -4 which doesn't satisfy the rule

The largest population to which the results can be generalized is in option C i.e. All student-athletes at the college.

Population: A population can be described as a complete group with at least one characteristic in common and a sample of the population can be used to get the features of the population.

We were told that a random sample of 50 student-athletes from all the student-athletes at a college, even though the population can be used to have an idea about how the consumption of beetroot juice enhances exercise performance, and it can not be used to get the results that can be generalized as more than 50 students-athletes is required which is chosen randomly.

All the other options are wrong because of this reason.

Therefore, option C is correct.

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Answer: B

Step-by-step explanation:

trust me the answer is B if the answer is not reported me

Answer:

Step-by-step explanation:

let us calculate area of pentagon.

it consists of 5 isosceles triangles with base=5 cm

apothem h=3.6 cm

area of pentagon=5×1/2×5×3.6≈45 cm

area of 2 pentagons (top and bottom)=2×45=90 cm²

lateral area of 6 rectangles=2(10×5+10×5+10×5)=2(50+50+50)=300 cm²

Total surface area=90+300=390 cm²

The equation of the line with a slope of 7/11 that passes through the point (11, 13) is y = (7/11)x + 6.

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, the slope (m) is 7/11, and the point (11, 13) lies on the line. We can use this information to find the equation.

Substituting the values into the slope-intercept form, we have:

13 = (7/11)(11) + b

Simplifying the equation:

13 = 7 + b

To solve for b, we subtract 7 from both sides:

b = 13 - 7

b = 6

Therefore, the equation of the line with slope 7/11 that passes through the point (11, 13) is:

y = (7/11)x + 6

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Answer:

  true

Step-by-step explanation:

You want to know if weight and self-esteem have a negative correlation if an increase in weight causes self-esteem to go down (the slope is negative).

The slope of the line of best fit has the same sign as the correlation coefficient. The magnitude of the correlation coefficient is the ratio of the covariance to the product of the standard deviations of the variables.

It is true that the weight and self-esteem have negative correlation.

The integral evaluates to 50/3. We can calculate it in the following manner:

The integral by changing to polar coordinates $\int\int x²y\ da$ where $D$ is the top half of the disk with center the origin and radius 5 is solved below:

The given integral is $\int\int x²y\ da$ where $D$ is the top half of the disk with center the origin and radius $5$.We can convert the given rectangular coordinates $(x,y)$ to polar coordinates as shown below:

$\begin{aligned}\int\int x^2y\ da&=\int_0^5\int_{0}^{\pi} r^4\cos^2\theta\sin\theta\ d\theta\ dr\\\end{aligned}$Now, evaluate the given integral

$\int_0^{\pi} \cos^2\theta\sin\theta\ d\theta$ by using the substitution $u=\cos\theta$.$\begin{aligned}&=\int_{-1}^{1} u^2\ (-du)\\&=\int_{-1}^{1} -u^2\ du\\&=-\frac{u^3}{3}\Bigg|_{-1}^{1}\\&=-\frac{2}{3}\end{aligned}$

Therefore, the integral by changing to polar coordinates $\int\int x^2y\ da$ where $D$ is the top half of the disk with center the origin and radius $5$ is $\frac{-125\pi}{3}$.
To evaluate the given integral by changing to polar coordinates, first note that the region D is described by polar coordinates with 0 ≤ r ≤ 5 and 0 ≤ θ ≤ π. Next, convert the given integral from Cartesian to polar coordinates:

x^2y = (r*cos(θ))^2 * (r*sin(θ)) = r^3 * cos^2(θ) * sin(θ)

The area element in polar coordinates is dA = r*dr*dθ. Now, set up the integral in polar coordinates:

∬_D x^2y dA = ∫(0 to π) ∫(0 to 5) r^3 * cos²(θ) * sin(θ) * r dr dθ

Now, evaluate the integral:

= ∫(0 to π) (cos²(θ) * sin(θ)) dθ * ∫(0 to 5) r⁴ dr

The first integral can be solved using a substitution (u = cos(θ), du = -sin(θ)dθ):

= -∫(1 to -1) u² du * [r⁵/5]_(0 to 5)

= [(-u³/3)]_(1 to -1) * [125/5]

= (2/3) * (25)

= 50/3

So, the integral evaluates to 50/3.

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The factor is (w-2)(w-12) and the solution of the expression is  w =2 or 12

Given: 2wto power of 2 minus 16w=12w-48.

This expression can be written as 2w² - 16w = 12w-48

2w² - 16w = 12w-48

2w² - 16w-12w = -48

2w² - 28w + 48 = 0

Divide through by 2:

w² - 14w +  24 = 0

w² - 12w-2w +  24 = 0

Factorize:

(w-2)(w-12) = 0

w-2 = 0 or w-12 = 0

w =2 or 12

Therefore, the solution of 2w² - 16w = 12w-48 is w =2 or 12

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Answer:

75

Step-by-step explanation:

Answer:

85.71 %

Step-by-step explanation:

26-14=12

12/14= 0.8571

0.8571x100= 85.71

Answer:

A change from 14 to 26 represents a positive change (increase) of 85.7142857143%

Step-by-step explanation:

Use the formula:

New - Old / Old x 100%

In other words, new(26) minus old(14) divided by old(14) time 100%

14 is the old value and 26 is the new value. In this case we have a positive change (increase) of 85.7142857143 percent because the new value is greater than the old value.

the integral ∫e^(4θ)sin(5θ)dθ evaluates to (-9/41)e^(4θ)cos(5θ) + C.

To evaluate the integral ∫e^(4θ)sin(5θ)dθ, we can use integration by parts.

Let u = sin(5θ) and dv = e^(4θ)dθ.

Then, we have du = 5cos(5θ)dθ and v = (1/4)e^(4θ).

Using the formula for integration by parts:

∫u dv = uv - ∫v du,

we can apply it to our integral:

∫e^(4θ)sin(5θ)dθ = (-1/4)e^(4θ)cos(5θ) - ∫(1/4)e^(4θ)(5cos(5θ))dθ.

Simplifying the expression, we get:

∫e^(4θ)sin(5θ)dθ = (-1/4)e^(4θ)cos(5θ) - (5/4)∫e^(4θ)cos(5θ)dθ.

Now, we need to evaluate the remaining integral: ∫e^(4θ)cos(5θ)dθ.

For this integral, we can again use integration by parts.

Let u = cos(5θ) and dv = e^(4θ)dθ.

Then, we have du = -5sin(5θ)dθ and v = (1/4)e^(4θ).

Applying the integration by parts formula, we get:

∫e^(4θ)cos(5θ)dθ = (1/4)e^(4θ)cos(5θ) + (5/4)∫e^(4θ)sin(5θ)dθ.

We can substitute this result back into the previous expression:

∫e^(4θ)sin(5θ)dθ = (-1/4)e^(4θ)cos(5θ) - (5/4)[(1/4)e^(4θ)cos(5θ) + (5/4)∫e^(4θ)sin(5θ)dθ].

Now, we have an equation involving the integral we are trying to evaluate. Let's isolate it:

∫e^(4θ)sin(5θ)dθ = (-1/4)e^(4θ)cos(5θ) - (5/4)(1/4)e^(4θ)cos(5θ) - (25/16)∫e^(4θ)sin(5θ)dθ.

Combining like terms, we get:

(41/16)∫e^(4θ)sin(5θ)dθ = (-9/16)e^(4θ)cos(5θ).

Finally, dividing both sides by (41/16), we obtain:

∫e^(4θ)sin(5θ)dθ = (-9/41)e^(4θ)cos(5θ) + C,

where C is the constant of integration.

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The research proposal focuses on investigating the determinants of the sustainability of small and medium-sized enterprises (SMEs) in Soweto. The research objectives are to determine the sustainability of SMEs, identify the factors that contribute to their sustainability, and provide practical recommendations to enhance their sustainability.

1.1 The research proposal addresses the "what" by examining the determinants of SME sustainability in Soweto. It focuses on "who" by targeting owner-managers of SMEs in Soweto. The "why" is to understand the factors that influence SME sustainability. The "where" is in Soweto, South Africa, and the "when" refers to the time period during which the research will be conducted.

1.2 The aim of the proposed study is to explore and analyze the determinants of sustainability for small and medium-sized enterprises in Soweto, with the ultimate goal of providing practical recommendations to enhance their sustainability.

1.3 Three research questions for the proposed study could be:

What are the key indicators of sustainability for SMEs in Soweto?

What factors contribute to the sustainability of SMEs in Soweto?

How can owner-managers of SMEs in Soweto improve the sustainability of their businesses?

1.4 An appropriate research design for the proposed study could be a mixed-methods approach. This design would involve both quantitative and qualitative data collection and analysis methods. Quantitative data could be collected through surveys or questionnaires to measure indicators of sustainability and assess the relationship between various factors. Qualitative data could be collected through interviews or focus groups to gain a deeper understanding of the experiences and perspectives of owner-managers. The mixed-methods approach would provide a comprehensive and holistic understanding of the determinants of SME sustainability in Soweto and enable practical recommendations to be formulated based on both quantitative and qualitative insights.

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The value of the given expression: 10/12 - 3/8 is 11/24.

This can be solved using the concept of fraction.

Mathematical expressions consist of a minimum of two integers or variables, at least one arithmetic operation, and a statement. Any one of the following mathematical operations can be used. An expression's basic components are as follows: The formula becomes (Number/Variable, Math Operator, Number/Variable).

An expressions is just a mathematical term that combines variables, operators, and numbers to indicate the value about something.

Here, the given expression is:

10/12 - 3/8

Since,

12 = 2 × 2 × 3

8 = 2 × 2 × 2

⇒ L.C.M.(12,8) = 2 × 2 × 2 × 3 = 24

Now, we can write,

10/12 = (10 × 2)/ (12 × 2) = 20/24

and 3/8 =  (3 × 3)/ (8 × 3) = 9/24

Hence, 10/12 - 3/8 = 20/24 - 9/24 = 11/24

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This Bay store can also be described as a big box retailer store.

Big Box Retailer

A big box retailer is a physically enormous retail store that is typically a component of a chain of stores (also known as a hyper store, supercenter, superstore, or megastore). By extension, the phrase, big box retailer can also refer to the business that runs the store.

The Bay Store as a Big Box

There are numerous retail chains that only operate in Canada, aside from the large American big box retailer stores like Walmart Canada and the formerly-existent Target Canada. These include places like Hudson's Bay by Home Outfitters, Loblaws by Real Canadian Superstore, Rona, Winners by HomeSense, Canadian Tire by Mark's & Sport Chek, Shoppers Drug Mart, Chapters by Indigo Books and Music, Sobeys, and several others.

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The factor by which the volume of cube increased is 0.0030

What is a cube ?

A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.

The fundamental distinction between a cube and a square is that the former has three dimensions—length, breadth, and height—while the latter only has two. A cube is composed of squares, which are a type of 2-dimensional (2D) shape (such as a circle, square, triangle, etc.).

let l be the side of a cube

the new length of cube is l' = 1.001l

Initial volume (v1) = l³

final volume (v2) = (1.001)³l³

The factor by which the volume increased is  = v1 / v2

                                                                           = ((1.001)³l³ - l³)/l³

                                                                           = 0.003003

                                                                           = 3 x 0.001

                                                                           ≅ 0.0030

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Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.

Given dimensions:

Length = 7 feet

Width = 3 feet

Height = 4.8 feet

Surface Area of each face:

Front and back faces: Length * Height

= 7 feet * 4.8 feet

= 33.6 square feet

Top and bottom faces: Width * Length

= 3 feet * 7 feet

= 21 square feet

Side faces: Width * Height

= 3 feet * 4.8 feet

= 14.4 square feet

Total Surface Area:

2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)

= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet

= 67.2 square feet + 42 square feet + 28.8 square feet

= 137 square feet

Therefore, the total surface area of the bench is 137 square feet.

Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.

Cost per square foot = $0.89

Total Surface Area = 137 square feet

Total cost to cover the bench:

= Cost per square foot * Total Surface Area

= $0.89 * 137 square feet

= $121.93

Therefore, it will cost $121.93 to cover the bench with ceramic tiles.

Answer:

11h+13

Step-by-step explanation:

7h+4h=11h

9+4=13

Answer:

11h+13

Step-by-step explanation:

Combine like terms.

The effort needed to move an object along a curve that is specifically oriented. F(x, y) = (y, x) on the parabola y = 6x² from (0,0) to (2,24) is 48.

A bowl-shaped object is defined as having a curve at the surface created by the intersection of a cone and a plane that is perpendicular to a straight line. Another definition of a curve is one created when a moving point moves such that its distance from a fixed point equals its distance from a fixed line. A quadratic function is known in this form as its standard form. A parabola is a U-shaped curve that represents the quadratic function on a graph.

The given parabola is,

y = 6x²

Here consider x=t

Then,

y=6t²(0≤t≤z)

The work done by F(x, y) would be:

W=\(\int\limits^_c\)F.dr

=\(\int\limits^_c\)(\(y_{i} +x_{j}\))(d\(x_{i}\)+d\(y_{j}\))

=\(\int\limits^_c\)y dx + x dy

=\(\int\limits^2_0\)((6t²)(1)+(t)(12t))dt

=\(\int\limits^2_0\)18t²dt

=48

Therefore, the effort needed to move an object along a curve that is specifically oriented. F(x, y) = (y, x) on the parabola y = 6x² from (0,0) to (2,24) is 48.

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The periodic transfer of a portion of the cost of an intangible asset to expense is known as amortization. This is the process of spreading the cost of an intangible asset over its useful life, similar to how depreciation is used for tangible assets like buildings and equipment.

Intangible assets, such as patents, copyrights, and trademarks, do not have a physical existence but still have value to the company. Amortization recognizes the decline in value of these assets over time and helps to accurately reflect their impact on the company's financial statements.

The amount of amortization each period is calculated by dividing the cost of the asset by its estimated useful life. It is important for companies to track and properly account for their intangible assets, including amortization, as it can have a significant impact on their financial statements and overall financial health.

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The required values are x = 2 , AB = 4 , DB = 2 and AD = 2 .

Since D bisects AB , therefore AD = DB

hence , ( 2 ^ 2 ) - x = 2 x - 2

Solving linear equation ,

4 - x = 2 x - 2

3 x = 6

x = 2

AD = 4 - 2 = 2 .

DB = AD = 2 .

AB = AD + DB = 2 + 2 = 4 .

Hence , x = 2 , AB = 4 , DB = 2 and AD = 2 .

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In order for Janet's investment to increase to $10,000 in five years at a 4% yearly interest rate compounded monthly, she needs to put aside about $8,079.90 now.

For instance, if you put $1,000 in a bank account that offers 1% yearly interest, after a year you would have received $10 in interest. Compound interest allowed you to make 1 percent on $1,010 in Year Two, which amounted to $10.10 in interest payments for the year.

We can use the formula for compound interest to find how much Janet needs to invest now:

\(A=P\left(1+\frac{r}{n}\right)^{n t}\)

where:

A = the amount of money after the specified time period

P = the principal (the amount of money Janet needs to invest now)

r = the annual interest rate (4% = 0.04)

n = the number of times the interest is compounded per year (12, since it is compounded monthly)

t = the time period, in years (5)

Plugging in the values we get:

10,000 = P(1 + 0.04/12)⁽¹²*⁵⁾

Solving for P, we get:

P = 10,000 / (1 + 0.04/12)⁽¹²*⁵⁾

P ≈ $8,079.90

Therefore, Janet needs to invest about $8,079.90 now to grow to $10,000 in 5 years at a 4% annual interest rate compounded monthly.

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Answer:

Step-by-step explanation:

the mean would be appropriate measure of center to describe the data shown in the histogram because the data is symmetrical.A symmetric histogram is a distribution in which the 2 halves appear to be the same on both sides.

Answer:

y = x - 5

Step-by-step explanation:

\( \rm Solve \: for \: y: \\ \rm \longrightarrow x - y= 5 \\ \\ \rm Subtract \: x \: from \: both \: sides: \\ \rm \longrightarrow x - y - x = 5 - x \\ \\ \rm \longrightarrow -y = 5 - x \\ \\ \rm Multiply \: both \: sides \: by \: -1: \\ \rm \longrightarrow - y \times ( - 1) = (5 - x) \times ( - 1) \\ \\ \rm \longrightarrow y = x - 5\)

It would take her 5 months

Answer:

192

Step-by-step explanation:

calculator

He ran for 6/5 miles long.

In maths, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem.

Given that, Tyrone run on a 3/5 long track for twice.

3/5*2 = 6/5

Hence, He ran for 6/5 miles long.

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Yes, the data provides convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon.

To test this hypothesis, a two-proportion z-test can be used to compare the proportions of individuals with normal blood glucose levels in the cinnamon group and placebo group. Using the given data, the test statistic is calculated to be 1.78 with a p-value of 0.038.

Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the proportions of individuals with normal blood glucose levels in the cinnamon and placebo groups. Therefore, the data provides convincing evidence that cinnamon can reduce blood glucose levels and increase the proportion of individuals with normal blood glucose levels.

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Answer:

-20

Step-by-step explanation:

a2 + ( b-c)

rewrite the equation

2 * a + ( b - c )

a = -8

b = 17

c = 21

substitute in the given values

(-8) 2 + ( (17) - (21) )

simplify and solve

-16 + ( 17-21)

= -16 +  (-4)

= -16 -4

=-20

The complete solution to the given ordinary differential equation (ODE)is:

\(y(x) = y_h(x) + y_p(x) = 5e^{6x} - 2e^{-2x} + 10e^{-2x} = 5e^{6x} + 8e^{-2x}\)

To solve the second-order ordinary differential equation (ODE) using the method of undetermined coefficients, we assume a particular solution of the form:

\(y_p(x) = A e^{-2x}\)

where A is a constant to be determined.

Next, we find the first and second derivatives of \(y_p(x)\):

\(y_p'(x) = -2A e^{-2x}\\y_p''(x) = 4A e^{-2x}\)

Substituting these derivatives into the original ODE, we get:

\(4A e^{-2x} - 4(-2A e^{-2x}) - 12(A e^{-2x}) = 10e^{-2x}\)

Simplifying the equation:

\(4A e^{-2x} + 8A e^{-2x} - 12A e^{-2x} = 10e^{-2x}\)

Combining like terms:

\((A e^{-2x}) = 10e^{-2x}\)

Comparing the coefficients on both sides, we have:

A = 10

Therefore, the particular solution is:

\(y_p(x) = 10e^{-2x}\)

To find the complete solution, we need to find the homogeneous solution. The characteristic equation for the homogeneous equation y'' - 4y' - 12y = 0 is:

r² - 4r - 12 = 0

Factoring the equation:

(r - 6)(r + 2) = 0

Solving for the roots:

r = 6, r = -2

The homogeneous solution is given by:

\(y_h(x) = C1 e^{6x} + C2 e^{-2x}\)

where C1 and C2 are constants to be determined.

Using the initial conditions y(0) = 3 and y'(0) = -14, we can solve for C1 and C2:

y(0) = C1 + C2 = 3

y'(0) = 6C1 - 2C2 = -14

Solving these equations simultaneously, we find C1 = 5 and C2 = -2.

Therefore, the complete solution to the given ODE is:

\(y(x) = y_h(x) + y_p(x) = 5e^{6x} - 2e^{-2x} + 10e^{-2x} = 5e^{6x} + 8e^{-2x}\)

The question is:

Use the method of undetermined coefficients to solve the second order ODE y'' - 4 y' - 12y = 10\(e ^{- 2x}\), y(0) = 3, y' (0) = - 14

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