Find the length of the arc on a circle of radius r intercepted by a central angle 0. Round to two decimal places. Use x = 3.141593. r=35 inches, 0 = 50° OA. 31.84 inches B. 28.70 inches. C. 30.55 inc

Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

Approximately 34% of American adults have a mobile phone but not a landline, based on the given proportions from the study conducted by the Centers for Disease Control.

The proportion of American adults who have a mobile phone but not a landline, we need to subtract the proportion of those who have both a mobile phone and a landline from the proportion of those who have a mobile phone.

Let's denote the proportion of American adults who have a mobile phone as P(M), the proportion who have a landline as P(L), and the proportion who have neither as P(N).

Given information:

P(M) = 89% (proportion with a mobile phone)

P(L) = 57% (proportion with a landline)

P(N) = 2% (proportion with neither)

We can now calculate the proportion of adults who have a mobile phone but not a landline using the following equation:

P(M and not L) = P(M) - P(M and L)

To find P(M and L), we can subtract P(N) from P(L) since those who have neither are not included in the group with a landline:

P(M and L) = P(L) - P(N)

P(M and L) = 57% - 2%

P(M and L) = 55%

Now we can substitute the values back into the equation to find P(M and not L):

P(M and not L) = P(M) - P(M and L)

P(M and not L) = 89% - 55%

P(M and not L) = 34%

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Answer:

no

Step-by-step explanation:

A parallelogram has 4 sides.

Answer:

-54x+18X2

Step-by-step explanation:

-9x(6-2x)

The answer is -54x+18x2

The diameter of the tungsten filament that has a resistance of 7×10−2 Ω. is approximately 16 x 10^-3 mm.

To find the diameter of the tungsten filament, we need to use the formula for the resistance of a wire:

R = ρL/A

where R is the resistance, ρ is the resistivity of tungsten, L is the length of the wire, and A is the cross-sectional area of the wire.

We know that the resistance of the filament is 7×10^−2 Ω and its length is 26 cm, which is 0.26 m. The resistivity of tungsten is approximately 5.6×10^−8 Ω⋅m.

We can rearrange the formula to solve for A:

A = ρL/R

Substituting the values we know, we get:

A = (5.6×10^−8 Ω⋅m)(0.26 m)/(7×10^−2 Ω) = 2.07×10^−10 m²

The cross-sectional area of a circle is given by A = πr², where r is the radius. Solving for the radius, we get:

r = √(A/π) = √(2.07×10^−10 m²/π) = 8.1×10^−6 m

To convert to millimeters, we multiply by 1000:

r = 8.1×10^−3 mm

Finally, to get the diameter, we multiply by 2:

D = 16×10^−3 mm

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Answer:

See below

Step-by-step explanation:

3 - 2(-2.6x) - 2(2.1)   =                  ( after expanding L side)

3 + 5.2x -4.2 =

5.2x - 1.2                   Yep. They are equal .

Let A be an n by n singular matrix. Then the homogeneous system AX = 0 has infinite solutions. (True )

The homogeneous system AX = 0, where A is a matrix and X is a column vector of variables, always has the trivial solution X = 0. The homogeneous system AX = 0 has infinite solutions if the rank of A is less than n, indicating that A is a singular matrix.

A matrix A is considered singular if its determinant is zero. If A is singular, it implies that A has at least one zero eigenvalue and its columns are linearly dependent. This property leads to the conclusion that the homogeneous system AX = 0 has infinite solutions. On the other hand, if A is non-singular, the homogeneous system AX = 0 has only the trivial solution X = 0.

In summary, if a matrix A is singular, the homogeneous system AX = 0 has infinite solutions, and a non-trivial solution exists. A nontrivial solution exists when a homogeneous system has more than one solution, which occurs if there are free variables.

Based on the explanations provided, it is concluded that the statement "Let A be an n by n singular matrix. Then the homogeneous system AX = 0 has infinite solutions" is true.

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Let's start by finding the derivative of the function f(x) = x^2 * e^x.

a) To determine the intervals of increase and decrease, we need to find the critical points of the function. The critical points occur where the derivative is equal to zero or does not exist.

Taking the derivative of f(x) with respect to x, we get f'(x) = (2x + x^2) * e^x.

Setting f'(x) equal to zero and solving for x, we get 2x + x^2 = 0. This equation does not have real solutions, so there are no critical points.

Since there are no critical points, the function f(x) = x^2 * e^x is always increasing or always decreasing on its entire domain, which is (-∞, +∞).

b) To determine the absolute minimum value of f(x), we need to find the minimum point of the function. Since there are no critical points, we need to check the behavior of the function as x approaches positive or negative infinity.

As x approaches negative infinity, both x^2 and e^x approach infinity, and the product of these two terms will also approach infinity.

As x approaches positive infinity, e^x grows much faster than x^2, so the product of these two terms will approach infinity as well.

Therefore, the function f(x) = x^2 * e^x does not have an absolute minimum value.

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Answer: \(\dfrac14\)

Step-by-step explanation:

Given: The factory produces equal quantities of four flavors cherry lemon orange and strawberry.

Let  orange candy= cherry = lemon = strawberry  = x

Total candies = x + x + x + x= 4x

The probability that a randomly selected candy is orange = \(\dfrac{x}{4x}=\dfrac14\)

Hence, the probability that a randomly selected candy is orange = \(\dfrac14\)

Answer:

2

Step-by-step explanation:

14/2=7

34/2=17

Answer:

one yard is equal to 3 feet so

\(x + y = 7~~~.....(i)\\\\xy=-30~~~~......(ii)\\\\\\\text{From (ii):}\\\\y= -\dfrac{30}x~~~~....(iii)\\\\\\\text{Substitute equation (iii) in equation (i):}\\\\\\x- \dfrac{30}x = 7\\\\\implies x^2 -30 = 7x\\\\\implies x^2 -7x -30 =0\\\\\implies x^2 -10x +3x -30 =0\\\\\implies x(x-10) +3(x-10) =0\\\\\implies (x+3)(x-10)=0\\\\\implies x = -3 ~~\text{or}~~ x=10\\\\\text{Substitute x = 10 in equation (iii):}\\\\\\y= -\dfrac{30}{10} =-3\\\\\)

\(\text{Substitute x = -3 in equation (iii):}\\\\y = \dfrac{-30}{-3} =10\\\\\\\text{So, (x,y) =(10,-3) and (x,y)=(-3,10)}\\\\\\\text{Hence, the two numbers are}~ 10~ \text{and}~ -3.\)

A spurious correlation is the implied causal relationships between events that are statistically  linked.

Spurious correlation;

A spurious correlation (or spuriousness) in statistics is an apparent causal relationship between two variables. Any reported dependencies between variables are solely the result of chance or are both a result of an unidentified confounder when there is misleading correlation.

When the price of higher education and the cost of living both rise, for instance, this doesn't necessarily indicate a causal link between the two factors because higher education tuition isn't always the result of rising living costs.

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It is a difference of squares, so we can factor this to

\((x+2)(x-2)=0\)

Then, we can solve for \(x\).

\(x=-2,2\)

Hope this helps.

頑張って!

The probabilities for the hypergeometric distribution with the given parameters are:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

To determine the probabilities for the hypergeometric distribution with the given parameters, we can use the following formula:

P(X = k) = (choose(K, k) * choose(N-K, n-k)) / choose(N, n)

where "choose(a, b)" represents the binomial coefficient, calculated as a! / (b! * (a - b)!)

Let's calculate the probabilities:

a. P(X = 1):

P(X = 1) = (choose(20, 1) * choose(100-20, 4-1)) / choose(100, 4)

        = (20 * 80) / 3921225

        ≈ 0.000407

b. P(X = 6):

P(X = 6) = (choose(20, 6) * choose(100-20, 4-6)) / choose(100, 4)

        = (38760 * 0) / 3921225

        = 0

c. P(X = 4):

P(X = 4) = (choose(20, 4) * choose(100-20, 4-4)) / choose(100, 4)

        = (4845 * 80) / 3921225

        ≈ 0.098117

d. P(X = 0):

P(X = 0) = (choose(20, 0) * choose(100-20, 4-0)) / choose(100, 4)

        = (1 * 77) / 3921225

        ≈ 1.97e-05

Therefore:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

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The complete question is:

Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. P(X = 0).

Answer:

jroteejktrsafh‍❤️♥️❣️❣️♥️♥️‍‍‍‍‍‍‍‍☘️

Answer:

D 108

Step-by-step explanation:

D + A = 180

72 + A = 180

A = 108

Step-by-step explanation:

The fraction she will complete is   1/2  /  3/5   = 1/2 * 5/3 =  5/6 completed

Matrix-vector multiplication is a linear operation because it satisfies the properties of scalar multiplication and vector addition, which are a(u+v) = au + av and a(cu) = cau, where a is a scalar and u and v are vectors.

Matrix-vector multiplication is a fundamental operation in linear algebra, where a matrix is multiplied by a vector to produce another vector. This operation is considered linear because it adheres to certain properties.

The first property is scalar multiplication, which states that multiplying a vector u by a scalar a and adding it to another vector v (a(u+v)) is equivalent to multiplying u by a (au) and v by a (av) separately and then adding the results (au + av). In other words, the operation distributes over vector addition.

The second property is the distributive property of scalar multiplication, which states that multiplying a vector u by a scalar c and then multiplying the resulting vector (cu) by another scalar a is equivalent to multiplying u by the product of the two scalars (cau). This property allows the scalar multiplication to be distributed over scalar multiplication.

These properties ensure that matrix-vector multiplication preserves the linearity of the underlying vector space. They enable the manipulation and analysis of systems of linear equations, transformations, and other mathematical operations involving matrices and vectors.

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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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Answer:

6x-2.50x-30=40

3.50x-30=40

3.50x=70

x=20 ornaments

Step-by-step explanation:

Answer:

-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2

Step-by-step explanation:

-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2

ANSWER

EXPLANATION

To find the number of miles that Janice walks, we have to convert from feet to miles.

We are given that:

Let the distance Janice walks be x.

This means that:

To find x, divide 5300 feet by 5280 feet. That is:

Therefore, Janice walks about 1.004 miles.

Answer:

118 ounces

Step-by-step explanation:

14.75 • 8 = 118

a) The speed of the police car equal to the speed of the sports car in 14.38 seconds. b) 153.7 meters. c) 16.37 seconds. d) The speed of the police car relative to the sports car when the police car reaches the sports car-2.24 m/s

a) We know the initial speed of the sports car is 117 km/h. Since the police car starts from rest and accelerates at a constant rate, we can use the following equation to find the time when their speeds are equal:

v_sports_car = v_police_car

117 km/h = 2.26 m/s² * t + v_reaction_time

First, we convert 117 km/h to m/s:

117 km/h = 117000 m/3600 s ≈ 32.5 m/s

Substituting the values into the equation:

32.5 m/s = 2.26 m/s² * t + 0 (assuming the police car starts from rest)

Solving for t:

t = 32.5 m/s / 2.26 m/s² ≈ 14.38 seconds

b) To find the distance between the cars at this time, we can use the equation for the displacement of the police car during its acceleration:

s = v_0 * t + 0.5 * a * t²

Substituting the values:

s = 0 * 14.38 + 0.5 * 2.26 m/s² * (14.38)²

s ≈ 153.7 meters

c) Since the police car starts moving after a reaction time of 1.99 seconds, we need to add this reaction time to the time calculated in part (a):

total_time = t + v_reaction_time

total_time = 14.38 seconds + 1.99 seconds

total_time ≈ 16.37 seconds

d) What is the speed of the police car relative to the sports car when the police car reaches the sports car?

To find the speed of the police car relative to the sports car, we subtract the speed of the sports car from the speed of the police car at the time when they meet:

v_police_relative = v_police_car - v_sports_car

v_police_relative = 2.26 m/s² * total_time + v_reaction_time - 32.5 m/s

Substituting the values:

v_police_relative = 2.26 m/s² * 16.37 s + 1.99 s - 32.5 m/s

v_police_relative ≈ -2.24 m/s

The negative sign indicates that the police car is moving slower than the sports car when they meet, i.e., the sports car is still ahead.

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$5 for 1 shirt

y = cost

x = number be shirts

10y = 2x

5y = x

Gabriela will claim $54550 as her taxable income.

The correct option is A.

Subtraction is a mathematic operation. Which is used to remove terms or objects in the expression.

Given:

Gabriela made $58,750 last year.

She paid $1200 in student loan interest and made a $3000 contribution to her IRA.

That means,

58750 - 1200 - 3000

= 54550

$54550 is the taxable income.

Hence, the taxable income is $54550.

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