Last week, Tina worked 7 hours on Monday, 9 hours on Tuesday, 9 hours on Wednesday, 10 hours on Thursday, 7 hours on Friday, and 4 hours on
Saturday. Her rate is $61 per hour. She gets paid time-and-a-half for all hours worked over 8 per day. What were her gross earnings for the
week?

The formula for the test hypothesis for proportion

Given

Substitute into the formula

The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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Answer:

A

Step-by-step explanation:

18 * 18 = 324

19 * 19 = 361

The area of the frame is 357 sq in. which is between 324 sq in. and 361 sq in., so the side is between 18 in. and 19 in.

Answer: A.

Answer:

Option A . Between 18 and 19

Step-by-step explanation:

Area = a²

357 = a²

\(\sqrt{357} = a\\\\a = 18.9 \ in\)

The rate of discount is approximately 6.4%.

Given that, the purchase at the store "Tias" come to $428.85 before any discounts and before any taxes.

The total price after a discount and taxes of 13% was $452.98.

The formula to find out the rate of discount is `tag=(1+r*t)(1-r*j)*p`, where `tag` is the total price after a discount and taxes, `p` is the initial price, `r` is the rate of discount, `t` is the tax rate, and `j` is the rate of tax.

So we can say that `452.98=(1-r*0.13)(1+r*0)*428.85`

On solving, we get, `r≈6.4%`

Hence, the rate of discount is approximately 6.4%.

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Answer:

(x-6)(x+5)^2 - 50

The function that would match the graph shown below is \(f(x) = k / (x^2 - 25)\)

where k is a constant.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

One example of a function that has intercepts on (5, 0) and (-5, 0) and continues to negative infinity and positive infinity is:

\(f(x) = k / (x^2 - 25)\)

where k is a constant that ensures the function continues to negative infinity and positive infinity.

To find the value of k, we can use one of the intercepts, say (5, 0):

0 = k / (5² - 25)

0 = k / 0

This tells us that k can take any value, as long as the denominator is not zero. So, we can choose any non-zero value for k.

For example, let's choose k = 1:

\(f(x) = 1 / (x^2 - 25)\)

This function has intercepts on (5, 0) and (-5, 0) and continues to negative infinity and positive infinity.

Thus,

The function that would match the graph shown below is \(f(x) = k / (x^2 - 25)\)

where k is a constant.

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Answer:

Inequality is \(4x+3y\leq 87\)

Slope intercept form is \(y\leq 29-\frac{4}{3}x\)

Solutions are \((2,3)\,,\,(3,4)\)

Graph: attached to the question

Step-by-step explanation:

Given: Group dance numbers last 4 minutes and a solo performance lasts 3 minutes. The maximum duration for the recital is 87 minutes.

To find: inequality (in standard form) that describes the given situation, inequality in slope-intercept form, solutions for the inequality

To graph: the inequality

Solution:

x denotes the number of group dances on the program

y denotes the number of solo numbers on the program

Total duration of group dance numbers = \(4x\) minutes

Total duration of solo performance = \(3y\) minutes

According to question,

\(4x+3y\leq 87\)

Slope intercept form of equation is \(y\leq mx+c\) where m denotes slope of line and c denotes y-intercept of the line.

Slope intercept form of \(4x+3y\leq 87\) :

\(4x+3y\leq 87\\3y\leq 87-4x\\y\leq 29-\frac{4}{3}x\)

For \((x,y)=(2,3)\),

\(4(2)+3(3)\leq 87\\8+9\leq 87\\17\leq 87\,\,which\,\,is\,\,true\)

So, \((2,3)\) is a solution of the inequality.

For \((x,y)=(3,4)\),

\(4(3)+3(4)\leq 87\\12+12\leq 87\\24\leq 87\,\,which\,\,is\,\,true\)

So, \((3,4)\) is a solution of the inequality.

Graph: attached as image

The probability that the mean contents of the 1024 sample cans is less than 11.994 ounces, is 0.055.

In the given question, a random sample of 1024 12-ounce cans of fruit nectar is drawn from among all cans produced in a run.

Prior experience has shown that the distribution of the contents has a mean of 12 ounces and a standard deviation of 0.12 ounce.

We have to find the probability that the mean contents of the 1024 sample cans is less than 11.994 ounces.

Given that,

Mean(μ) = 12

Standard Deviation(σ) = 0.12

n = 1024

So, μ = 12

σ/√n = 0.12/1024 = 0.00375

P( x<11.994) = P[(x-μ)/(σ/√n) < (11.994-12)/0.00375]

P( x<11.994) = P(z < -1.6)

(using z table)

P( x<11.994) = 0.055

Probability = 0.055

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Answer:

$372

Step-by-step explanation:

108.50 / 7 = 15.50

he earns $15.50 each hour

24 x 15.50 = 372

he would earn $372 in 24 hours

Answer:

$372

Explaination :

7 hour $108.50

1 hour - (180.50 ÷ 7) = $15.5

24 hours - (15.5x24) = $372

Answer:

(2, 1 )

Step-by-step explanation:

Using differential calculus

Given

y = (2x - 3)² = 4x² - 12x + 9 , then

\(\frac{dy}{dx}\) = 8x - 12

\(\frac{dy}{dx}\) is the measure of the gradient of the tangent , thus equate to 4

8x - 12 = 4 ( add 12 to both sides )

8x = 16 ( divide both sides by 8 )

x = 2

Substitute x = 2 into the equation for corresponding y- coordinate

y = (4 - 3)² = 1² = 1

The gradient of tangent is 4 at (2, 1 ) on the curve

Step-by-step explanation:

10p¹⁶q⁷

Basta Yan Yung answer

thanks me later

Answer:

Area = 104

Step-by-step explanation:

In the middle, 8x10 = 80

We see that the two outside sides are both width of 3, height of 8.

We can do 8x3 = 24 to find both, so 80+24 = 104

Answer:

A = 104

Step-by-step explanation:

The conditional statement to determine if the 10 cents off promotion applies at the local gas station would be "If today is Wednesday, then the price of gas is reduced by 10 cents."

This statement establishes a condition (today being Wednesday) and states the resulting action (a 10 cent reduction in gas price). By using the "if-then" structure, the statement indicates that the promotion is contingent upon the specific day of the week. If it is not Wednesday, the promotion does not apply, and the price of gas remains unchanged. This conditional statement allows customers to easily determine if they can take advantage of the 10 cents off promotion when planning their visit to the gas station.

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It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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Answer:

A=l×b

18 = l × b

b = 18/6

b = 3

Answer: The domain is all values of x that make the expression defined. The range is the set of all valid y values

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be Domain: (-∞, ∞) and   Range: (0,∞).

Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.

Here,

Given :  f(x)=\(2^{x}\)+1

If a value has not been added, an exponential function's curve normally approaches a horizontal asymptote at y=0 or the x-axis. The curve changes if it has.

The asymptote is unaffected by this function's addition on the exponent because it does not apply to the entire function.

The values of its y-axis remain between 0 and. This is the set of y values, or the range.

However, depending on the leading coefficient, the range of exponentials can vary. If the value is negative, the graph turns inside-out and the range reaches -. It's also lacking in this.

The exponent's addition to 1 moves the function to the left without changing the range.

The x values in exponential functions are often unaffected and all are taken into account in the function. The domain stays the same even while it changes. Its range is (0,∞)

 Range: (0,∞)

Therefore , the solution of the given problem of function comes out to be

Domain: (-∞, ∞) and   Range: (0,∞).

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The value of Circulation = 7p²π + 7p³/3 and Flux = 0

To find the circulation and flux of the vector field F = -7yi + 7xj around and across the closed semicircular path, we need to calculate the line integral of F along the path.

Circulation:

The circulation is given by the line integral of F along the closed path. We split the closed path into two segments: the semicircular arch and the line segment.

a) Semicircular arch (r1(t) = (-pcos(t))i + (-psin(t))j):

To calculate the line integral along the semicircular arch, we parameterize the path as r1(t) = (-pcos(t))i + (-psin(t))j, where t ranges from 0 to π.

The line integral along the semicircular arch is:

Circulation1 = ∮ F · dr1 = ∫ F · dr1

Substituting the values into the equation, we have:

Circulation1 = ∫ (-7(-psin(t))) · ((-pcos(t))i + (-psin(t))j) dt

Simplifying and integrating, we get:

Circulation1 = ∫ 7p²sin²(t) + 7p²cos²(t) dt

Circulation1 = ∫ 7p² dt

Circulation1 = 7p²t

Evaluating the integral from 0 to π, we find:

Circulation1 = 7p²π

b) Line segment (r2(t) = -ti, -p ≤ t ≤ 0):

To calculate the line integral along the line segment, we parameterize the path as r2(t) = -ti, where t ranges from -p to 0.

The line integral along the line segment is:

Circulation2 = ∮ F · dr2 = ∫ F · dr2

Substituting the values into the equation, we have:

Circulation2 = ∫ (-7(-ti)) · (-ti) dt

Simplifying and integrating, we get:

Circulation2 = ∫ 7t² dt

Circulation2 = 7(t³/3)

Evaluating the integral from -p to 0, we find:

Circulation2 = 7(0 - (-p)³/3)

Circulation2 = 7p³/3

The total circulation is the sum of the circulation along the semicircular arch and the line segment:

Circulation = Circulation1 + Circulation2

Circulation = 7p²π + 7p³/3

Flux:

To calculate the flux of F across the closed semicircular path, we need to use the divergence theorem. However, since the field F is conservative (curl F = 0), the flux across any closed path is zero.

Therefore, the flux of F across the closed semicircular path is zero.

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Step-by-step explanation:

1. 5x-4 =4x

5x-4x =4

x=4

2. 7x=8x+12

7x-8x =12

-x=12

x= -12

3. 27-3x=3x+27

27-27 = 3+3x

0=6x

0/6 =x

x=0/6

4. 34-2x=7x

34 =7x+2x

34 =9x

34/9=9x/9

3.78=x

x=3.78

5. 5r-7 =2r+14

5r-2r=14+7

3r=21

3r/3 =21/3

r=7

6.-x=7x-56

56=7x+x

56 =8x

x=7

7. 5n -35 =2r +14

5n-2n =14+35

3n =49

n=16.33

8.6w-33 = 12w-15

-33+15= 12w-6w

-18=6w

-3=w

Answer:

0.1759

Step-by-step explanation:

The student's heights between 93 centimeters and 100.5 centimeters will be 0.17586.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

A bunch of primary school understudy levels is regularly circulated with a mean of 105 centimeters and a standard deviation of 5 centimeters.

The student's heights between 93 centimeters and 100.5 centimeters will be given as,

z = (93 - 105) / 5

z = -2.4

z = (100.5 - 105) / 5

z = -0.9

Then the proportion is given as,

P(93 < x < 100.5) = P(-2.4 < z < -0.9)

P(93 < x < 100.5) = 0.17586

The student's heights between 93 centimeters and 100.5 centimeters will be 0.17586.

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Answer:

84

Step-by-step explanation:

let numver be x

x/4+3=24

x/4=21

x=84

The probability that a randomly selected gas station in Russia charges more than the mean price in the United States is quite low.

This is because the prices of gas in Russia are typically much lower than the mean price of gas in the United States. The average cost of gasoline in Russia is around $0.50 per liter while in the United States, the average price of gas is around $1.78 per liter.

To explain further, the cost of living in Russia is lower than the cost of living in the United States. This means that there is more disposable income for people living in Russia and as a result, the price of gas is much lower than in the United States.

In addition, the cost of transportation and other production costs are lower in Russia than in the United States, which also keeps the prices of gas in Russia lower.

All of these factors make it unlikely that a randomly selected gas station in Russia would be charging more than the mean price in the United States.

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To add or subtract the two quadratic or polynomial equation, add or subtract the same power variables from each other.

The result of the difference of the given quadratic equation is,

\(h(x)=-4x^2-6x+6\\\)

Hence option 3 is the correct option.

A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.

The standard form of the quadratic equation is,

\(ax^2+bx+c=0\)

Here,  \(a,b,c\) is the real numbers and  \(x\) is the variable.

To add or subtract the two quadratic or polynomial equation, add or subtract the same power variables from each other.

Given information-

The given quadratic equations are,

\(f(x)=8x^2-2x+3\)

\(g(x)=12x^2+4x-3\)

The function \(h(x)\) is the difference of the two given functions. Thus,

\(h(x)=f(x)-g(x)\)

Put the values,

\(h(x)=(8x^2-2x+3)-(12x^2+4x-3)\)

Open the brackets by multiplying with sign as,

\(h(x)=8x^2-2x+3-12x^2-4x+3\)

Separate the terms with same power of variable as,

\(h(x)=8x^2-12x^2-2x-4x+3+3\\\)

To add or subtract the two quadratic or polynomial equation, add or subtract the same power variables from each other.Thus,

\(h(x)=-4x^2-6x+6\\\)

Thus the result of the difference of the given quadratic equation is,

\(h(x)=-4x^2-6x+6\\\)

Hence option 3 is the correct option.

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Answer:

c

Step-by-step explanation:

magic

When a peddle dropping into Lake Then a circular ripple results. The rate at which the area of the ripple changing at this instant is 48π inches per second.

The rate-related word problem can be solved by creating an equation that relates her two parameters of the system. Using this equation, we can find its derivative and determine the rate of change of the parameter. Let us consider

'r' is the radius of the circle, r = 8 inches

The area of a circle with radius r is

A = πr² ---(1)

Rate of increase radius (dr /dt )

= 3 inches/sec .

Now we know that the area increases as the radius increases. The rate of increase in area can be expressed as the rate of increase in radius by differentiating the area equation with respect to time. Therefore, differentiating area with respect to time gives,

dA/dt = 2πr dr/dt

We can substitute these known values into the derivation of the area equation to get, dA/dt = 2π(8)3

=> dA/dt = 48π

Therefore, the ripple area increases at a rate of 48π inches per second.

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Answer:

g(

x

2

−

3

)

=

2

x

2

−

7

Step-by-step explanation:

brainliest

The procedures below must be carried out in order to use a compass and straightedge to create a line through a given point that is parallel to a given line:

1. Position the straightedge on the indicated line, and then draw a line segment through the indicated point.

2. Set the compass on the indicated point and draw two arcs that cross the line segment on either side without adjusting the compass's width.

3. Draw an arc that crosses the original line while maintaining the same compass width by setting the compass on one of the arcs' junction points.

4. Repetition of step 3 using the opposite arc's junction point.

5. Using the straightedge, draw a line between the indicated point to the locations where the

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Answer:

397/20

Step-by-step explanation:

i think?

if im wrong im sorry

Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23